From 6d0e0aab928a13c1a2d8b8e83ef9a48b537fd3e2 Mon Sep 17 00:00:00 2001
From: Joseph Weston <joseph@weston.cloud>
Date: Thu, 2 May 2019 15:14:16 +0200
Subject: [PATCH] remove old tutorial script machinery
---
doc/source/code/README | 42 --
doc/source/code/figure/_defs.py | 34 --
doc/source/code/figure/ab_ring.py.diff | 202 --------
doc/source/code/figure/ab_ring_sketch.svg | 140 -----
doc/source/code/figure/ab_ring_sketch2.svg | 319 ------------
doc/source/code/figure/band_structure.py.diff | 67 ---
doc/source/code/figure/closed_system.py.diff | 168 ------
doc/source/code/figure/discretize.py.diff | 248 ---------
doc/source/code/figure/faq.py.diff | 483 ------------------
doc/source/code/figure/graphene.py.diff | 217 --------
.../figure/kernel_polynomial_method.py.diff | 374 --------------
.../code/figure/magnetic_texture.py.diff | 286 -----------
doc/source/code/figure/plot_graphene.py.diff | 141 -----
doc/source/code/figure/plot_qahe.py.diff | 78 ---
.../code/figure/plot_zincblende.py.diff | 71 ---
doc/source/code/figure/quantum_well.py.diff | 103 ----
doc/source/code/figure/quantum_wire.py.diff | 136 -----
doc/source/code/figure/spin_orbit.py.diff | 118 -----
doc/source/code/figure/superconductor.py.diff | 148 ------
.../superconductor_transport_sketch.svg | 325 ------------
.../code/include/quantum_wire_revisited.py | 91 ----
21 files changed, 3791 deletions(-)
delete mode 100644 doc/source/code/README
delete mode 100644 doc/source/code/figure/_defs.py
delete mode 100644 doc/source/code/figure/ab_ring.py.diff
delete mode 100644 doc/source/code/figure/ab_ring_sketch.svg
delete mode 100644 doc/source/code/figure/ab_ring_sketch2.svg
delete mode 100644 doc/source/code/figure/band_structure.py.diff
delete mode 100644 doc/source/code/figure/closed_system.py.diff
delete mode 100644 doc/source/code/figure/discretize.py.diff
delete mode 100644 doc/source/code/figure/faq.py.diff
delete mode 100644 doc/source/code/figure/graphene.py.diff
delete mode 100644 doc/source/code/figure/kernel_polynomial_method.py.diff
delete mode 100644 doc/source/code/figure/magnetic_texture.py.diff
delete mode 100644 doc/source/code/figure/plot_graphene.py.diff
delete mode 100644 doc/source/code/figure/plot_qahe.py.diff
delete mode 100644 doc/source/code/figure/plot_zincblende.py.diff
delete mode 100644 doc/source/code/figure/quantum_well.py.diff
delete mode 100644 doc/source/code/figure/quantum_wire.py.diff
delete mode 100644 doc/source/code/figure/spin_orbit.py.diff
delete mode 100644 doc/source/code/figure/superconductor.py.diff
delete mode 100644 doc/source/code/figure/superconductor_transport_sketch.svg
delete mode 100644 doc/source/code/include/quantum_wire_revisited.py
diff --git a/doc/source/code/README b/doc/source/code/README
deleted file mode 100644
index 896e658a..00000000
--- a/doc/source/code/README
+++ /dev/null
@@ -1,42 +0,0 @@
-This directory contains the code examples from the documentation.
-Most scripts are present in three related but different versions that
-correspond to three different usages.
-
-* Subdirectory 'figure': scripts used for figure generation. Figures
- are not displayed but saved to disk.
-
-* Subdirectory 'include': scripts that display figures on screen.
- They contain commented marks for including snippets in the
- documentation.
-
-* Subdirectory 'download': complete scripts to be offered for download
- by readers. Like 'include' but with the include marks removed.
-
-Most scripts are extracted from corresponding '*.py.diff' files inside
-'figure/'. These are patches from the 'include' version to the
-'figure' version. The patches include complete context and as such
-can be used to recreate both files. It's these patches that are kept
-under version control.
-
-running 'make html' or 'make latex' inside '/doc' will automatically
-update all these scripts according to the following scheme:
-
- ---->------------->------
- / \
- / download/x.py \
-figure/x.py.diff ^ \
- ^ \ | \
- | -> include/x.py ---(patch)---> figure/x.py
- | | |
- | | |
- \ v /
- ----<----------(diff)--------------<--------
-
-Thus, it is possible to update figure/x.py.diff, include/x.py or
-figure/x.py and any changes will be propagated automatically when
-'make' is run. (Only download/x.py is a dead end.) The user will be
-informed about any conflicts. The makefile will only update files
-that are older than their sources and is careful to propagate time
-stamps in order to avoid infinite loops.
-
-Editing only figure/x.py.diff is a sure way to avoid any conflicts.
diff --git a/doc/source/code/figure/_defs.py b/doc/source/code/figure/_defs.py
deleted file mode 100644
index 985e2e9a..00000000
--- a/doc/source/code/figure/_defs.py
+++ /dev/null
@@ -1,34 +0,0 @@
-################################################################
-# Make matplotlib work without X11
-################################################################
-import matplotlib
-matplotlib.use('Agg')
-
-################################################################
-# Prepend Kwant's build directory to sys.path
-################################################################
-import sys
-from distutils.util import get_platform
-sys.path.insert(0, "../../../../build/lib.{0}-{1}.{2}".format(
- get_platform(), *sys.version_info[:2]))
-
-################################################################
-# Define constants for plotting
-################################################################
-pt_to_in = 1. / 72.
-
-# Default width of figures in pts
-figwidth_pt = 600
-figwidth_in = figwidth_pt * pt_to_in
-
-# Width for smaller figures
-figwidth_small_pt = 400
-figwidth_small_in = figwidth_small_pt * pt_to_in
-
-# Sizes for matplotlib figures
-mpl_width_in = figwidth_pt * pt_to_in
-mpl_label_size = None # font sizes in points
-mpl_tick_size = None
-
-# dpi for conversion from inches
-dpi = 90
diff --git a/doc/source/code/figure/ab_ring.py.diff b/doc/source/code/figure/ab_ring.py.diff
deleted file mode 100644
index c4fb178b..00000000
--- a/doc/source/code/figure/ab_ring.py.diff
+++ /dev/null
@@ -1,202 +0,0 @@
-@@ -1,127 +1,196 @@
- # Tutorial 2.3.3. Nontrivial shapes
- # =================================
- #
- # Physics background
- # ------------------
- # Flux-dependent transmission through a quantum ring
- #
- # Kwant features highlighted
- # --------------------------
- # - More complex shapes with lattices
- # - Allows for discussion of subtleties of `attach_lead` (not in the
- # example, but in the tutorial main text)
- # - Modifcations of hoppings/sites after they have been added
-
-+import _defs
- from cmath import exp
- from math import pi
-
- import kwant
-
- # For plotting
- from matplotlib import pyplot
-
-
- #HIDDEN_BEGIN_eusz
- def make_system(a=1, t=1.0, W=10, r1=10, r2=20):
- # Start with an empty tight-binding system and a single square lattice.
- # `a` is the lattice constant (by default set to 1 for simplicity).
-
- lat = kwant.lattice.square(a)
-
- syst = kwant.Builder()
-
- #### Define the scattering region. ####
- # Now, we aim for a more complex shape, namely a ring (or annulus)
- def ring(pos):
- (x, y) = pos
- rsq = x ** 2 + y ** 2
- return (r1 ** 2 < rsq < r2 ** 2)
- #HIDDEN_END_eusz
-
- # and add the corresponding lattice points using the `shape`-function
- #HIDDEN_BEGIN_lcak
- syst[lat.shape(ring, (0, r1 + 1))] = 4 * t
- syst[lat.neighbors()] = -t
- #HIDDEN_END_lcak
-
- # In order to introduce a flux through the ring, we introduce a phase on
- # the hoppings on the line cut through one of the arms. Since we want to
- # change the flux without modifying the Builder instance repeatedly, we
- # define the modified hoppings as a function that takes the flux as its
- # parameter phi.
- #HIDDEN_BEGIN_lvkt
- def hopping_phase(site1, site2, phi):
- return -t * exp(1j * phi)
-
- def crosses_branchcut(hop):
- ix0, iy0 = hop[0].tag
-
- # builder.HoppingKind with the argument (1, 0) below
- # returns hoppings ordered as ((i+1, j), (i, j))
- return iy0 < 0 and ix0 == 1 # ix1 == 0 then implied
-
- # Modify only those hopings in x-direction that cross the branch cut
- def hops_across_cut(syst):
- for hop in kwant.builder.HoppingKind((1, 0), lat, lat)(syst):
- if crosses_branchcut(hop):
- yield hop
- syst[hops_across_cut] = hopping_phase
- #HIDDEN_END_lvkt
-
- #### Define the leads. ####
- # left lead
- #HIDDEN_BEGIN_qwgr
- sym_lead = kwant.TranslationalSymmetry((-a, 0))
- lead = kwant.Builder(sym_lead)
-
- def lead_shape(pos):
- (x, y) = pos
- return (-W / 2 < y < W / 2)
-
- lead[lat.shape(lead_shape, (0, 0))] = 4 * t
- lead[lat.neighbors()] = -t
- #HIDDEN_END_qwgr
-
- #### Attach the leads and return the system. ####
- #HIDDEN_BEGIN_skbz
- syst.attach_lead(lead)
- syst.attach_lead(lead.reversed())
- #HIDDEN_END_skbz
-
- return syst
-
-
-+def make_system_note1(a=1, t=1.0, W=10, r1=10, r2=20):
-+ lat = kwant.lattice.square(a)
-+ syst = kwant.Builder()
-+ def ring(pos):
-+ (x, y) = pos
-+ rsq = x**2 + y**2
-+ return ( r1**2 < rsq < r2**2)
-+ syst[lat.shape(ring, (0, 11))] = 4 * t
-+ syst[lat.neighbors()] = -t
-+ sym_lead0 = kwant.TranslationalSymmetry((-a, 0))
-+ lead0 = kwant.Builder(sym_lead0)
-+ def lead_shape(pos):
-+ (x, y) = pos
-+ return (-1 < x < 1) and ( 0.5 * W < y < 1.5 * W )
-+ lead0[lat.shape(lead_shape, (0, W))] = 4 * t
-+ lead0[lat.neighbors()] = -t
-+ lead1 = lead0.reversed()
-+ syst.attach_lead(lead0)
-+ syst.attach_lead(lead1)
-+ return syst
-+
-+
-+def make_system_note2(a=1, t=1.0, W=10, r1=10, r2=20):
-+ lat = kwant.lattice.square(a)
-+ syst = kwant.Builder()
-+ def ring(pos):
-+ (x, y) = pos
-+ rsq = x**2 + y**2
-+ return ( r1**2 < rsq < r2**2)
-+ syst[lat.shape(ring, (0, 11))] = 4 * t
-+ syst[lat.neighbors()] = -t
-+ sym_lead0 = kwant.TranslationalSymmetry((-a, 0))
-+ lead0 = kwant.Builder(sym_lead0)
-+ def lead_shape(pos):
-+ (x, y) = pos
-+ return (-1 < x < 1) and ( -W/2 < y < W/2 )
-+ lead0[lat.shape(lead_shape, (0, 0))] = 4 * t
-+ lead0[lat.neighbors()] = -t
-+ lead1 = lead0.reversed()
-+ syst.attach_lead(lead0)
-+ syst.attach_lead(lead1, lat(0, 0))
-+ return syst
-+
-+
- def plot_conductance(syst, energy, fluxes):
- # compute conductance
-
- normalized_fluxes = [flux / (2 * pi) for flux in fluxes]
- data = []
- for flux in fluxes:
- smatrix = kwant.smatrix(syst, energy, params=dict(phi=flux))
- data.append(smatrix.transmission(1, 0))
-
-- pyplot.figure()
-+ fig = pyplot.figure()
- pyplot.plot(normalized_fluxes, data)
-- pyplot.xlabel("flux [flux quantum]")
-- pyplot.ylabel("conductance [e^2/h]")
-- pyplot.show()
-+ pyplot.xlabel("flux [flux quantum]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.ylabel("conductance [e^2/h]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+ fig.savefig("ab_ring_result.pdf")
-+ fig.savefig("ab_ring_result.png", dpi=_defs.dpi)
-
-
- def main():
- syst = make_system()
-
- # Check that the system looks as intended.
-- kwant.plot(syst)
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, file="ab_ring_syst." + extension,
-+ fig_size=size, dpi=_defs.dpi)
-+
-
- # Finalize the system.
