From 60d6fb90d7521b15553939595720386d1d21d5ac Mon Sep 17 00:00:00 2001
From: Christoph Groth <christoph.groth@cea.fr>
Date: Sat, 17 Nov 2012 10:42:06 +0100
Subject: [PATCH] generate image creation scripts from tutorial scripts by
patching
---
.gitignore | 1 +
doc/Makefile | 9 +-
doc/source/images/1-quantum_wire.py | 116 -----------
doc/source/images/1-quantum_wire.py.diff | 39 ++++
doc/source/images/2-ab_ring.py | 190 -----------------
doc/source/images/2-ab_ring.py.diff | 116 +++++++++++
doc/source/images/2-quantum_well.py | 112 ----------
doc/source/images/2-quantum_well.py.diff | 44 ++++
doc/source/images/2-spin_orbit.py | 107 ----------
doc/source/images/2-spin_orbit.py.diff | 43 ++++
doc/source/images/3-band_structure.py | 73 -------
doc/source/images/3-band_structure.py.diff | 35 ++++
doc/source/images/3-closed_system.py | 111 ----------
doc/source/images/3-closed_system.py.diff | 46 +++++
doc/source/images/4-graphene.py | 193 ------------------
doc/source/images/4-graphene.py.diff | 97 +++++++++
.../images/5-superconductor_band_structure.py | 81 --------
.../5-superconductor_band_structure.py.diff | 33 +++
.../images/5-superconductor_transport.py | 126 ------------
.../images/5-superconductor_transport.py.diff | 40 ++++
doc/source/images/generate-diffs.sh | 10 +
tutorial/3-closed_system.py | 2 +-
tutorial/README | 14 ++
23 files changed, 526 insertions(+), 1112 deletions(-)
delete mode 100644 doc/source/images/1-quantum_wire.py
create mode 100644 doc/source/images/1-quantum_wire.py.diff
delete mode 100644 doc/source/images/2-ab_ring.py
create mode 100644 doc/source/images/2-ab_ring.py.diff
delete mode 100644 doc/source/images/2-quantum_well.py
create mode 100644 doc/source/images/2-quantum_well.py.diff
delete mode 100644 doc/source/images/2-spin_orbit.py
create mode 100644 doc/source/images/2-spin_orbit.py.diff
delete mode 100644 doc/source/images/3-band_structure.py
create mode 100644 doc/source/images/3-band_structure.py.diff
delete mode 100644 doc/source/images/3-closed_system.py
create mode 100644 doc/source/images/3-closed_system.py.diff
delete mode 100644 doc/source/images/4-graphene.py
create mode 100644 doc/source/images/4-graphene.py.diff
delete mode 100644 doc/source/images/5-superconductor_band_structure.py
create mode 100644 doc/source/images/5-superconductor_band_structure.py.diff
delete mode 100644 doc/source/images/5-superconductor_transport.py
create mode 100644 doc/source/images/5-superconductor_transport.py.diff
create mode 100755 doc/source/images/generate-diffs.sh
create mode 100644 tutorial/README
diff --git a/.gitignore b/.gitignore
index af93de50..4493ae39 100644
--- a/.gitignore
+++ b/.gitignore
@@ -12,4 +12,5 @@ MANIFEST
/doc/source/images/*.png
/doc/source/images/*.pdf
/doc/source/images/.*_flag
+/doc/source/images/[0-9]-*.py
/build.conf
diff --git a/doc/Makefile b/doc/Makefile
index 7856c9a1..3de1f635 100644
--- a/doc/Makefile
+++ b/doc/Makefile
@@ -54,7 +54,7 @@ clean:
-rm -rf source/reference/generated
realclean: clean
- -rm -f $(ALL_IMAGES) source/images/.*_flag
+ -rm -f $(ALL_IMAGES) source/images/.*_flag source/images/[0-9]-*.py
html: $(ALL_IMAGES)
$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
@@ -118,7 +118,12 @@ doctest:
inkscape --export-pdf=$@ $<
-# Generation of tutorial images. This requires some serious make trickery, see
+# Make the image generation scripts by patching tutorial scipts.