- syst = syst.finalized()
-
- # We should see a conductance that is periodic with the flux quantum
- plot_conductance(syst, energy=0.15, fluxes=[0.01 * i * 3 * 2 * pi
- for i in range(100)])
-
-
-+ # Finally, some plots needed for the notes
-+ syst = make_system_note1()
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, file="ab_ring_note1." + extension,
-+ fig_size=size, dpi=_defs.dpi)
-+ syst = make_system_note2()
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, file="ab_ring_note2." + extension,
-+ fig_size=size, dpi=_defs.dpi)
-+
-+
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/ab_ring_sketch.svg b/doc/source/code/figure/ab_ring_sketch.svg
deleted file mode 100644
index 0b2e9428..00000000
--- a/doc/source/code/figure/ab_ring_sketch.svg
+++ /dev/null
@@ -1,140 +0,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!-- Created with Inkscape (http://www.inkscape.org/) -->
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- xmlns:dc="http://purl.org/dc/elements/1.1/"
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- xmlns:svg="http://www.w3.org/2000/svg"
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diff --git a/doc/source/code/figure/ab_ring_sketch2.svg b/doc/source/code/figure/ab_ring_sketch2.svg
deleted file mode 100644
index 2bf7bf06..00000000
--- a/doc/source/code/figure/ab_ring_sketch2.svg
+++ /dev/null
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diff --git a/doc/source/code/figure/band_structure.py.diff b/doc/source/code/figure/band_structure.py.diff
deleted file mode 100644
index 8a265207..00000000
--- a/doc/source/code/figure/band_structure.py.diff
+++ /dev/null
@@ -1,67 +0,0 @@
-@@ -1,52 +1,62 @@
- # Tutorial 2.4.1. Band structure calculations
- # ===========================================
- #
- # Physics background
- # ------------------
- # band structure of a simple quantum wire in tight-binding approximation
- #
- # Kwant features highlighted
- # --------------------------
- # - Computing the band structure of a finalized lead.
-
-+import _defs
- import kwant
-
- # For plotting.
- from matplotlib import pyplot
-
- #HIDDEN_BEGIN_zxip
- def make_lead(a=1, t=1.0, W=10):
- # Start with an empty lead with a single square lattice
- lat = kwant.lattice.square(a)
-
- sym_lead = kwant.TranslationalSymmetry((-a, 0))
- lead = kwant.Builder(sym_lead)
-
- # build up one unit cell of the lead, and add the hoppings
- # to the next unit cell
- for j in range(W):
- lead[lat(0, j)] = 4 * t
-
- if j > 0:
- lead[lat(0, j), lat(0, j - 1)] = -t
-
- lead[lat(1, j), lat(0, j)] = -t
-
- return lead
- #HIDDEN_END_zxip
-
-
- #HIDDEN_BEGIN_pejz
- def main():
- lead = make_lead().finalized()
-- kwant.plotter.bands(lead, show=False)
-- pyplot.xlabel("momentum [(lattice constant)^-1]")
-- pyplot.ylabel("energy [t]")
-- pyplot.show()
-+ fig = kwant.plotter.bands(lead, show=False)
-+ pyplot.xlabel("momentum [(lattice constant)^-1]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.ylabel("energy [t]", fontsize=_defs.mpl_label_size)
-+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+ for extension in ('pdf', 'png'):
-+ fig.savefig("band_structure_result." + extension, dpi=_defs.dpi)
-+
- #HIDDEN_END_pejz
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/closed_system.py.diff b/doc/source/code/figure/closed_system.py.diff
deleted file mode 100644
index 748e9eca..00000000
--- a/doc/source/code/figure/closed_system.py.diff
+++ /dev/null
@@ -1,168 +0,0 @@
-@@ -1,144 +1,161 @@
- # Tutorial 2.4.2. Closed systems
- # ==============================
- #
- # Physics background
- # ------------------
- # Fock-darwin spectrum of a quantum dot (energy spectrum in
- # as a function of a magnetic field)
- #
- # Kwant features highlighted
- # --------------------------
- # - Use of `hamiltonian_submatrix` in order to obtain a Hamiltonian
- # matrix.
-
-+import _defs
- from cmath import exp
- import numpy as np
- import kwant
-
- # For eigenvalue computation
- #HIDDEN_BEGIN_tibv
- import scipy.sparse.linalg as sla
- #HIDDEN_END_tibv
-
- # For plotting
- from matplotlib import pyplot
-
-
- def make_system(a=1, t=1.0, r=10):
- # Start with an empty tight-binding system and a single square lattice.
- # `a` is the lattice constant (by default set to 1 for simplicity).
-
- #HIDDEN_BEGIN_qlyd
- lat = kwant.lattice.square(a, norbs=1)
-
- syst = kwant.Builder()
-
- # Define the quantum dot
- def circle(pos):
- (x, y) = pos
- rsq = x ** 2 + y ** 2
- return rsq < r ** 2
-
- def hopx(site1, site2, B):
- # The magnetic field is controlled by the parameter B
- y = site1.pos[1]
- return -t * exp(-1j * B * y)
-
- syst[lat.shape(circle, (0, 0))] = 4 * t
- # hoppings in x-direction
- syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx
- # hoppings in y-directions
- syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = -t
-
- # It's a closed system for a change, so no leads
- return syst
- #HIDDEN_END_qlyd
-
-
- #HIDDEN_BEGIN_yvri
- def plot_spectrum(syst, Bfields):
-
- energies = []
- for B in Bfields:
- # Obtain the Hamiltonian as a sparse matrix
- ham_mat = syst.hamiltonian_submatrix(params=dict(B=B), sparse=True)
-
- # we only calculate the 15 lowest eigenvalues
- ev = sla.eigsh(ham_mat.tocsc(), k=15, sigma=0,
- return_eigenvectors=False)
-
- energies.append(ev)
-
-- pyplot.figure()
-+ fig = pyplot.figure()
- pyplot.plot(Bfields, energies)
-- pyplot.xlabel("magnetic field [arbitrary units]")
-- pyplot.ylabel("energy [t]")
-- pyplot.show()
-+ pyplot.xlabel("magnetic field [arbitrary units]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.ylabel("energy [t]", fontsize=_defs.mpl_label_size)
-+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+ for extension in ('pdf', 'png'):
-+ fig.savefig("closed_system_result." + extension, dpi=_defs.dpi)
- #HIDDEN_END_yvri
-
- def sorted_eigs(ev):
- evals, evecs = ev
- evals, evecs = map(np.array, zip(*sorted(zip(evals, evecs.transpose()))))
- return evals, evecs.transpose()
-
- #HIDDEN_BEGIN_wave
- def plot_wave_function(syst, B=0.001):
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+
- # Calculate the wave functions in the system.
- ham_mat = syst.hamiltonian_submatrix(sparse=True, params=dict(B=B))
- evals, evecs = sorted_eigs(sla.eigsh(ham_mat.tocsc(), k=20, sigma=0))
-
- # Plot the probability density of the 10th eigenmode.
-- kwant.plotter.map(syst, np.abs(evecs[:, 9])**2,
-- colorbar=False, oversampling=1)
-+ for extension in ('pdf', 'png'):
-+ kwant.plotter.map(
-+ syst, np.abs(evecs[:, 9])**2, colorbar=False, oversampling=1,
-+ file="closed_system_eigenvector." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_wave
-
-
- #HIDDEN_BEGIN_current
- def plot_current(syst, B=0.001):
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+
- # Calculate the wave functions in the system.
- ham_mat = syst.hamiltonian_submatrix(sparse=True, params=dict(B=B))
- evals, evecs = sorted_eigs(sla.eigsh(ham_mat.tocsc(), k=20, sigma=0))
-
- # Calculate and plot the local current of the 10th eigenmode.
- J = kwant.operator.Current(syst)
- current = J(evecs[:, 9], params=dict(B=B))
-- kwant.plotter.current(syst, current, colorbar=False)
-+ for extension in ('pdf', 'png'):
-+ kwant.plotter.current(
-+ syst, current, colorbar=False,
-+ file="closed_system_current." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_current
-
-
- def main():
- syst = make_system()
-
-- # Check that the system looks as intended.
-- kwant.plot(syst)
--
- # Finalize the system.
- syst = syst.finalized()
-
- # The following try-clause can be removed once SciPy 0.9 becomes uncommon.
- try:
- # We should observe energy levels that flow towards Landau
- # level energies with increasing magnetic field.
- plot_spectrum(syst, [iB * 0.002 for iB in range(100)])
-
- # Plot an eigenmode of a circular dot. Here we create a larger system for
- # better spatial resolution.
- syst = make_system(r=30).finalized()
- plot_wave_function(syst)
- plot_current(syst)
- except ValueError as e:
- if e.message == "Input matrix is not real-valued.":
- print("The calculation of eigenvalues failed because of a bug in SciPy 0.9.")
- print("Please upgrade to a newer version of SciPy.")
- else:
- raise
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/discretize.py.diff b/doc/source/code/figure/discretize.py.diff
deleted file mode 100644
index aebaf3e0..00000000
--- a/doc/source/code/figure/discretize.py.diff
+++ /dev/null
@@ -1,248 +0,0 @@
-@@ -1,225 +1,239 @@
- # Tutorial 2.9. Processing continuum Hamiltonians with discretize
- # ===============================================================
- #
- # Physics background
- # ------------------
- # - tight-binding approximation of continuous Hamiltonians
- #
- # Kwant features highlighted
- # --------------------------
- # - kwant.continuum.discretize
-
-+import _defs
-
- import kwant
- #HIDDEN_BEGIN_import
- import kwant.continuum
- #HIDDEN_END_import
- import scipy.sparse.linalg
- import scipy.linalg
- import numpy as np
-
- # For plotting
- import matplotlib as mpl
- from matplotlib import pyplot as plt
-
-
-+def save_figure(file_name):
-+ if not file_name:
-+ return
-+ for extension in ('pdf', 'png'):
-+ plt.savefig('.'.join((file_name,extension)),
-+ dpi=_defs.dpi, bbox_inches='tight')
-+
-+
- def stadium_system(L=20, W=20):
- #HIDDEN_BEGIN_template
- hamiltonian = "k_x**2 + k_y**2 + V(x, y)"
- template = kwant.continuum.discretize(hamiltonian)
-- print(template)
-+ with open('discretizer_verbose.txt', 'w') as f:
-+ print(template, file=f)
- #HIDDEN_END_template
-
- #HIDDEN_BEGIN_fill
- def stadium(site):
- (x, y) = site.pos
- x = max(abs(x) - 20, 0)
- return x**2 + y**2 < 30**2
-
- syst = kwant.Builder()
- syst.fill(template, stadium, (0, 0));
- syst = syst.finalized()
- #HIDDEN_END_fill
- return syst
-
-
- #HIDDEN_BEGIN_plot_eigenstate
- def plot_eigenstate(syst, n=2, Vx=.0003, Vy=.0005):
-
- def potential(x, y):
- return Vx * x + Vy * y
-
- ham = syst.hamiltonian_submatrix(params=dict(V=potential), sparse=True)
- evecs = scipy.sparse.linalg.eigsh(ham, k=10, which='SM')[1]
- kwant.plotter.map(syst, abs(evecs[:, n])**2, show=False)
- #HIDDEN_END_plot_eigenstate
-- plt.show()
-+ save_figure('discretizer_gs')
-
-
- def qsh_system(a=20, L=2000, W=1000):
- #HIDDEN_BEGIN_define_qsh
- hamiltonian = """
- + C * identity(4) + M * kron(sigma_0, sigma_z)
- - B * (k_x**2 + k_y**2) * kron(sigma_0, sigma_z)
- - D * (k_x**2 + k_y**2) * kron(sigma_0, sigma_0)
- + A * k_x * kron(sigma_z, sigma_x)
- - A * k_y * kron(sigma_0, sigma_y)
- """
-
- template = kwant.continuum.discretize(hamiltonian, grid=a)
- #HIDDEN_END_define_qsh
-
- #HIDDEN_BEGIN_define_qsh_build
- def shape(site):
- (x, y) = site.pos
- return (0 <= y < W and 0 <= x < L)
-
- def lead_shape(site):
- (x, y) = site.pos
- return (0 <= y < W)
-
- syst = kwant.Builder()
- syst.fill(template, shape, (0, 0))
-
- lead = kwant.Builder(kwant.TranslationalSymmetry([-a, 0]))
- lead.fill(template, lead_shape, (0, 0))
-
- syst.attach_lead(lead)
- syst.attach_lead(lead.reversed())
-
- syst = syst.finalized()
- #HIDDEN_END_define_qsh_build
- return syst
-
-
- def analyze_qsh():
- params = dict(A=3.65, B=-68.6, D=-51.1, M=-0.01, C=0)
- syst = qsh_system()
-
- #HIDDEN_BEGIN_plot_qsh_band
- kwant.plotter.bands(syst.leads[0], params=params,
- momenta=np.linspace(-0.3, 0.3, 201), show=False)
- #HIDDEN_END_plot_qsh_band
-
- plt.grid()
- plt.xlim(-.3, 0.3)
- plt.ylim(-0.05, 0.05)
- plt.xlabel('momentum [1/A]')
- plt.ylabel('energy [eV]')
-- plt.show()
-+ save_figure('discretizer_qsh_band')
- #HIDDEN_BEGIN_plot_qsh_wf
-+
- # get scattering wave functions at E=0
- wf = kwant.wave_function(syst, energy=0, params=params)
-
- # prepare density operators
- sigma_z = np.array([[1, 0], [0, -1]])
- prob_density = kwant.operator.Density(syst, np.eye(4))
- spin_density = kwant.operator.Density(syst, np.kron(sigma_z, np.eye(2)))
-
- # calculate expectation values and plot them
- wf_sqr = sum(prob_density(psi) for psi in wf(0)) # states from left lead
- rho_sz = sum(spin_density(psi) for psi in wf(0)) # states from left lead
-
- fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(16, 4))
- kwant.plotter.map(syst, wf_sqr, ax=ax1)
- kwant.plotter.map(syst, rho_sz, ax=ax2)
- #HIDDEN_END_plot_qsh_wf
- ax = ax1
- im = [obj for obj in ax.get_children()
- if isinstance(obj, mpl.image.AxesImage)][0]
- fig.colorbar(im, ax=ax)
-
- ax = ax2
- im = [obj for obj in ax.get_children()
- if isinstance(obj, mpl.image.AxesImage)][0]
- fig.colorbar(im, ax=ax)
-
- ax1.set_title('Probability density')
- ax2.set_title('Spin density')
-- plt.show()
-+ save_figure('discretizer_qsh_wf')
-
-
- def lattice_spacing():
- #HIDDEN_BEGIN_ls_def
- hamiltonian = "k_x**2 * identity(2) + alpha * k_x * sigma_y"
- params = dict(alpha=.5)
- #HIDDEN_END_ls_def
-
- def plot(ax, a=1):
- #HIDDEN_BEGIN_ls_hk_cont
- h_k = kwant.continuum.lambdify(hamiltonian, locals=params)
- k_cont = np.linspace(-4, 4, 201)
- e_cont = [scipy.linalg.eigvalsh(h_k(k_x=ki)) for ki in k_cont]
- #HIDDEN_END_ls_hk_cont
-
- #HIDDEN_BEGIN_ls_hk_tb
- template = kwant.continuum.discretize(hamiltonian, grid=a)
- syst = kwant.wraparound.wraparound(template).finalized()
-
- def h_k(k_x):
- p = dict(k_x=k_x, **params)
- return syst.hamiltonian_submatrix(params=p)
-
- k_tb = np.linspace(-np.pi/a, np.pi/a, 201)
- e_tb = [scipy.linalg.eigvalsh(h_k(k_x=a*ki)) for ki in k_tb]
- #HIDDEN_END_ls_hk_tb
-
- ax.plot(k_cont, e_cont, 'r-')
- ax.plot(k_tb, e_tb, 'k-')
-
- ax.plot([], [], 'r-', label='continuum')
- ax.plot([], [], 'k-', label='tight-binding')
-
- ax.set_xlim(-4, 4)
- ax.set_ylim(-1, 14)
- ax.set_title('a={}'.format(a))
-
- ax.set_xlabel('momentum [a.u.]')
- ax.set_ylabel('energy [a.u.]')
- ax.grid()
- ax.legend()
-
- _, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(12, 4))
-
- plot(ax1, a=1)
- plot(ax2, a=.25)
-- plt.show()
-+ save_figure('discretizer_lattice_spacing')
-
-
- def substitutions():
- #HIDDEN_BEGIN_subs_1
- sympify = kwant.continuum.sympify
- subs = {'sx': [[0, 1], [1, 0]], 'sz': [[1, 0], [0, -1]]}
-
- e = (
- sympify('[[k_x**2, alpha * k_x], [k_x * alpha, -k_x**2]]'),
- sympify('k_x**2 * sigma_z + alpha * k_x * sigma_x'),
- sympify('k_x**2 * sz + alpha * k_x * sx', locals=subs),
- )
-
-- print(e[0] == e[1] == e[2])
-+ with open('discretizer_subs_1.txt', 'w') as f:
-+ print(e[0] == e[1] == e[2], file=f)
- #HIDDEN_END_subs_1
-
- #HIDDEN_BEGIN_subs_2
- subs = {'A': 'A(x) + B', 'V': 'V(x) + V_0', 'C': 5}
-- print(sympify('k_x * A * k_x + V + C', locals=subs))
-+ with open('discretizer_subs_2.txt', 'w') as f:
-+ print(sympify('k_x * A * k_x + V + C', locals=subs), file=f)
- #HIDDEN_END_subs_2
-
-
- def main():
- #HIDDEN_BEGIN_symbolic_discretization
- template = kwant.continuum.discretize('k_x * A(x) * k_x')
-- print(template)
-+ with open('discretizer_intro_verbose.txt', 'w') as f:
-+ print(template, file=f)
- #HIDDEN_END_symbolic_discretization
-
- syst = stadium_system()
- plot_eigenstate(syst)
-
- analyze_qsh()
- lattice_spacing()
- substitutions()
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/faq.py.diff b/doc/source/code/figure/faq.py.diff
deleted file mode 100644
index 7c8889dc..00000000
--- a/doc/source/code/figure/faq.py.diff
+++ /dev/null
@@ -1,483 +0,0 @@
-@@ -1,450 +1,479 @@
- # Frequently asked questions
- #
- # This script is a disorganized collection of code snippets. As a whole, it is
- # not meant as an example of good programming practice.
-
-+import _defs
- import kwant
- import numpy as np
- import tinyarray
- import matplotlib
- from matplotlib import pyplot as plt
- matplotlib.rcParams['figure.figsize'] = (3.5, 3.5)
-
-
-+def save_figure(file_name):
-+ for extension in ('pdf', 'png'):
-+ plt.savefig('.'.join((file_name, extension)),
-+ dpi=_defs.dpi, bbox_inches='tight')
-+
-+
- #### What is a Site?
-
- #HIDDEN_BEGIN_site
- a = 1
- lat = kwant.lattice.square(a)
- syst = kwant.Builder()
-
- syst[lat(1, 0)] = 4
- syst[lat(1, 1)] = 4
-
- kwant.plot(syst)
-+save_figure("faq_site")
- #HIDDEN_END_site
-
-
- #### What is a hopping?
-
- a = 1
- lat = kwant.lattice.square(a)
- syst = kwant.Builder()
-
- syst[lat(1, 0)] = 4
- syst[lat(1, 1)] = 4
- #HIDDEN_BEGIN_hopping
- syst[(lat(1, 0), lat(1, 1))] = 1j
- #HIDDEN_END_hopping
-
- kwant.plot(syst)
-+save_figure("faq_hopping")
-
-
- #### What is a lattice?
-
- #HIDDEN_BEGIN_lattice_monatomic
- # Two monatomic lattices
- primitive_vectors = [(1, 0), (0, 1)]
- lat_a = kwant.lattice.Monatomic(primitive_vectors, offset=(0, 0))
- lat_b = kwant.lattice.Monatomic(primitive_vectors, offset=(0.5, 0.5))
- # lat1 is equivalent to kwant.lattice.square()
-
- syst = kwant.Builder()
-
- syst[lat_a(0, 0)] = 4
- syst[lat_b(0, 0)] = 4
-
- kwant.plot(syst)
-+save_figure("faq_lattice")
- #HIDDEN_END_lattice_monatomic
-
- #HIDDEN_BEGIN_lattice_polyatomic
- # One polyatomic lattice containing two sublattices
- lat = kwant.lattice.Polyatomic([(1, 0), (0, 1)], [(0, 0), (0.5, 0.5)])
- sub_a, sub_b = lat.sublattices
- #HIDDEN_END_lattice_polyatomic
-
- #### How to make a hole in a system?
-
- #HIDDEN_BEGIN_hole
- # Define the lattice and the (empty) system
- a = 2
- lat = kwant.lattice.cubic(a)
- syst = kwant.Builder()
-
- L = 10
- W = 10
- H = 2
-
- # Add sites to the system in a cuboid
-
- syst[(lat(i, j, k) for i in range(L) for j in range(W) for k in range(H))] = 4
- kwant.plot(syst)
-+save_figure("faq_hole1")
-
- # Delete sites to create a hole
-
- def in_hole(site):
- x, y, z = site.pos / a - (L/2, W/2, H/2) # position relative to centre
- return abs(x) < L / 4 and abs(y) < W / 4
-
- for site in filter(in_hole, list(syst.sites())):
- del syst[site]
-
- kwant.plot(syst)
-+save_figure("faq_hole2")
- #HIDDEN_END_hole
-
-
- #### How can we get access to the sites of our system?
-
- builder = kwant.Builder()
- lat = kwant.lattice.square()
- builder[(lat(i, j) for i in range(3) for j in range(3))] = 4
- #HIDDEN_BEGIN_sites1
- # Before finalizing the system
-
- sites = list(builder.sites()) # sites() doe *not* return a list
- #HIDDEN_END_sites1
- #HIDDEN_BEGIN_sites2
- # After finalizing the system
- syst = builder.finalized()
- sites = syst.sites # syst.sites is an actual list
- #HIDDEN_END_sites2
- #HIDDEN_BEGIN_sites3
- i = syst.id_by_site[lat(0, 2)] # we want the id of the site lat(0, 2)
- #HIDDEN_END_sites3
-
-
- #### How to plot a polyatomic lattice with different colors?
-
- #HIDDEN_BEGIN_colors1
- lat = kwant.lattice.kagome()
- syst = kwant.Builder()
-
- a, b, c = lat.sublattices # The kagome lattice has 3 sublattices
- #HIDDEN_END_colors1
-
- #HIDDEN_BEGIN_colors2
- # Plot sites from different families in different colors
- def family_color(site):
- if site.family == a:
- return 'red'
- if site.family == b:
- return 'green'
- else:
- return 'blue'
-
- def plot_system(syst):
- kwant.plot(syst, site_lw=0.1, site_color=family_color)
-
- ## Add sites and hoppings.
- for i in range(4):
- for j in range (4):
- syst[a(i, j)] = 4
- syst[b(i, j)] = 4
- syst[c(i, j)] = 4
-
- syst[lat.neighbors()] = -1
-
- ## Plot the system.
- plot_system(syst)
-+save_figure("faq_colors")
- #HIDDEN_END_colors2
-
--
- #### How to create all hoppings in a given direction using Hoppingkind?
-
- # Monatomic lattice
-
- #HIDDEN_BEGIN_direction1
- # Create hopping between neighbors with HoppingKind
- a = 1
- syst = kwant.Builder()
- lat = kwant.lattice.square(a)
- syst[ (lat(i, j) for i in range(5) for j in range(5)) ] = 4
-
- syst[kwant.builder.HoppingKind((1, 0), lat)] = -1
- kwant.plot(syst)
-+save_figure("faq_direction1")
- #HIDDEN_END_direction1
-
- # Polyatomic lattice
-
- lat = kwant.lattice.kagome()
- syst = kwant.Builder()
-
- a, b, c = lat.sublattices # The kagome lattice has 3 sublattices
-
- def family_color(site):
- if site.family == a:
- return 'red'
- if site.family == b:
- return 'green'
- else:
- return 'blue'
-
- def plot_system(syst):
- kwant.plot(syst, site_size=0.15, site_lw=0.05, site_color=family_color)
-
-
- for i in range(4):
- for j in range (4):
- syst[a(i, j)] = 4
- syst[b(i, j)] = 4
- syst[c(i, j)] = 4
-
-
- #HIDDEN_BEGIN_direction2
- # equivalent to syst[kwant.builder.HoppingKind((0, 1), b)] = -1
- syst[kwant.builder.HoppingKind((0, 1), b, b)] = -1
- #HIDDEN_END_direction2
- plot_system(syst)
-+save_figure("faq_direction2")
- # Delete the hoppings previously created
- del syst[kwant.builder.HoppingKind((0, 1), b, b)]
- #HIDDEN_BEGIN_direction3
- syst[kwant.builder.HoppingKind((0, 0), a, b)] = -1
- syst[kwant.builder.HoppingKind((0, 0), a, c)] = -1
- syst[kwant.builder.HoppingKind((0, 0), c, b)] = -1
- #HIDDEN_END_direction3
- plot_system(syst)
-+save_figure("faq_direction3")
-
-
- #### How to create the hoppings between adjacent sites?
-
- # Monatomic lattice
-
- #HIDDEN_BEGIN_adjacent1
- # Create hoppings with lat.neighbors()
- syst = kwant.Builder()
- lat = kwant.lattice.square()
- syst[(lat(i, j) for i in range(3) for j in range(3))] = 4
-
- syst[lat.neighbors()] = -1 # Equivalent to lat.neighbors(1)
- kwant.plot(syst)
-+save_figure("faq_adjacent1")
-
- del syst[lat.neighbors()] # Delete all nearest-neighbor hoppings
- syst[lat.neighbors(2)] = -1
-
- kwant.plot(syst)
-+save_figure("faq_adjacent2")
- #HIDDEN_END_adjacent1
-
- # Polyatomic lattice
-
- #HIDDEN_BEGIN_FAQ6
-
- # Hoppings using .neighbors()
- #HIDDEN_BEGIN_adjacent2
- # Create the system
- lat = kwant.lattice.kagome()
- syst = kwant.Builder()
- a, b, c = lat.sublattices # The kagome lattice has 3 sublattices
-
- for i in range(4):
- for j in range (4):
- syst[a(i, j)] = 4 # red
- syst[b(i, j)] = 4 # green
- syst[c(i, j)] = 4 # blue
-
- syst[lat.neighbors()] = -1
- #HIDDEN_END_adjacent2
- plot_system(syst)
-+save_figure("faq_adjacent3")
- del syst[lat.neighbors()] # Delete the hoppings previously created
- #HIDDEN_BEGIN_adjacent3
- syst[a.neighbors()] = -1
- #HIDDEN_END_adjacent3
- plot_system(syst)
-+save_figure("faq_adjacent4")
- del syst[a.neighbors()] # Delete the hoppings previously created
-
-
- syst[lat.neighbors(2)] = -1
- plot_system(syst)
- del syst[lat.neighbors(2)]
-
-
- #### How to create a lead with a lattice different from the scattering region?