+%.py: %.py.diff
+ @cp ../tutorial/$(notdir $@) $(dir $@)
+ @patch $@ $<
+
+# Generation of tutorial images. This requires some make trickery, see
# http://article.gmane.org/gmane.comp.gnu.make.general/5806
.%_flag: %.py
diff --git a/doc/source/images/1-quantum_wire.py b/doc/source/images/1-quantum_wire.py
deleted file mode 100644
index 835b0a96..00000000
--- a/doc/source/images/1-quantum_wire.py
+++ /dev/null
@@ -1,116 +0,0 @@
-# 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 kwant
-import latex, html
-
-# First, define the tight-binding system
-
-sys = kwant.Builder()
-
-# Here, we are only working with square lattices
-a = 1
-lat = kwant.lattice.Square(a)
-
-t = 1.0
-W = 10
-L = 30
-
-# Define the scattering region
-
-for i in xrange(L):
- for j in xrange(W):
- sys[lat(i, j)] = 4 * t
-
- # hoppig in y-direction
- if j > 0:
- sys[lat(i, j), lat(i, j - 1)] = - t
-
- #hopping in x-direction
- if i > 0:
- sys[lat(i, j), lat(i - 1, j)] = -t
-
-# Then, define the leads:
-
-# First the lead to the left
-
-# (Note: in the current version, TranslationalSymmetry takes a
-# realspace vector)
-sym_lead0 = kwant.TranslationalSymmetry([lat.vec((-1, 0))])
-lead0 = kwant.Builder(sym_lead0)
-
-for j in xrange(W):
- lead0[lat(0, j)] = 4 * t
-
- if j > 0:
- lead0[lat(0, j), lat(0, j - 1)] = - t
-
- lead0[lat(1, j), lat(0, j)] = - t
-
-# Then the lead to the right
-
-sym_lead1 = kwant.TranslationalSymmetry([lat.vec((1, 0))])
-lead1 = kwant.Builder(sym_lead1)
-
-for j in xrange(W):
- lead1[lat(0, j)] = 4 * t
-
- if j > 0:
- lead1[lat(0, j), lat(0, j - 1)] = - t
-
- lead1[lat(1, j), lat(0, j)] = - t
-
-# Then attach the leads to the system
-
-sys.attach_lead(lead0)
-sys.attach_lead(lead1)
-
-# Plot it, to make sure it's OK
-
-kwant.plot(sys, "1-quantum_wire_sys.pdf", width=latex.figwidth_pt)
-kwant.plot(sys, "1-quantum_wire_sys.png", width=html.figwidth_px)
-
-# Finalize the system
-
-sys = sys.finalized()
-
-# Now that we have the system, we can compute conductance
-
-energies = []
-data = []
-for ie in xrange(100):
- energy = ie * 0.01
-
- # compute the scattering matrix at energy energy
- smatrix = kwant.solve(sys, energy)
-
- # compute the transmission probability from lead 0 to
- # lead 1
- energies.append(energy)
- data.append(smatrix.transmission(1, 0))
-
-# Use matplotlib to write output
-# We should see conductance steps
-from matplotlib import pyplot
-
-fig = pyplot.figure()
-pyplot.plot(energies, data)
-pyplot.xlabel("energy [in units of t]",
- fontsize=latex.mpl_label_size)
-pyplot.ylabel("conductance [in units of e^2/h]",
- fontsize=latex.mpl_label_size)
-pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
-pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
-fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
-fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
-fig.savefig("1-quantum_wire_result.pdf")
-fig.savefig("1-quantum_wire_result.png", dpi=(html.figwidth_px/latex.mpl_width_in))
diff --git a/doc/source/images/1-quantum_wire.py.diff b/doc/source/images/1-quantum_wire.py.diff
new file mode 100644
index 00000000..ed74c097
--- /dev/null
+++ b/doc/source/images/1-quantum_wire.py.diff
@@ -0,0 +1,39 @@
+--- original
++++ modified
+@@ -9,6 +9,7 @@
+ # - Using the simple sparse solver for computing Landauer conductance
+
+ import kwant
++import latex, html