-
- # Plot sites from different families in different colors
-
- def plot_system(syst):
-
- def family_color(site):
- if site.family == subA:
- return 'blue'
- if site.family == subB:
- return 'yellow'
- else:
- return 'green'
-
- kwant.plot(syst, site_lw=0.1, site_color=family_color)
-
-
- #HIDDEN_BEGIN_different_lattice1
- # Define the scattering Region
- L = 5
- W = 5
-
- lat = kwant.lattice.honeycomb()
- subA, subB = lat.sublattices
-
- syst = kwant.Builder()
- syst[(subA(i, j) for i in range(L) for j in range(W))] = 4
- syst[(subB(i, j) for i in range(L) for j in range(W))] = 4
- syst[lat.neighbors()] = -1
- #HIDDEN_END_different_lattice1
- plot_system(syst)
-+save_figure("faq_different_lattice1")
-
- #HIDDEN_BEGIN_different_lattice2
- # Create a lead
- lat_lead = kwant.lattice.square()
- sym_lead1 = kwant.TranslationalSymmetry((0, 1))
-
- lead1 = kwant.Builder(sym_lead1)
- lead1[(lat_lead(i, 0) for i in range(2, 7))] = 4
- lead1[lat_lead.neighbors()] = -1
- #HIDDEN_END_different_lattice2
- plot_system(lead1)
-+save_figure("faq_different_lattice2")
-
- #HIDDEN_BEGIN_different_lattice3
- syst[(lat_lead(i, 5) for i in range(2, 7))] = 4
- syst[lat_lead.neighbors()] = -1
-
- # Manually attach sites from graphene to square lattice
- syst[((lat_lead(i+2, 5), subB(i, 4)) for i in range(5))] = -1
- #HIDDEN_END_different_lattice3
- plot_system(syst)
-+save_figure("faq_different_lattice3")
-
- #HIDDEN_BEGIN_different_lattice4
- syst.attach_lead(lead1)
- #HIDDEN_END_different_lattice4
- plot_system(syst)
-+save_figure("faq_different_lattice4")
-
-
- #### How to cut a finite system out of a system with translationnal symmetries?
-
- #HIDDEN_BEGIN_fill1
- # Create 3d model.
- cubic = kwant.lattice.cubic()
- sym_3d = kwant.TranslationalSymmetry([1, 0, 0], [0, 1, 0], [0, 0, 1])
- model = kwant.Builder(sym_3d)
- model[cubic(0, 0, 0)] = 4
- model[cubic.neighbors()] = -1
- #HIDDEN_END_fill1
-
- #HIDDEN_BEGIN_fill2
- # Build scattering region (white).
- def cuboid_shape(site):
- x, y, z = abs(site.pos)
- return x < 4 and y < 10 and z < 3
-
- cuboid = kwant.Builder()
- cuboid.fill(model, cuboid_shape, (0, 0, 0));
- #HIDDEN_END_fill2
- kwant.plot(cuboid);
-+save_figure("faq_fill2")
-
- #HIDDEN_BEGIN_fill3
- # Build electrode (black).
- def electrode_shape(site):
- x, y, z = site.pos - (0, 5, 2)
- return y**2 + z**2 < 2.3**2
-
- electrode = kwant.Builder(kwant.TranslationalSymmetry([1, 0, 0]))
- electrode.fill(model, electrode_shape, (0, 5, 2)) # lead
-
- # Scattering region
- cuboid.fill(electrode, lambda s: abs(s.pos[0]) < 7, (0, 5, 4))
-
- cuboid.attach_lead(electrode)
- #HIDDEN_END_fill3
- kwant.plot(cuboid);
-+save_figure("faq_fill3")
-
-
- #### How does Kwant order the propagating modes of a lead?
-
- #HIDDEN_BEGIN_pm
- lat = kwant.lattice.square()
-
- lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))
- lead[(lat(0, i) for i in range(3))] = 4
- lead[lat.neighbors()] = -1
-
- flead = lead.finalized()
-
- E = 2.5
- prop_modes, _ = flead.modes(energy=E)
- #HIDDEN_END_pm
-
- def plot_and_label_modes(lead, E):
- # Plot the different modes
- pmodes, _ = lead.modes(energy=E)
- kwant.plotter.bands(lead, show=False)
- for i, k in enumerate(pmodes.momenta):
- plt.plot(k, E, 'ko')
- plt.annotate(str(i), xy=(k, E), xytext=(-5, 8),
- textcoords='offset points',
- bbox=dict(boxstyle='round,pad=0.1',fc='white', alpha=0.7))
- plt.plot([-3, 3], [E, E], 'r--')
- plt.ylim(E-1, E+1)
- plt.xlim(-2, 2)
- plt.xlabel("momentum")
- plt.ylabel("energy")
- plt.show()
-
- plot_and_label_modes(flead, E)
-+save_figure('faq_pm1')
-
- # More involved example
-
- s0 = np.eye(2)
- sz = np.array([[1, 0], [0, -1]])
-
- lead2 = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))
-
- lead2[(lat(0, i) for i in range(2))] = np.diag([1.8, -1])
- lead2[lat.neighbors()] = -1 * sz
-
- flead2 = lead2.finalized()
-
- plot_and_label_modes(flead2, 1)
-+save_figure('faq_pm2')
-
-
- #### How does Kwant order components of an individual wavefunction?
- def circle(R):
- return lambda r: np.linalg.norm(r) < R
-
-
- def make_system(lat):
- norbs = lat.norbs
- syst = kwant.Builder()
- syst[lat.shape(circle(3), (0, 0))] = 4 * np.eye(norbs)
- syst[lat.neighbors()] = -1 * np.eye(norbs)
-
- lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))
- lead[(lat(0, i) for i in range(-1, 2))] = 4 * np.eye(norbs)
- lead[lat.neighbors()] = -1 * np.eye(norbs)
-
- syst.attach_lead(lead)
- syst.attach_lead(lead.reversed())
-
- return syst.finalized()
-
-
- #HIDDEN_BEGIN_ord1
- lat = kwant.lattice.square(norbs=1)
- syst = make_system(lat)
- scattering_states = kwant.wave_function(syst, energy=1)
- wf = scattering_states(0)[0] # scattering state from lead 0 incoming in mode 0
-
- idx = syst.id_by_site[lat(0, 0)] # look up index of site
-
--print('wavefunction on lat(0, 0): ', wf[idx])
-+with open('faq_ord1.txt', 'w') as f:
-+ print('wavefunction on lat(0, 0): ', wf[idx], file=f)
- #HIDDEN_END_ord1
-
- #HIDDEN_BEGIN_ord2
- lat = kwant.lattice.square(norbs=2)
- syst = make_system(lat)
- scattering_states = kwant.wave_function(syst, energy=1)
- wf = scattering_states(0)[0] # scattering state from lead 0 incoming in mode 0
-
- idx = syst.id_by_site[lat(0, 0)] # look up index of site
-
- # Group consecutive degrees of freedom from 'wf' together; these correspond
- # to degrees of freedom on the same site.
- wf = wf.reshape(-1, 2)
-
--print('wavefunction on lat(0, 0): ', wf[idx])
-+with open('faq_ord2.txt', 'w') as f:
-+ print('wavefunction on lat(0, 0): ', wf[idx], file=f)
- #HIDDEN_END_ord2
diff --git a/doc/source/code/figure/graphene.py.diff b/doc/source/code/figure/graphene.py.diff
deleted file mode 100644
index 1352ed27..00000000
--- a/doc/source/code/figure/graphene.py.diff
+++ /dev/null
@@ -1,217 +0,0 @@
-@@ -1,179 +1,203 @@
- # Tutorial 2.5. Beyond square lattices: graphene
- # ==============================================
- #
- # Physics background
- # ------------------
- # Transport through a graphene quantum dot with a pn-junction
- #
- # Kwant features highlighted
- # --------------------------
- # - Application of all the aspects of tutorials 1-3 to a more complicated
- # lattice, namely graphene
-
-+import _defs
- from math import pi, sqrt, tanh
-
- import kwant
-
- # For computing eigenvalues
- import scipy.sparse.linalg as sla
-
- # For plotting
- from matplotlib import pyplot
-
-
- # Define the graphene lattice
- sin_30, cos_30 = (1 / 2, sqrt(3) / 2)
- #HIDDEN_BEGIN_hnla
- graphene = kwant.lattice.general([(1, 0), (sin_30, cos_30)],
- [(0, 0), (0, 1 / sqrt(3))])
- a, b = graphene.sublattices
- #HIDDEN_END_hnla
-
-
- #HIDDEN_BEGIN_shzy
- def make_system(r=10, w=2.0, pot=0.1):
-
- #### Define the scattering region. ####
- # circular scattering region
- def circle(pos):
- x, y = pos
- return x ** 2 + y ** 2 < r ** 2
-
- syst = kwant.Builder()
-
- # w: width and pot: potential maximum of the p-n junction
- def potential(site):
- (x, y) = site.pos
- d = y * cos_30 + x * sin_30
- return pot * tanh(d / w)
-
- syst[graphene.shape(circle, (0, 0))] = potential
- #HIDDEN_END_shzy
-
- # specify the hoppings of the graphene lattice in the
- # format expected by builder.HoppingKind
- #HIDDEN_BEGIN_hsmc
- hoppings = (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b))
- #HIDDEN_END_hsmc
- #HIDDEN_BEGIN_bfwb
- syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1
- #HIDDEN_END_bfwb
-
- # Modify the scattering region
- #HIDDEN_BEGIN_efut
- del syst[a(0, 0)]
- syst[a(-2, 1), b(2, 2)] = -1
- #HIDDEN_END_efut
-
- #### Define the leads. ####
- #HIDDEN_BEGIN_aakh
- # left lead
- sym0 = kwant.TranslationalSymmetry(graphene.vec((-1, 0)))
-
- def lead0_shape(pos):
- x, y = pos
- return (-0.4 * r < y < 0.4 * r)
-
- lead0 = kwant.Builder(sym0)
- lead0[graphene.shape(lead0_shape, (0, 0))] = -pot
- lead0[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1
-
- # The second lead, going to the top right
- sym1 = kwant.TranslationalSymmetry(graphene.vec((0, 1)))
-
- def lead1_shape(pos):
- v = pos[1] * sin_30 - pos[0] * cos_30
- return (-0.4 * r < v < 0.4 * r)
-
- lead1 = kwant.Builder(sym1)
- lead1[graphene.shape(lead1_shape, (0, 0))] = pot
- lead1[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1
- #HIDDEN_END_aakh
-
- #HIDDEN_BEGIN_kmmw
- return syst, [lead0, lead1]
- #HIDDEN_END_kmmw
-
-
- #HIDDEN_BEGIN_zydk
- def compute_evs(syst):
- # Compute some eigenvalues of the closed system
- sparse_mat = syst.hamiltonian_submatrix(sparse=True)
-
- evs = sla.eigs(sparse_mat, 2)[0]
- print(evs.real)
- #HIDDEN_END_zydk
-
-
- def plot_conductance(syst, energies):
- # Compute transmission as a function of energy
- data = []
- for energy in energies:
- smatrix = kwant.smatrix(syst, energy)
- data.append(smatrix.transmission(0, 1))
-
-- pyplot.figure()
-+ fig = pyplot.figure()
- pyplot.plot(energies, data)
-- pyplot.xlabel("energy [t]")
-- pyplot.ylabel("conductance [e^2/h]")
-- pyplot.show()
-+ pyplot.xlabel("energy [t]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.ylabel("conductance [e^2/h]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+ for extension in ('pdf', 'png'):
-+ fig.savefig("graphene_result." + extension, dpi=_defs.dpi)
-
-
- def plot_bandstructure(flead, momenta):
- bands = kwant.physics.Bands(flead)
- energies = [bands(k) for k in momenta]
-
-- pyplot.figure()
-+ fig = pyplot.figure()
- pyplot.plot(momenta, energies)
-- pyplot.xlabel("momentum [(lattice constant)^-1]")
-- pyplot.ylabel("energy [t]")
-- pyplot.show()
-+ pyplot.xlabel("momentum [(lattice constant)^-1]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.ylabel("energy [t]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+ for extension in ('pdf', 'png'):
-+ fig.savefig("graphene_bs." + extension, dpi=_defs.dpi)
-
-
- #HIDDEN The part of the following code block which begins with family_colors
- #HIDDEN is included verbatim in the tutorial text because nested code examples
- #HIDDEN are not supported. Remember to update the tutorial text when you
- #HIDDEN modify this block.
- #HIDDEN_BEGIN_itkk
- def main():
- pot = 0.1
- syst, leads = make_system(pot=pot)
-
- # To highlight the two sublattices of graphene, we plot one with
- # a filled, and the other one with an open circle:
- def family_colors(site):
- return 0 if site.family == a else 1
-
-- # Plot the closed system without leads.
-- kwant.plot(syst, site_color=family_colors, site_lw=0.1, colorbar=False)
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, site_color=family_colors, site_lw=0.1, colorbar=False,
-+ file="graphene_syst1." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_itkk
-
- # Compute some eigenvalues.
- #HIDDEN_BEGIN_jmbi
- compute_evs(syst.finalized())
- #HIDDEN_END_jmbi
-
- # Attach the leads to the system.
- for lead in leads:
- syst.attach_lead(lead)
-
-- # Then, plot the system with leads.
-- kwant.plot(syst, site_color=family_colors, site_lw=0.1,
-- lead_site_lw=0, colorbar=False)
-+ size = (_defs.figwidth_in, 0.9 * _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, site_color=family_colors, colorbar=False, site_lw=0.1,
-+ file="graphene_syst2." + extension,
-+ fig_size=size, dpi=_defs.dpi, lead_site_lw=0)
-
- # Finalize the system.
- syst = syst.finalized()
-
- # Compute the band structure of lead 0.
- momenta = [-pi + 0.02 * pi * i for i in range(101)]
- plot_bandstructure(syst.leads[0], momenta)
-
- # Plot conductance.
- energies = [-2 * pot + 4. / 50. * pot * i for i in range(51)]
- plot_conductance(syst, energies)
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/kernel_polynomial_method.py.diff b/doc/source/code/figure/kernel_polynomial_method.py.diff
deleted file mode 100644
index 3ac53251..00000000
--- a/doc/source/code/figure/kernel_polynomial_method.py.diff
+++ /dev/null
@@ -1,374 +0,0 @@
-@@ -1,219 +1,242 @@
- # Tutorial 2.8. Calculating spectral density with the Kernel Polynomial Method
- # ============================================================================
- #
- # Physics background
- # ------------------
- # - Chebyshev polynomials, random trace approximation, spectral densities.
- #
- # Kwant features highlighted
- # --------------------------
- # - kpm module,kwant operators.
-
- import scipy
-
-+import _defs
-+from contextlib import redirect_stdout
-+
- # For plotting
- from matplotlib import pyplot as plt
-
- #HIDDEN_BEGIN_sys1
- # necessary imports
- import kwant
- import numpy as np
-
-
- # define the system
- def make_syst(r=30, t=-1, a=1):
- syst = kwant.Builder()
- lat = kwant.lattice.honeycomb(a, norbs=1)
-
- def circle(pos):
- x, y = pos
- return x ** 2 + y ** 2 < r ** 2
-
- syst[lat.shape(circle, (0, 0))] = 0.
- syst[lat.neighbors()] = t
- syst.eradicate_dangling()
-
- return syst
- #HIDDEN_END_sys1
-
- #HIDDEN_BEGIN_sys2
- # define a Haldane system
- def make_syst_topo(r=30, a=1, t=1, t2=0.5):
- syst = kwant.Builder()
- lat = kwant.lattice.honeycomb(a, norbs=1, name=['a', 'b'])
-
- def circle(pos):
- x, y = pos
- return x ** 2 + y ** 2 < r ** 2
-
- syst[lat.shape(circle, (0, 0))] = 0.
- syst[lat.neighbors()] = t
- # add second neighbours hoppings
- syst[lat.a.neighbors()] = 1j * t2
- syst[lat.b.neighbors()] = -1j * t2
- syst.eradicate_dangling()
-
- return lat, syst.finalized()
- #HIDDEN_END_sys2
-
-
- #HIDDEN_BEGIN_sys3
- # define the system
- def make_syst_staggered(r=30, t=-1, a=1, m=0.1):
- syst = kwant.Builder()
- lat = kwant.lattice.honeycomb(a, norbs=1)
-
- def circle(pos):
- x, y = pos
- return x ** 2 + y ** 2 < r ** 2
-
- syst[lat.a.shape(circle, (0, 0))] = m
- syst[lat.b.shape(circle, (0, 0))] = -m
- syst[lat.neighbors()] = t
- syst.eradicate_dangling()
-
- return syst
- #HIDDEN_END_sys3
-
- # Plot several density of states curves on the same axes.
--def plot_dos(labels_to_data):
-+def plot_dos(labels_to_data, file_name=None, ylabel="DoS [a.u.]"):
- plt.figure(figsize=(5,4))
- for label, (x, y) in labels_to_data:
- plt.plot(x, y.real, label=label, linewidth=2)
- plt.legend(loc=2, framealpha=0.5)
- plt.xlabel("energy [t]")
- plt.ylabel(ylabel)
-- plt.show()
-+ save_figure(file_name)
- plt.clf()
-
-
- # Plot fill density of states plus curves on the same axes.
--def plot_dos_and_curves(dos labels_to_data):
-+def plot_dos_and_curves(dos, labels_to_data, file_name=None, ylabel="DoS [a.u.]"):
- plt.figure(figsize=(5,4))
- plt.fill_between(dos[0], dos[1], label="DoS [a.u.]",
- alpha=0.5, color='gray')
- for label, (x, y) in labels_to_data:
- plt.plot(x, y, label=label, linewidth=2)
- plt.legend(loc=2, framealpha=0.5)
- plt.xlabel("energy [t]")
- plt.ylabel(ylabel)
-- plt.show()
-+ save_figure(file_name)
- plt.clf()
-
- def site_size_conversion(densities):
- return 3 * np.abs(densities) / max(densities)
-
-
- # Plot several local density of states maps in different subplots
- def plot_ldos(syst, densities, file_name=None):
- fig, axes = plt.subplots(1, len(densities), figsize=(7*len(densities), 7))
- for ax, (title, rho) in zip(axes, densities):
- kwant.plotter.density(syst, rho.real, ax=ax)
- ax.set_title(title)
- ax.set(adjustable='box', aspect='equal')
-- plt.show()
-+ save_figure(file_name)
- plt.clf()
-
-+def save_figure(file_name):
-+ if not file_name:
-+ return
-+ for extension in ('pdf', 'png'):
-+ plt.savefig('.'.join((file_name,extension)),
-+ dpi=_defs.dpi, bbox_inches='tight')
-+
-+
- def simple_dos_example():
- #HIDDEN_BEGIN_kpm1
- fsyst = make_syst().finalized()
-
- spectrum = kwant.kpm.SpectralDensity(fsyst)
- #HIDDEN_END_kpm1
-
- #HIDDEN_BEGIN_kpm2
- energies, densities = spectrum()
- #HIDDEN_END_kpm2
-
- #HIDDEN_BEGIN_kpm3
- energy_subset = np.linspace(0, 2)
- density_subset = spectrum(energy_subset)
- #HIDDEN_END_kpm3
-
- plot_dos([
- ('densities', (energies, densities)),
- ('density subset', (energy_subset, density_subset)),
-- ])
-+ ],
-+ file_name='kpm_dos'
-+ )
-
-
- def dos_integrating_example(fsyst):
- spectrum = kwant.kpm.SpectralDensity(fsyst)
-
- #HIDDEN_BEGIN_int1
-- print('identity resolution:', spectrum.integrate())
-+ with open('kpm_normalization.txt', 'w') as f:
-+ with redirect_stdout(f):
-+ print('identity resolution:', spectrum.integrate())
- #HIDDEN_END_int1
-
- #HIDDEN_BEGIN_int2
- # Fermi energy 0.1 and temperature 0.2
- fermi = lambda E: 1 / (np.exp((E - 0.1) / 0.2) + 1)
-
-- print('number of filled states:', spectrum.integrate(fermi))
-+ with open('kpm_total_states.txt', 'w') as f:
-+ with redirect_stdout(f):
-+ print('number of filled states:', spectrum.integrate(fermi))
- #HIDDEN_END_int2
-
-
- def increasing_accuracy_example(fsyst):
- spectrum = kwant.kpm.SpectralDensity(fsyst)
- original_dos = spectrum() # get unaltered DoS
-
- #HIDDEN_BEGIN_acc1
- spectrum.add_moments(energy_resolution=0.03)
- #HIDDEN_END_acc1
-
- increased_resolution_dos = spectrum()
-
- plot_dos([
- ('density', original_dos),
- ('higher energy resolution', increased_resolution_dos),
-- ])
-+ ],
-+ file_name='kpm_dos_acc'
-+ )
-
- #HIDDEN_BEGIN_acc2
- spectrum.add_moments(100)
- spectrum.add_vectors(5)
- #HIDDEN_END_acc2
-
- increased_moments_dos = spectrum()
-
- plot_dos([
- ('density', original_dos),
- ('higher number of moments', increased_moments_dos),
-- ])
-+ ],
-+ file_name='kpm_dos_r'
-+ )
-
-
- def operator_example(fsyst):
- #HIDDEN_BEGIN_op1
- # identity matrix
- matrix_op = scipy.sparse.eye(len(fsyst.sites))
- matrix_spectrum = kwant.kpm.SpectralDensity(fsyst, operator=matrix_op)
- #HIDDEN_END_op1
-
- #HIDDEN_BEGIN_op2
- # 'sum=True' means we sum over all the sites
- kwant_op = kwant.operator.Density(fsyst, sum=True)
- operator_spectrum = kwant.kpm.SpectralDensity(fsyst, operator=kwant_op)
- #HIDDEN_END_op2
-
- plot_dos([
- ('identity matrix', matrix_spectrum()),
- ('kwant.operator.Density', operator_spectrum()),
- ])
-
-
- def ldos_example(fsyst):
- #HIDDEN_BEGIN_op3
- # 'sum=False' is the default, but we include it explicitly here for clarity.
- kwant_op = kwant.operator.Density(fsyst, sum=False)
- local_dos = kwant.kpm.SpectralDensity(fsyst, operator=kwant_op)
- #HIDDEN_END_op3
-
- #HIDDEN_BEGIN_op4
- zero_energy_ldos = local_dos(energy=0)
- finite_energy_ldos = local_dos(energy=1)
- plot_ldos(fsyst, [
- ('energy = 0', zero_energy_ldos),
- ('energy = 1', finite_energy_ldos)
-- ])
-+ ],
-+ file_name='kpm_ldos'
-+ )
- #HIDDEN_END_op4
-
-
- def ldos_sites_example():
- fsyst = make_syst_staggered().finalized()
- #HIDDEN_BEGIN_op5
- # find 'A' and 'B' sites in the unit cell at the center of the disk
- center_tag = np.array([0, 0])
- where = lambda s: s.tag == center_tag
- # make local vectors
- vector_factory = kwant.kpm.LocalVectors(fsyst, where)
- #HIDDEN_END_op5
-
- #HIDDEN_BEGIN_op6
- # 'num_vectors' can be unspecified when using 'LocalVectors'
- local_dos = kwant.kpm.SpectralDensity(fsyst, num_vectors=None,
- vector_factory=vector_factory,
- mean=False)
- energies, densities = local_dos()
- plot_dos([
- ('A sublattice', (energies, densities[:, 0])),
- ('B sublattice', (energies, densities[:, 1])),
-- ])
-+ ],
-+ file_name='kpm_ldos_sites'
-+ )
- #HIDDEN_END_op6
-
-
- def vector_factory_example(fsyst):
- spectrum = kwant.kpm.SpectralDensity(fsyst)
- #HIDDEN_BEGIN_fact1
- # construct a generator of vectors with n random elements -1 or +1.