+
+ # First, define the tight-binding system
+
+@@ -73,7 +74,8 @@
+
+ # Plot it, to make sure it's OK
+
+-kwant.plot(sys)
++kwant.plot(sys, "1-quantum_wire_sys.pdf", width=latex.figwidth_pt)
++kwant.plot(sys, "1-quantum_wire_sys.png", width=html.figwidth_px)
+
+ # Finalize the system
+
+@@ -98,8 +100,14 @@
+ # We should see conductance steps
+ from matplotlib import pyplot
+
+-pyplot.figure()
++fig = pyplot.figure()
+ pyplot.plot(energies, data)
+-pyplot.xlabel("energy [in units of t]")
+-pyplot.ylabel("conductance [in units of e^2/h]")
+-pyplot.show()
++pyplot.xlabel("energy [in units of t]", fontsize=latex.mpl_label_size)
++pyplot.ylabel("conductance [in units of e^2/h]", fontsize=latex.mpl_label_size)
++pyplot.setp(fig.get_axes()[0].get_xticklabels(), fontsize=latex.mpl_tick_size)
++pyplot.setp(fig.get_axes()[0].get_yticklabels(), fontsize=latex.mpl_tick_size)
++fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++fig.savefig("1-quantum_wire_result.pdf")
++fig.savefig("1-quantum_wire_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
diff --git a/doc/source/images/2-ab_ring.py b/doc/source/images/2-ab_ring.py
deleted file mode 100644
index ad6ba6e1..00000000
--- a/doc/source/images/2-ab_ring.py
+++ /dev/null
@@ -1,190 +0,0 @@
-# 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
-
-from cmath import exp
-from math import pi
-
-import kwant
-
-# For plotting
-from matplotlib import pyplot
-
-import latex, html
-
-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)
-
- sys = 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)
-
- # and add the corresponding lattice points using the `shape`-function
- sys[lat.shape(ring, (0, r1 + 1))] = 4 * t
- for hopping in lat.nearest:
- sys[sys.possible_hoppings(*hopping)] = - t
-
- # 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 Builder repeatedly,
- # we define the modified hoppings as a function that takes the flux
- # through the global variable phi.
- def fluxphase(site1, site2):
- return exp(1j * phi)
-
- def crosses_branchcut(hop):
- ix0, iy0 = hop[0].tag
-
- # possible_hoppings 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
- sys[(hop for hop in sys.possible_hoppings((1, 0), lat, lat)
- if crosses_branchcut(hop))] = fluxphase
-
- #### Define the leads. ####
- # left lead
- sym_lead0 = kwant.TranslationalSymmetry([lat.vec((-1, 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
- for hopping in lat.nearest:
- lead0[lead0.possible_hoppings(*hopping)] = - t
-
- # Then the lead to the right
- # [again, obtained using reversed()]
- lead1 = lead0.reversed()
-
- #### Attach the leads and return the system. ####
- sys.attach_lead(lead0)
- sys.attach_lead(lead1)
-
- return sys
-
-
-def make_system_note1(a=1, t=1.0, W=10, r1=10, r2=20):
- lat = kwant.lattice.Square(a)
- sys = kwant.Builder()
- def ring(pos):
- (x, y) = pos
- rsq = x**2 + y**2
- return ( r1**2 < rsq < r2**2)
- sys[lat.shape(ring, (0, 11))] = 4 * t
- for hopping in lat.nearest:
- sys[sys.possible_hoppings(*hopping)] = - t
- sym_lead0 = kwant.TranslationalSymmetry([lat.vec((-1, 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
- for hopping in lat.nearest:
- lead0[lead0.possible_hoppings(*hopping)] = - t
- lead1 = lead0.reversed()
- sys.attach_lead(lead0)
- sys.attach_lead(lead1)
- return sys
-
-
-def make_system_note2(a=1, t=1.0, W=10, r1=10, r2=20):