- n = fsyst.hamiltonian_submatrix(sparse=True).shape[0]
- def binary_vectors():
- while True:
- yield np.rint(np.random.random_sample(n)) * 2 - 1
-
- custom_factory = kwant.kpm.SpectralDensity(fsyst,
- vector_factory=binary_vectors())
- #HIDDEN_END_fact1
- plot_dos([
- ('default vector factory', spectrum()),
- ('binary vector factory', custom_factory()),
- ])
-
-
- def bilinear_map_operator_example(fsyst):
- #HIDDEN_BEGIN_blm
- rho = kwant.operator.Density(fsyst, sum=True)
-
- # sesquilinear map that does the same thing as `rho`
- def rho_alt(bra, ket):
- return np.vdot(bra, ket)
-
- rho_spectrum = kwant.kpm.SpectralDensity(fsyst, operator=rho)
- rho_alt_spectrum = kwant.kpm.SpectralDensity(fsyst, operator=rho_alt)
- #HIDDEN_END_blm
-
- plot_dos([
- ('kwant.operator.Density', rho_spectrum()),
- ('bilinear operator', rho_alt_spectrum()),
- ])
-
- def conductivity_example():
- #HIDDEN_BEGIN_cond
- # construct the Haldane model
- lat, fsyst = make_syst_topo()
- # find 'A' and 'B' sites in the unit cell at the center of the disk
- where = lambda s: np.linalg.norm(s.pos) < 1
-
- # component 'xx'
- s_factory = kwant.kpm.LocalVectors(fsyst, where)
- cond_xx = kwant.kpm.conductivity(fsyst, alpha='x', beta='x', mean=True,
- num_vectors=None, vector_factory=s_factory)
- # component 'xy'
- s_factory = kwant.kpm.LocalVectors(fsyst, where)
- cond_xy = kwant.kpm.conductivity(fsyst, alpha='x', beta='y', mean=True,
- num_vectors=None, vector_factory=s_factory)
-
- energies = cond_xx.energies
- cond_array_xx = np.array([cond_xx(e, temperature=0.01) for e in energies])
- cond_array_xy = np.array([cond_xy(e, temperature=0.01) for e in energies])
-
- # area of the unit cell per site
- area_per_site = np.abs(np.cross(*lat.prim_vecs)) / len(lat.sublattices)
- cond_array_xx /= area_per_site
- cond_array_xy /= area_per_site
- #HIDDEN_END_cond
- # ldos
- s_factory = kwant.kpm.LocalVectors(fsyst, where)
- spectrum = kwant.kpm.SpectralDensity(fsyst, num_vectors=None,
- vector_factory=s_factory)
-
- plot_dos_and_curves(
- (spectrum.energies, spectrum.densities * 8),
- [
- (r'Longitudinal conductivity $\sigma_{xx} / 4$',
- (energies, cond_array_xx / 4)),
- (r'Hall conductivity $\sigma_{xy}$',
- (energies, cond_array_xy))],
- ylabel=r'$\sigma [e^2/h]$',
- file_name='kpm_cond'
- )
-
-
- def main():
- simple_dos_example()
-
- fsyst = make_syst().finalized()
-
- dos_integrating_example(fsyst)
- increasing_accuracy_example(fsyst)
- operator_example(fsyst)
- ldos_example(fsyst)
- ldos_sites_example()
- vector_factory_example(fsyst)
- bilinear_map_operator_example(fsyst)
- conductivity_example()
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/magnetic_texture.py.diff b/doc/source/code/figure/magnetic_texture.py.diff
deleted file mode 100644
index a29a458e..00000000
--- a/doc/source/code/figure/magnetic_texture.py.diff
+++ /dev/null
@@ -1,286 +0,0 @@
-@@ -1,245 +1,268 @@
- # Tutorial 2.7. Spin textures
- # ===========================
- #
- # Physics background
- # ------------------
- # - Spin textures
- # - Skyrmions
- #
- # Kwant features highlighted
- # --------------------------
- # - operators
- # - plotting vector fields
-
-+import _defs
-+from contextlib import redirect_stdout
-+
- from math import sin, cos, tanh, pi
- import itertools
- import numpy as np
- import tinyarray as ta
- import matplotlib.pyplot as plt
-
- import kwant
-
- sigma_0 = ta.array([[1, 0], [0, 1]])
- sigma_x = ta.array([[0, 1], [1, 0]])
- sigma_y = ta.array([[0, -1j], [1j, 0]])
- sigma_z = ta.array([[1, 0], [0, -1]])
-
- # vector of Pauli matrices σ_αiβ where greek
- # letters denote spinor indices
- sigma = np.rollaxis(np.array([sigma_x, sigma_y, sigma_z]), 1)
-
- #HIDDEN_BEGIN_model
- def field_direction(pos, r0, delta):
- x, y = pos
- r = np.linalg.norm(pos)
- r_tilde = (r - r0) / delta
- theta = (tanh(r_tilde) - 1) * (pi / 2)
-
- if r == 0:
- m_i = [0, 0, -1]
- else:
- m_i = [
- (x / r) * sin(theta),
- (y / r) * sin(theta),
- cos(theta),
- ]
-
- return np.array(m_i)
-
-
- def scattering_onsite(site, r0, delta, J):
- m_i = field_direction(site.pos, r0, delta)
- return J * np.dot(m_i, sigma)
-
-
- def lead_onsite(site, J):
- return J * sigma_z
- #HIDDEN_END_model
-
-
- #HIDDEN_BEGIN_syst
- lat = kwant.lattice.square(norbs=2)
-
- def make_system(L=80):
-
- syst = kwant.Builder()
-
- def square(pos):
- return all(-L/2 < p < L/2 for p in pos)
-
- syst[lat.shape(square, (0, 0))] = scattering_onsite
- syst[lat.neighbors()] = -sigma_0
-
- lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)),
- conservation_law=-sigma_z)
-
- lead[lat.shape(square, (0, 0))] = lead_onsite
- lead[lat.neighbors()] = -sigma_0
-
- syst.attach_lead(lead)
- syst.attach_lead(lead.reversed())
-
- return syst
- #HIDDEN_END_syst
-
-
--def plot_vector_field(syst, params):
-+def save_plot(fname):
-+ for extension in ('.pdf', '.png'):
-+ plt.savefig(fname + extension,
-+ dpi=_defs.dpi, bbox_inches='tight')
-+
-+
-+def plot_vector_field(syst, params, fname=None):
- xmin, ymin = min(s.tag for s in syst.sites)
- xmax, ymax = max(s.tag for s in syst.sites)
- x, y = np.meshgrid(np.arange(xmin, xmax+1), np.arange(ymin, ymax+1))
-
- m_i = [field_direction(p, **params) for p in zip(x.flat, y.flat)]
- m_i = np.reshape(m_i, x.shape + (3,))
- m_i = np.rollaxis(m_i, 2, 0)
-
-- fig, ax = plt.subplots(1, 1)
-+ fig, ax = plt.subplots(1, 1, figsize=(9, 7))
- im = ax.quiver(x, y, *m_i, pivot='mid', scale=75)
- fig.colorbar(im)
-- plt.show()
-+ if fname:
-+ save_plot(fname)
-+ else:
-+ plt.show()
-
-
--def plot_densities(syst, densities):
-- fig, axes = plt.subplots(1, len(densities))
-+def plot_densities(syst, densities, fname=None):
-+ fig, axes = plt.subplots(1, len(densities), figsize=(7*len(densities), 7))
- for ax, (title, rho) in zip(axes, densities):
- kwant.plotter.map(syst, rho, ax=ax, a=4)
- ax.set_title(title)
-- plt.show()
-+ if fname:
-+ save_plot(fname)
-+ else:
-+ plt.show()
-
-
--def plot_currents(syst, currents):
-- fig, axes = plt.subplots(1, len(currents))
-+
-+def plot_currents(syst, currents, fname=None):
-+ fig, axes = plt.subplots(1, len(currents), figsize=(7*len(currents), 7))
- if not hasattr(axes, '__len__'):
- axes = (axes,)
- for ax, (title, current) in zip(axes, currents):
- kwant.plotter.current(syst, current, ax=ax, colorbar=False)
- ax.set_title(title)
-- plt.show()
-+ if fname:
-+ save_plot(fname)
-+ else:
-+ plt.show()
-
-
- def main():
- syst = make_system().finalized()
-
- #HIDDEN_BEGIN_wavefunction
- params = dict(r0=20, delta=10, J=1)
- wf = kwant.wave_function(syst, energy=-1, params=params)
- psi = wf(0)[0]
- #HIDDEN_END_wavefunction
-
-- plot_vector_field(syst, dict(r0=20, delta=10))
-+ plot_vector_field(syst, dict(r0=20, delta=10), fname='mag_field_direction')
-
- #HIDDEN_BEGIN_ldos
- # even (odd) indices correspond to spin up (down)
- up, down = psi[::2], psi[1::2]
- density = np.abs(up)**2 + np.abs(down)**2
- #HIDDEN_END_ldos
-
- #HIDDEN_BEGIN_lsdz
- # spin down components have a minus sign
- spin_z = np.abs(up)**2 - np.abs(down)**2
- #HIDDEN_END_lsdz
-
- #HIDDEN_BEGIN_lsdy
- # spin down components have a minus sign
- spin_y = 1j * (down.conjugate() * up - up.conjugate() * down)
- #HIDDEN_END_lsdy
-
- #HIDDEN_BEGIN_lden
- rho = kwant.operator.Density(syst)
- rho_sz = kwant.operator.Density(syst, sigma_z)
- rho_sy = kwant.operator.Density(syst, sigma_y)
-
- # calculate the expectation values of the operators with 'psi'
- density = rho(psi)
- spin_z = rho_sz(psi)
- spin_y = rho_sy(psi)
- #HIDDEN_END_lden
-
- plot_densities(syst, [
- ('$σ_0$', density),
- ('$σ_z$', spin_z),
- ('$σ_y$', spin_y),
-- ])
-+ ], fname='spin_densities')
-
- #HIDDEN_BEGIN_current
- J_0 = kwant.operator.Current(syst)
- J_z = kwant.operator.Current(syst, sigma_z)
- J_y = kwant.operator.Current(syst, sigma_y)
-
- # calculate the expectation values of the operators with 'psi'
- current = J_0(psi)
- spin_z_current = J_z(psi)
- spin_y_current = J_y(psi)
- #HIDDEN_END_current
-
- plot_currents(syst, [
- ('$J_{σ_0}$', current),
- ('$J_{σ_z}$', spin_z_current),
- ('$J_{σ_y}$', spin_y_current),
-- ])
-+ ], fname='spin_currents')
-
- #HIDDEN_BEGIN_following
- def following_m_i(site, r0, delta):
- m_i = field_direction(site.pos, r0, delta)
- return np.dot(m_i, sigma)
-
- J_m = kwant.operator.Current(syst, following_m_i)
-
- # evaluate the operator
- m_current = J_m(psi, params=dict(r0=25, delta=10))
- #HIDDEN_END_following
-
- plot_currents(syst, [
- (r'$J_{\mathbf{m}_i}$', m_current),
- ('$J_{σ_z}$', spin_z_current),
-- ])
-+ ], fname='spin_current_comparison')
-
-
- #HIDDEN_BEGIN_density_cut
- def circle(site):
- return np.linalg.norm(site.pos) < 20
-
- rho_circle = kwant.operator.Density(syst, where=circle, sum=True)
-
- all_states = np.vstack((wf(0), wf(1)))
- dos_in_circle = sum(rho_circle(p) for p in all_states) / (2 * pi)
-- print('density of states in circle:', dos_in_circle)
-+ with open('circle_dos.txt', 'w') as f:
-+ with redirect_stdout(f):
-+ print('density of states in circle:', dos_in_circle)
- #HIDDEN_END_density_cut
-
- #HIDDEN_BEGIN_current_cut
- def left_cut(site_to, site_from):
- return site_from.pos[0] <= -39 and site_to.pos[0] > -39
-
- def right_cut(site_to, site_from):
- return site_from.pos[0] < 39 and site_to.pos[0] >= 39
-
- J_left = kwant.operator.Current(syst, where=left_cut, sum=True)
- J_right = kwant.operator.Current(syst, where=right_cut, sum=True)
-
- Jz_left = kwant.operator.Current(syst, sigma_z, where=left_cut, sum=True)
- Jz_right = kwant.operator.Current(syst, sigma_z, where=right_cut, sum=True)
-
-- print('J_left:', J_left(psi), ' J_right:', J_right(psi))
-- print('Jz_left:', Jz_left(psi), ' Jz_right:', Jz_right(psi))
-+ with open('current_cut.txt', 'w') as f:
-+ with redirect_stdout(f):
-+ print('J_left:', J_left(psi), ' J_right:', J_right(psi))
-+ print('Jz_left:', Jz_left(psi), ' Jz_right:', Jz_right(psi))
- #HIDDEN_END_current_cut
-
- #HIDDEN_BEGIN_bind
- J_m = kwant.operator.Current(syst, following_m_i)
- J_z = kwant.operator.Current(syst, sigma_z)
-
- J_m_bound = J_m.bind(params=dict(r0=25, delta=10, J=1))
- J_z_bound = J_z.bind(params=dict(r0=25, delta=10, J=1))
-
- # Sum current local from all scattering states on the left at energy=-1
- wf_left = wf(0)
- J_m_left = sum(J_m_bound(p) for p in wf_left)
- J_z_left = sum(J_z_bound(p) for p in wf_left)
- #HIDDEN_END_bind
-
- plot_currents(syst, [
- (r'$J_{\mathbf{m}_i}$ (from left)', J_m_left),
- (r'$J_{σ_z}$ (from left)', J_z_left),
-- ])
-+ ], fname='bound_current')
-
-
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/plot_graphene.py.diff b/doc/source/code/figure/plot_graphene.py.diff
deleted file mode 100644
index 82c75554..00000000
--- a/doc/source/code/figure/plot_graphene.py.diff
+++ /dev/null
@@ -1,141 +0,0 @@
-@@ -1,112 +1,130 @@
- # Tutorial 2.8.1. 2D example: graphene quantum dot
- # ================================================
- #
- # Physics background
- # ------------------
- # - graphene edge states
- #
- # Kwant features highlighted
- # --------------------------
- # - demonstrate different ways of plotting
-
-+import _defs
- import kwant
- from matplotlib import pyplot
-
- #HIDDEN_BEGIN_makesyst
- lat = kwant.lattice.honeycomb()
- a, b = lat.sublattices
-
- def make_system(r=8, t=-1, tp=-0.1):
-
- def circle(pos):
- x, y = pos
- return x**2 + y**2 < r**2
-
- syst = kwant.Builder()
-- syst[lat.shape(circle, (0, 0))] = 0
-+ syst[lat.shape(circle, (0,0))] = 0
- syst[lat.neighbors()] = t
- syst.eradicate_dangling()
- if tp:
- syst[lat.neighbors(2)] = tp
-
- return syst
- #HIDDEN_END_makesyst
-
-
- #HIDDEN_BEGIN_plotsyst1
- def plot_system(syst):
-- kwant.plot(syst)
- #HIDDEN_END_plotsyst1
-- # the standard plot is ok, but not very intelligible. One can do
-- # better by playing wioth colors and linewidths
-+ # standard plot - not very intelligible for this particular situation
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, file="plot_graphene_syst1." + extension,
-+ fig_size=size, dpi=_defs.dpi)
-
- # use color and linewidths to get a better plot
- #HIDDEN_BEGIN_plotsyst2
- def family_color(site):
- return 'black' if site.family == a else 'white'
-
- def hopping_lw(site1, site2):
- return 0.04 if site1.family == site2.family else 0.1
-
-- kwant.plot(syst, site_lw=0.1, site_color=family_color, hop_lw=hopping_lw)
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, site_lw=0.1, site_color=family_color,
-+ hop_lw=hopping_lw, file="plot_graphene_syst2." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_plotsyst2
-
-
- #HIDDEN_BEGIN_plotdata1
- def plot_data(syst, n):
- import scipy.linalg as la
-
- syst = syst.finalized()
- ham = syst.hamiltonian_submatrix()
- evecs = la.eigh(ham)[1]
-
- wf = abs(evecs[:, n])**2
- #HIDDEN_END_plotdata1
-
- # the usual - works great in general, looks just a bit crufty for
- # small systems
-
- #HIDDEN_BEGIN_plotdata2
-- kwant.plotter.map(syst, wf, oversampling=10, cmap='gist_heat_r')
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plotter.map(syst, wf, oversampling=10, cmap='gist_heat_r',
-+ file="plot_graphene_data1." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_plotdata2
-
- # use two different sort of triangles to cleanly fill the space
- #HIDDEN_BEGIN_plotdata3
- def family_shape(i):
- site = syst.sites[i]
- return ('p', 3, 180) if site.family == a else ('p', 3, 0)
-
- def family_color(i):
- return 'black' if syst.sites[i].family == a else 'white'
-
-- kwant.plot(syst, site_color=wf, site_symbol=family_shape,
-- site_size=0.5, hop_lw=0, cmap='gist_heat_r')
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, site_color=wf, site_symbol=family_shape,
-+ site_size=0.5, hop_lw=0, cmap='gist_heat_r',
-+ file="plot_graphene_data2." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_plotdata3
-
- # plot by changing the symbols itself
- #HIDDEN_BEGIN_plotdata4
- def site_size(i):
- return 3 * wf[i] / wf.max()
-
-- kwant.plot(syst, site_size=site_size, site_color=(0, 0, 1, 0.3),
-- hop_lw=0.1)
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, site_size=site_size, site_color=(0,0,1,0.3),
-+ hop_lw=0.1, file="plot_graphene_data3." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_plotdata4
-
-
- def main():
- # plot the graphene system in different styles
- syst = make_system()
-
- plot_system(syst)
-
- # compute a wavefunction (number 225) and plot it in different
- # styles
- syst = make_system(tp=0)
-
- plot_data(syst, 225)
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/plot_qahe.py.diff b/doc/source/code/figure/plot_qahe.py.diff
deleted file mode 100644
index 1788f677..00000000
--- a/doc/source/code/figure/plot_qahe.py.diff
+++ /dev/null
@@ -1,78 +0,0 @@
-@@ -1,72 +1,76 @@
- # Comprehensive example: quantum anomalous Hall effect
- # ====================================================
- #
- # Physics background
- # ------------------
- # + Quantum anomalous Hall effect
- #
- # Features highlighted
- # --------------------
- # + Use of `kwant.continuum` to discretize a continuum Hamiltonian
- # + Use of `kwant.operator` to compute local current
- # + Use of `kwant.plotter.current` to plot local current
-
-+import _defs
- import math
- import matplotlib.pyplot
- import kwant
- import kwant.continuum
-
-
- # 2 band model exhibiting quantum anomalous Hall effect
- #HIDDEN_BEGIN_model
- def make_model(a):
- ham = ("alpha * (k_x * sigma_x - k_y * sigma_y)"
- "+ (m + beta * kk) * sigma_z"
- "+ (gamma * kk + U) * sigma_0")
- subs = {"kk": "k_x**2 + k_y**2"}
- return kwant.continuum.discretize(ham, locals=subs, grid=a)
- #HIDDEN_END_model
-
-
- def make_system(model, L):
- def lead_shape(site):
- x, y = site.pos / L
- return abs(y) < 0.5
-
- # QPC shape: a rectangle with 2 gaussians
- # etched out of the top and bottom edge.
- def central_shape(site):
- x, y = site.pos / L
- return abs(x) < 3/5 and abs(y) < 0.5 - 0.4 * math.exp(-40 * x**2)
-
- lead = kwant.Builder(kwant.TranslationalSymmetry(
- model.lattice.vec((-1, 0))))
- lead.fill(model, lead_shape, (0, 0))
-
- syst = kwant.Builder()
- syst.fill(model, central_shape, (0, 0))
- syst.attach_lead(lead)
- syst.attach_lead(lead.reversed())
-
- return syst.finalized()
-
-
- def main():
- # Set up our model and system, and define the model parameters.
- params = dict(alpha=0.365, beta=0.686, gamma=0.512, m=-0.01, U=0)
- model = make_model(1)
- syst = make_system(model, 70)
- kwant.plot(syst)
-
- # Calculate the scattering states at energy 'm' coming from the left
- # lead, and the associated particle current.
- psi = kwant.wave_function(syst, energy=params['m'], params=params)(0)
- #HIDDEN_BEGIN_current
- J = kwant.operator.Current(syst).bind(params=params)
- current = sum(J(p) for p in psi)
-- kwant.plotter.current(syst, current)
-+ for extension in ('pdf', 'png'):
-+ kwant.plotter.current(syst, current,
-+ file="plot_qahe_current." + extension,
-+ dpi=_defs.dpi)
- #HIDDEN_END_current
-
-
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/plot_zincblende.py.diff b/doc/source/code/figure/plot_zincblende.py.diff
deleted file mode 100644
index ad500787..00000000
--- a/doc/source/code/figure/plot_zincblende.py.diff
+++ /dev/null
@@ -1,71 +0,0 @@
-@@ -1,59 +1,67 @@
- # Tutorial 2.8.2. 3D example: zincblende structure
- # ================================================
- #
- # Physical background
- # -------------------
- # - 3D Bravais lattices
- #
- # Kwant features highlighted
- # --------------------------
- # - demonstrate different ways of plotting in 3D
-
-+import _defs
- import kwant
- from matplotlib import pyplot
-
- #HIDDEN_BEGIN_zincblende1
- lat = kwant.lattice.general([(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)],
- [(0, 0, 0), (0.25, 0.25, 0.25)])
- a, b = lat.sublattices
- #HIDDEN_END_zincblende1
-
- #HIDDEN_BEGIN_zincblende2
- def make_cuboid(a=15, b=10, c=5):
- def cuboid_shape(pos):
- x, y, z = pos
- return 0 <= x < a and 0 <= y < b and 0 <= z < c
-
- syst = kwant.Builder()
- syst[lat.shape(cuboid_shape, (0, 0, 0))] = None
- syst[lat.neighbors()] = None
-
- return syst
- #HIDDEN_END_zincblende2
-
-
- def main():
- # the standard plotting style for 3D is mainly useful for
- # checking shapes:
- #HIDDEN_BEGIN_plot1
- syst = make_cuboid()
-
-- kwant.plot(syst)
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, file="plot_zincblende_syst1." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_plot1
-
- # visualize the crystal structure better for a very small system
- #HIDDEN_BEGIN_plot2
- syst = make_cuboid(a=1.5, b=1.5, c=1.5)
-
- def family_colors(site):
- return 'r' if site.family == a else 'g'
-
-- kwant.plot(syst, site_size=0.18, site_lw=0.01, hop_lw=0.05,
-- site_color=family_colors)
-+ size = (_defs.figwidth_in, _defs.figwidth_in)
-+ for extension in ('pdf', 'png'):
-+ kwant.plot(syst, site_size=0.18, site_lw=0.01, hop_lw=0.05,
-+ site_color=family_colors,
-+ file="plot_zincblende_syst2." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_plot2
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/quantum_well.py.diff b/doc/source/code/figure/quantum_well.py.diff
deleted file mode 100644
index 8b1be4bb..00000000
--- a/doc/source/code/figure/quantum_well.py.diff
+++ /dev/null
@@ -1,103 +0,0 @@
-@@ -1,88 +1,95 @@
- # Tutorial 2.3.2. Spatially dependent values through functions
- # ============================================================
- #
- # Physics background
- # ------------------
- # transmission through a quantum well
- #
- # Kwant features highlighted
- # --------------------------
- # - Functions as values in Builder
-
-+import _defs
- import kwant
-
- # For plotting
- from matplotlib import pyplot
-
-
- #HIDDEN_BEGIN_ehso
- def make_system(a=1, t=1.0, W=10, L=30, L_well=10):
- # Start with an empty tight-binding system and a single square lattice.
- # `a` is the lattice constant (by default set to 1 for simplicity.
- lat = kwant.lattice.square(a)
-
- syst = kwant.Builder()
-
- #### Define the scattering region. ####
- # Potential profile
- def potential(site, pot):
- (x, y) = site.pos
- if (L - L_well) / 2 < x < (L + L_well) / 2:
- return pot
- else:
- return 0
- #HIDDEN_END_ehso
-
- #HIDDEN_BEGIN_coid
- def onsite(site, pot):
- return 4 * t + potential(site, pot)
-
- syst[(lat(x, y) for x in range(L) for y in range(W))] = onsite
- syst[lat.neighbors()] = -t
- #HIDDEN_END_coid
-
- #### Define and attach the leads. ####
- lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0)))
- lead[(lat(0, j) for j in range(W))] = 4 * t
- lead[lat.neighbors()] = -t
- syst.attach_lead(lead)
- syst.attach_lead(lead.reversed())
-
- return syst
-
-
- def plot_conductance(syst, energy, welldepths):
- #HIDDEN_BEGIN_sqvr
-
- # Compute conductance
- data = []
- for welldepth in welldepths:
- smatrix = kwant.smatrix(syst, energy, params=dict(pot=-welldepth))
- data.append(smatrix.transmission(1, 0))
-
-- pyplot.figure()
-+ fig = pyplot.figure()
- pyplot.plot(welldepths, data)
-- pyplot.xlabel("well depth [t]")
-- pyplot.ylabel("conductance [e^2/h]")
-- pyplot.show()
-+ pyplot.xlabel("well depth [t]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.ylabel("conductance [e^2/h]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+ for extension in ('pdf', 'png'):
-+ fig.savefig("quantum_well_result." + extension, dpi=_defs.dpi)
- #HIDDEN_END_sqvr
-
-
- def main():
- syst = make_system()
-
-- # Check that the system looks as intended.
-- kwant.plot(syst)
--
- # Finalize the system.
- syst = syst.finalized()
-
- # We should see conductance steps.
- plot_conductance(syst, energy=0.2,
- welldepths=[0.01 * i for i in range(100)])
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/quantum_wire.py.diff b/doc/source/code/figure/quantum_wire.py.diff
deleted file mode 100644
index 396ab255..00000000
--- a/doc/source/code/figure/quantum_wire.py.diff
+++ /dev/null
@@ -1,136 +0,0 @@
-@@ -1,121 +1,130 @@
- # Tutorial 2.2.2. Transport through a quantum wire
- # ================================================
- #
- # Physics background
- # ------------------
- # Conductance of a quantum wire; subbands
- #
- # Kwant features highlighted
- # --------------------------
- # - Builder for setting up transport systems easily
- # - Making scattering region and leads
- # - Using the simple sparse solver for computing Landauer conductance
-
-+import _defs
- from matplotlib import pyplot
- #HIDDEN_BEGIN_dwhx
- import kwant
- #HIDDEN_END_dwhx
-
- # First, define the tight-binding system
-
- #HIDDEN_BEGIN_goiq
- syst = kwant.Builder()
- #HIDDEN_END_goiq
-
- # Here, we are only working with square lattices
- #HIDDEN_BEGIN_suwo
- a = 1
- lat = kwant.lattice.square(a)
- #HIDDEN_END_suwo
-
- #HIDDEN_BEGIN_zfvr
- t = 1.0
- W = 10
- L = 30
-
- # Define the scattering region
-
- for i in range(L):
- for j in range(W):
- # On-site Hamiltonian
- syst[lat(i, j)] = 4 * t
-
- # Hopping in y-direction
- if j > 0:
- syst[lat(i, j), lat(i, j - 1)] = -t
-
- # Hopping in x-direction
- if i > 0:
- syst[lat(i, j), lat(i - 1, j)] = -t
- #HIDDEN_END_zfvr
-
- # Then, define and attach the leads:
-
- # First the lead to the left
- # (Note: TranslationalSymmetry takes a real-space vector)
- #HIDDEN_BEGIN_xcmc
- sym_left_lead = kwant.TranslationalSymmetry((-a, 0))
- left_lead = kwant.Builder(sym_left_lead)
- #HIDDEN_END_xcmc
-
- #HIDDEN_BEGIN_ndez
- for j in range(W):
- left_lead[lat(0, j)] = 4 * t
- if j > 0:
- left_lead[lat(0, j), lat(0, j - 1)] = -t
- left_lead[lat(1, j), lat(0, j)] = -t
- #HIDDEN_END_ndez
-
- #HIDDEN_BEGIN_fskr
- syst.attach_lead(left_lead)
- #HIDDEN_END_fskr
-
- # Then the lead to the right
- #HIDDEN_BEGIN_xhqc
- sym_right_lead = kwant.TranslationalSymmetry((a, 0))
- right_lead = kwant.Builder(sym_right_lead)
-
- for j in range(W):
- right_lead[lat(0, j)] = 4 * t
- if j > 0:
- right_lead[lat(0, j), lat(0, j - 1)] = -t
- right_lead[lat(1, j), lat(0, j)] = -t
-
- syst.attach_lead(right_lead)
- #HIDDEN_END_xhqc
-
- # Plot it, to make sure it's OK
- #HIDDEN_BEGIN_wsgh
--kwant.plot(syst)
-+size = (_defs.figwidth_in, 0.3 * _defs.figwidth_in)
-+for extension in ('pdf', 'png'):
-+ kwant.plot(syst, file="quantum_wire_syst." + extension,
-+ fig_size=size, dpi=_defs.dpi)
- #HIDDEN_END_wsgh
-
- # Finalize the system
- #HIDDEN_BEGIN_dngj
- syst = syst.finalized()
- #HIDDEN_END_dngj
-
- # Now that we have the system, we can compute conductance
- #HIDDEN_BEGIN_buzn
- energies = []
- data = []
- for ie in range(100):
- energy = ie * 0.01
-
- # compute the scattering matrix at a given energy
- smatrix = kwant.smatrix(syst, energy)
-
- # compute the transmission probability from lead 0 to
- # lead 1
- energies.append(energy)
- data.append(smatrix.transmission(1, 0))
- #HIDDEN_END_buzn
-
- # Use matplotlib to write output
- # We should see conductance steps
- #HIDDEN_BEGIN_lliv
--pyplot.figure()
-+fig = pyplot.figure()
- pyplot.plot(energies, data)
--pyplot.xlabel("energy [t]")
--pyplot.ylabel("conductance [e^2/h]")
--pyplot.show()
-+pyplot.xlabel("energy [t]", fontsize=_defs.mpl_label_size)
-+pyplot.ylabel("conductance [e^2/h]", fontsize=_defs.mpl_label_size)
-+pyplot.setp(fig.get_axes()[0].get_xticklabels(), fontsize=_defs.mpl_tick_size)
-+pyplot.setp(fig.get_axes()[0].get_yticklabels(), fontsize=_defs.mpl_tick_size)
-+fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+for extension in ('pdf', 'png'):
-+ fig.savefig("quantum_wire_result." + extension, dpi=_defs.dpi)
- #HIDDEN_END_lliv
diff --git a/doc/source/code/figure/spin_orbit.py.diff b/doc/source/code/figure/spin_orbit.py.diff
deleted file mode 100644
index 794c1b5b..00000000
--- a/doc/source/code/figure/spin_orbit.py.diff
+++ /dev/null
@@ -1,118 +0,0 @@
-@@ -1,104 +1,110 @@
- # Tutorial 2.3.1. Matrix structure of on-site and hopping elements
- # ================================================================
- #
- # Physics background
- # ------------------
- # Gaps in quantum wires with spin-orbit coupling and Zeeman splititng,
- # as theoretically predicted in
- # http://prl.aps.org/abstract/PRL/v90/i25/e256601
- # and (supposedly) experimentally oberved in
- # http://www.nature.com/nphys/journal/v6/n5/abs/nphys1626.html
- #
- # Kwant features highlighted
- # --------------------------
- # - Numpy matrices as values in Builder
-
-+import _defs
- import kwant
-
- # For plotting
- from matplotlib import pyplot
-
- # For matrix support
- #HIDDEN_BEGIN_xumz
- import tinyarray
- #HIDDEN_END_xumz
-
- # define Pauli-matrices for convenience
- #HIDDEN_BEGIN_hwbt
- sigma_0 = tinyarray.array([[1, 0], [0, 1]])
- sigma_x = tinyarray.array([[0, 1], [1, 0]])
- sigma_y = tinyarray.array([[0, -1j], [1j, 0]])
- sigma_z = tinyarray.array([[1, 0], [0, -1]])
- #HIDDEN_END_hwbt
-
-
- def make_system(t=1.0, alpha=0.5, e_z=0.08, W=10, L=30):
- # Start with an empty tight-binding system and a single square lattice.