- lat = kwant.lattice.Square(a)
- sys = kwant.Builder()
- def ring(pos):
- (x, y) = pos
- rsq = x**2 + y**2
- return ( r1**2 < rsq < r2**2)
- sys[lat.shape(ring, (0, 11))] = 4 * t
- for hopping in lat.nearest:
- sys[sys.possible_hoppings(*hopping)] = - t
- sym_lead0 = kwant.TranslationalSymmetry([lat.vec((-1, 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
- for hopping in lat.nearest:
- lead0[lead0.possible_hoppings(*hopping)] = - t
- lead1 = lead0.reversed()
- sys.attach_lead(lead0)
- sys.attach_lead(lead1, lat(0, 0))
- return sys
-
-
-def plot_conductance(sys, energy, fluxes):
- # compute conductance
- # global variable phi controls the flux
- global phi
-
- normalized_fluxes = [flux / (2 * pi) for flux in fluxes]
- data = []
- for flux in fluxes:
- phi = flux
-
- smatrix = kwant.solve(sys, energy)
- data.append(smatrix.transmission(1, 0))
-
- fig = pyplot.figure()
- pyplot.plot(normalized_fluxes, data)
- pyplot.xlabel("flux [in units of the flux quantum]",
- fontsize=latex.mpl_label_size)
- pyplot.ylabel("conductance [in units of e^2/h]",
- fontsize=latex.mpl_label_size)
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("2-ab_ring_result.pdf")
- fig.savefig("2-ab_ring_result.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def main():
- sys = make_system()
-
- # Check that the system looks as intended.
- kwant.plot(sys, "2-ab_ring_sys.pdf", width=latex.figwidth_pt)
- kwant.plot(sys, "2-ab_ring_sys.png", width=html.figwidth_px)
-
- # Finalize the system.
- sys = sys.finalized()
-
- # We should see a conductance that is periodic with the flux quantum
- plot_conductance(sys, energy=0.15, fluxes=[0.01 * i * 3 * 2 * pi
- for i in xrange(100)])
-
- # Finally, some plots needed for the notes
- sys = make_system_note1()
- kwant.plot(sys, "2-ab_ring_note1.pdf", width=latex.figwidth_small_pt)
- kwant.plot(sys, "2-ab_ring_note1.png", width=html.figwidth_small_px)
- sys = make_system_note2()
- kwant.plot(sys, "2-ab_ring_note2.pdf", width=latex.figwidth_small_pt)
- kwant.plot(sys, "2-ab_ring_note2.png", width=html.figwidth_small_px)
-
-
-# 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/images/2-ab_ring.py.diff b/doc/source/images/2-ab_ring.py.diff
new file mode 100644
index 00000000..29bd464f
--- /dev/null
+++ b/doc/source/images/2-ab_ring.py.diff
@@ -0,0 +1,116 @@
+--- original
++++ modified
+@@ -16,6 +16,7 @@
+
+ # For plotting
+ from matplotlib import pyplot
++import latex, html
+
+
+ def make_system(a=1, t=1.0, W=10, r1=10, r2=20):
+@@ -82,6 +83,54 @@
+ return sys
+
+
++def make_system_note1(a=1, t=1.0, W=10, r1=10, r2=20):
++ lat = kwant.lattice.Square(a)
++ sys = kwant.Builder()
++ def ring(pos):
++ (x, y) = pos
++ rsq = x**2 + y**2
++ return ( r1**2 < rsq < r2**2)
++ sys[lat.shape(ring, (0, 11))] = 4 * t
++ for hopping in lat.nearest:
++ sys[sys.possible_hoppings(*hopping)] = -t
++ sym_lead0 = kwant.TranslationalSymmetry([lat.vec((-1, 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
++ for hopping in lat.nearest:
++ lead0[lead0.possible_hoppings(*hopping)] = -t
++ lead1 = lead0.reversed()
++ sys.attach_lead(lead0)
++ sys.attach_lead(lead1)
++ return sys
++
++
++def make_system_note2(a=1, t=1.0, W=10, r1=10, r2=20):
++ lat = kwant.lattice.Square(a)
++ sys = kwant.Builder()
++ def ring(pos):
++ (x, y) = pos
++ rsq = x**2 + y**2