- # `a` is the lattice constant (by default set to 1 for simplicity).
- lat = kwant.lattice.square()
-
- syst = kwant.Builder()
-
- #### Define the scattering region. ####
- #HIDDEN_BEGIN_uxrm
- syst[(lat(x, y) for x in range(L) for y in range(W))] = \
- 4 * t * sigma_0 + e_z * sigma_z
- # hoppings in x-direction
- syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = \
- -t * sigma_0 + 1j * alpha * sigma_y / 2
- # hoppings in y-directions
- syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = \
- -t * sigma_0 - 1j * alpha * sigma_x / 2
- #HIDDEN_END_uxrm
-
- #### Define the left lead. ####
- lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))
-
- #HIDDEN_BEGIN_yliu
- lead[(lat(0, j) for j in range(W))] = 4 * t * sigma_0 + e_z * sigma_z
- # hoppings in x-direction
- lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \
- -t * sigma_0 + 1j * alpha * sigma_y / 2
- # hoppings in y-directions
- lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \
- -t * sigma_0 - 1j * alpha * sigma_x / 2
- #HIDDEN_END_yliu
-
- #### Attach the leads and return the finalized system. ####
- syst.attach_lead(lead)
- syst.attach_lead(lead.reversed())
-
- return syst
-
-
- def plot_conductance(syst, energies):
- # Compute conductance
- data = []
- for energy in energies:
- smatrix = kwant.smatrix(syst, energy)
- data.append(smatrix.transmission(1, 0))
-
-- pyplot.figure()
-+ fig = pyplot.figure()
- pyplot.plot(energies, data)
-- pyplot.xlabel("energy [t]")
-- pyplot.ylabel("conductance [e^2/h]")
-- pyplot.show()
-+ pyplot.xlabel("energy [t]", fontsize=_defs.mpl_label_size)
-+ pyplot.ylabel("conductance [e^2/h]",
-+ fontsize=_defs.mpl_label_size)
-+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+ for extension in ('pdf', 'png'):
-+ fig.savefig("spin_orbit_result." + extension, dpi=_defs.dpi)
-
-
- def main():
- syst = make_system()
-
-- # Check that the system looks as intended.
-- kwant.plot(syst)
--
- # Finalize the system.
- syst = syst.finalized()
-
- # We should see non-monotonic conductance steps.
- plot_conductance(syst, energies=[0.01 * i - 0.3 for i in range(100)])
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/superconductor.py.diff b/doc/source/code/figure/superconductor.py.diff
deleted file mode 100644
index 75d9b061..00000000
--- a/doc/source/code/figure/superconductor.py.diff
+++ /dev/null
@@ -1,148 +0,0 @@
-@@ -1,132 +1,141 @@
- # Tutorial 2.6. "Superconductors": orbitals, conservation laws and symmetries
- # ===========================================================================
- #
- # Physics background
- # ------------------
- # - conductance of a NS-junction (Andreev reflection, superconducting gap)
- #
- # Kwant features highlighted
- # --------------------------
- # - Implementing electron and hole ("orbital") degrees of freedom
- # using conservation laws.
- # - Use of discrete symmetries to relate scattering states.
-
-+import _defs
- import kwant
-
- import tinyarray
- import numpy as np
-
- # For plotting
- from matplotlib import pyplot
-+from contextlib import redirect_stdout
-
- tau_x = tinyarray.array([[0, 1], [1, 0]])
- tau_y = tinyarray.array([[0, -1j], [1j, 0]])
- tau_z = tinyarray.array([[1, 0], [0, -1]])
-
- #HIDDEN_BEGIN_nbvn
- def make_system(a=1, W=10, L=10, barrier=1.5, barrierpos=(3, 4),
- mu=0.4, Delta=0.1, Deltapos=4, t=1.0):
- # Start with an empty tight-binding system. On each site, there
- # are now electron and hole orbitals, so we must specify the
- # number of orbitals per site. The orbital structure is the same
- # as in the Hamiltonian.
- lat = kwant.lattice.square(norbs=2)
- syst = kwant.Builder()
-
- #### Define the scattering region. ####
- # The superconducting order parameter couples electron and hole orbitals
- # on each site, and hence enters as an onsite potential.
- # The pairing is only included beyond the point 'Deltapos' in the scattering region.
- syst[(lat(x, y) for x in range(Deltapos) for y in range(W))] = (4 * t - mu) * tau_z
- syst[(lat(x, y) for x in range(Deltapos, L) for y in range(W))] = (4 * t - mu) * tau_z + Delta * tau_x
-
- # The tunnel barrier
- syst[(lat(x, y) for x in range(barrierpos[0], barrierpos[1])
- for y in range(W))] = (4 * t + barrier - mu) * tau_z
-
- # Hoppings
- syst[lat.neighbors()] = -t * tau_z
- #HIDDEN_END_nbvn
- #HIDDEN_BEGIN_ttth
- #### Define the leads. ####
- # Left lead - normal, so the order parameter is zero.
- sym_left = kwant.TranslationalSymmetry((-a, 0))
- # Specify the conservation law used to treat electrons and holes separately.
- # We only do this in the left lead, where the pairing is zero.
- lead0 = kwant.Builder(sym_left, conservation_law=-tau_z, particle_hole=tau_y)
- lead0[(lat(0, j) for j in range(W))] = (4 * t - mu) * tau_z
- lead0[lat.neighbors()] = -t * tau_z
- #HIDDEN_END_ttth
- #HIDDEN_BEGIN_zuuw
- # Right lead - superconducting, so the order parameter is included.
- sym_right = kwant.TranslationalSymmetry((a, 0))
- lead1 = kwant.Builder(sym_right)
- lead1[(lat(0, j) for j in range(W))] = (4 * t - mu) * tau_z + Delta * tau_x
- lead1[lat.neighbors()] = -t * tau_z
-
- #### Attach the leads and return the system. ####
- syst.attach_lead(lead0)
- syst.attach_lead(lead1)
-
- return syst
- #HIDDEN_END_zuuw
-
- #HIDDEN_BEGIN_jbjt
- def plot_conductance(syst, energies):
- # Compute conductance
- data = []
- for energy in energies:
- smatrix = kwant.smatrix(syst, energy)
- # Conductance is N - R_ee + R_he
- data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -
- smatrix.transmission((0, 0), (0, 0)) +
- smatrix.transmission((0, 1), (0, 0)))
- #HIDDEN_END_jbjt
-- pyplot.figure()
-+ fig = pyplot.figure()
- pyplot.plot(energies, data)
- pyplot.xlabel("energy [t]")
- pyplot.ylabel("conductance [e^2/h]")
-- pyplot.show()
-+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
-+ fontsize=_defs.mpl_tick_size)
-+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
-+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-+ for extension in ('pdf', 'png'):
-+ fig.savefig("superconductor_transport_result." + extension,
-+ dpi=_defs.dpi)
-
- #HIDDEN_BEGIN_pqmp
- def check_PHS(syst):
- # Scattering matrix
- s = kwant.smatrix(syst, energy=0)
- # Electron to electron block
- s_ee = s.submatrix((0,0), (0,0))
- # Hole to hole block
- s_hh = s.submatrix((0,1), (0,1))
- print('s_ee: \n', np.round(s_ee, 3))
- print('s_hh: \n', np.round(s_hh[::-1, ::-1], 3))
- print('s_ee - s_hh^*: \n',
- np.round(s_ee - s_hh[::-1, ::-1].conj(), 3), '\n')
- # Electron to hole block
- s_he = s.submatrix((0,1), (0,0))
- # Hole to electron block
- s_eh = s.submatrix((0,0), (0,1))
- print('s_he: \n', np.round(s_he, 3))
- print('s_eh: \n', np.round(s_eh[::-1, ::-1], 3))
- print('s_he + s_eh^*: \n',
- np.round(s_he + s_eh[::-1, ::-1].conj(), 3))
- #HIDDEN_END_pqmp
-
- def main():
- syst = make_system(W=10)
-
-- # Check that the system looks as intended.
-- kwant.plot(syst)
--
- # Finalize the system.
- syst = syst.finalized()
-
- # Check particle-hole symmetry of the scattering matrix
-- check_PHS(syst)
-+ with open('check_PHS_out.txt', 'w') as f:
-+ with redirect_stdout(f):
-+ check_PHS(syst)
-
- # Compute and plot the conductance
- plot_conductance(syst, energies=[0.002 * i for i in range(-10, 100)])
-
-
- # Call the main function if the script gets executed (as opposed to imported).
- # See <http://docs.python.org/library/__main__.html>.
- if __name__ == '__main__':
- main()
diff --git a/doc/source/code/figure/superconductor_transport_sketch.svg b/doc/source/code/figure/superconductor_transport_sketch.svg
deleted file mode 100644
index 35f087cd..00000000
--- a/doc/source/code/figure/superconductor_transport_sketch.svg
+++ /dev/null
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diff --git a/doc/source/code/include/quantum_wire_revisited.py b/doc/source/code/include/quantum_wire_revisited.py
deleted file mode 100644
index 60add478..00000000
--- a/doc/source/code/include/quantum_wire_revisited.py
+++ /dev/null
@@ -1,91 +0,0 @@
-# Tutorial 2.2.3. Building the same system with less code
-# =======================================================
-#
-# Physics background
-# ------------------
-# Conductance of a quantum wire; subbands
-#
-# Kwant features highlighted
-# --------------------------
-# - Using iterables and builder.HoppingKind for making systems
-# - introducing `reversed()` for the leads
-#
-# Note: Does the same as tutorial1a.py, but using other features of Kwant.
-
-#HIDDEN_BEGIN_xkzy
-import kwant
-
-# For plotting
-from matplotlib import pyplot
-
-
-def make_system(a=1, t=1.0, W=10, L=30):
- # Start with an empty tight-binding system and a single square lattice.
- # `a` is the lattice constant (by default set to 1 for simplicity.
- lat = kwant.lattice.square(a)
-
- syst = kwant.Builder()
-#HIDDEN_END_xkzy
-
- #### Define the scattering region. ####
-#HIDDEN_BEGIN_vvjt
- syst[(lat(x, y) for x in range(L) for y in range(W))] = 4 * t
-#HIDDEN_END_vvjt
-#HIDDEN_BEGIN_nooi
- syst[lat.neighbors()] = -t
-#HIDDEN_END_nooi
-
- #### Define and attach the leads. ####
- # Construct the left lead.
-#HIDDEN_BEGIN_iepx
- lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0)))
- lead[(lat(0, j) for j in range(W))] = 4 * t
- lead[lat.neighbors()] = -t
-#HIDDEN_END_iepx
-
- # Attach the left lead and its reversed copy.
-#HIDDEN_BEGIN_yxot
- syst.attach_lead(lead)
- syst.attach_lead(lead.reversed())
-
- return syst
-#HIDDEN_END_yxot
-
-
-#HIDDEN_BEGIN_ayuk
-def plot_conductance(syst, energies):
- # Compute conductance
- data = []
- for energy in energies:
- smatrix = kwant.smatrix(syst, energy)
- data.append(smatrix.transmission(1, 0))
-
- pyplot.figure()
- pyplot.plot(energies, data)
- pyplot.xlabel("energy [t]")
- pyplot.ylabel("conductance [e^2/h]")
- pyplot.show()
-#HIDDEN_END_ayuk
-
-
-#HIDDEN_BEGIN_cjel
-def main():
- syst = make_system()
-
- # Check that the system looks as intended.
- kwant.plot(syst)
-
- # Finalize the system.
- syst = syst.finalized()
-
- # We should see conductance steps.
- plot_conductance(syst, energies=[0.01 * i for i in range(100)])
-#HIDDEN_END_cjel
-
-
-# Call the main function if the script gets executed (as opposed to imported).
-# See <http://docs.python.org/library/__main__.html>.
-#HIDDEN_BEGIN_ypbj
-if __name__ == '__main__':
- main()
-#HIDDEN_END_ypbj
--
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