++ return ( r1**2 < rsq < r2**2)
++ sys[lat.shape(ring, (0, 11))] = 4 * t
++ for hopping in lat.nearest:
++ sys[sys.possible_hoppings(*hopping)] = -t
++ sym_lead0 = kwant.TranslationalSymmetry([lat.vec((-1, 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
++ for hopping in lat.nearest:
++ lead0[lead0.possible_hoppings(*hopping)] = -t
++ lead1 = lead0.reversed()
++ sys.attach_lead(lead0)
++ sys.attach_lead(lead1, lat(0, 0))
++ return sys
++
++
+ def plot_conductance(sys, energy, fluxes):
+ # compute conductance
+ # global variable phi controls the flux
+@@ -95,18 +144,29 @@
+ smatrix = kwant.solve(sys, energy)
+ data.append(smatrix.transmission(1, 0))
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(normalized_fluxes, data)
+- pyplot.xlabel("flux [in units of the flux quantum]")
+- pyplot.ylabel("conductance [in units of e^2/h]")
+- pyplot.show()
++ pyplot.xlabel("flux [in units of the flux quantum]",
++ fontsize=latex.mpl_label_size)
++ pyplot.ylabel("conductance [in units of e^2/h]",
++ fontsize=latex.mpl_label_size)
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("2-ab_ring_result.pdf")
++ fig.savefig("2-ab_ring_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def main():
+ sys = make_system()
+
+ # Check that the system looks as intended.
+- kwant.plot(sys)
++ kwant.plot(sys, "2-ab_ring_sys.pdf", width=latex.figwidth_pt)
++ kwant.plot(sys, "2-ab_ring_sys.png", width=html.figwidth_px)
+
+ # Finalize the system.
+ sys = sys.finalized()
+@@ -115,6 +175,15 @@
+ plot_conductance(sys, energy=0.15, fluxes=[0.01 * i * 3 * 2 * pi
+ for i in xrange(100)])
+
++ # Finally, some plots needed for the notes
++ sys = make_system_note1()
++ kwant.plot(sys, "2-ab_ring_note1.pdf", width=latex.figwidth_small_pt)
++ kwant.plot(sys, "2-ab_ring_note1.png", width=html.figwidth_small_px)
++ sys = make_system_note2()
++ kwant.plot(sys, "2-ab_ring_note2.pdf", width=latex.figwidth_small_pt)
++ kwant.plot(sys, "2-ab_ring_note2.png", width=html.figwidth_small_px)
++
++
+ # Call the main function if the script gets executed (as opposed to imported).
+ # See <http://docs.python.org/library/__main__.html>.
+ if __name__ == '__main__':
diff --git a/doc/source/images/2-quantum_well.py b/doc/source/images/2-quantum_well.py
deleted file mode 100644
index 1b90a7e1..00000000
--- a/doc/source/images/2-quantum_well.py
+++ /dev/null
@@ -1,112 +0,0 @@
-# Physics background
-# ------------------
-# transmission through a quantum well
-#
-# Kwant features highlighted
-# --------------------------
-# - Functions as values in Builder
-
-import kwant
-
-# For plotting
-from matplotlib import pyplot
-
-import latex, html
-
-# global variable governing the behavior of potential() in
-# make_system()
-pot = 0
-
-
-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)
-
- sys = kwant.Builder()
-
- #### Define the scattering region. ####
- # Potential profile
- def potential(site):
- (x, y) = site.pos
- if (L - L_well) / 2 < x < (L + L_well) / 2:
- # The potential value is provided using a global variable
- return pot
- else:
- return 0
-
- def onsite(site):
- return 4 * t + potential(site)
-
- sys[(lat(x, y) for x in range(L) for y in range(W))] = onsite
- for hopping in lat.nearest:
- sys[sys.possible_hoppings(*hopping)] = -t
-
- #### Define the leads. ####
- # First the lead to the left, ...
- # (Note: in the current version, TranslationalSymmetry takes a
- # realspace vector)
- sym_lead0 = kwant.TranslationalSymmetry([lat.vec((-1, 0))])
- lead0 = kwant.Builder(sym_lead0)
-
- lead0[(lat(0, j) for j in xrange(W))] = 4 * t
- for hopping in lat.nearest:
- lead0[lead0.possible_hoppings(*hopping)] = - t
-
- # ... then the lead to the right. We use a method that returns a copy of
- # `lead0` with its direction reversed.
- lead1 = lead0.reversed()
-
- #### Attach the leads and return the finalized system. ####
- sys.attach_lead(lead0)
- sys.attach_lead(lead1)
-
- return sys
-
-
-def plot_conductance(sys, energy, welldepths):
- # We specify that we want to not only read, but also write to a
- # global variable.
- global pot
-
- # Compute conductance
- data = []
- for welldepth in welldepths:
- # Set the global variable that defines the potential well depth
- pot = -welldepth
-
- smatrix = kwant.solve(sys, energy)
- data.append(smatrix.transmission(1, 0))
-
- fig = pyplot.figure()
- pyplot.plot(welldepths, data)
- pyplot.xlabel("well depth [in units of t]",
- fontsize=latex.mpl_label_size)
- pyplot.ylabel("conductance [in units of e^2/h]",
- fontsize=latex.mpl_label_size)
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("2-quantum_well_result.pdf")
- fig.savefig("2-quantum_well_result.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def main():
- sys = make_system()
-
- # Finalize the system.
- sys = sys.finalized()
-
- # We should see conductance steps.
- plot_conductance(sys, energy=0.2,
- welldepths=[0.01 * i for i in xrange(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/images/2-quantum_well.py.diff b/doc/source/images/2-quantum_well.py.diff
new file mode 100644
index 00000000..40988f9f
--- /dev/null
+++ b/doc/source/images/2-quantum_well.py.diff
@@ -0,0 +1,44 @@
+--- original
++++ modified
+@@ -10,6 +10,7 @@
+
+ # For plotting
+ from matplotlib import pyplot
++import latex, html
+
+ # global variable governing the behavior of potential() in
+ # make_system()
+@@ -75,19 +76,26 @@
+ smatrix = kwant.solve(sys, energy)
+ data.append(smatrix.transmission(1, 0))
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(welldepths, data)
+- pyplot.xlabel("well depth [in units of t]")
+- pyplot.ylabel("conductance [in units of e^2/h]")
+- pyplot.show()
++ pyplot.xlabel("well depth [in units of t]",
++ fontsize=latex.mpl_label_size)
++ pyplot.ylabel("conductance [in units of e^2/h]",
++ fontsize=latex.mpl_label_size)
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("2-quantum_well_result.pdf")
++ fig.savefig("2-quantum_well_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def main():
+ sys = make_system()
+
+- # Check that the system looks as intended.
+- kwant.plot(sys)
+-
+ # Finalize the system.
+ sys = sys.finalized()
+
diff --git a/doc/source/images/2-spin_orbit.py b/doc/source/images/2-spin_orbit.py
deleted file mode 100644
index cab6df71..00000000
--- a/doc/source/images/2-spin_orbit.py
+++ /dev/null
@@ -1,107 +0,0 @@
-# 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 kwant
-
-# For plotting
-from matplotlib import pyplot
-
-# For matrix support
-import numpy
-
-import latex, html
-
-# define Pauli-matrices for convenience
-sigma_0 = numpy.eye(2)
-sigma_x = numpy.array([[0, 1], [1, 0]])
-sigma_y = numpy.array([[0, -1j], [1j, 0]])
-sigma_z = numpy.array([[1, 0], [0, -1]])
-
-
-def make_system(a=1, 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(a)
-
- sys = kwant.Builder()
-
- #### Define the scattering region. ####
- sys[(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
- sys[sys.possible_hoppings((1, 0), lat, lat)] = - t * sigma_0 - \
- 1j * alpha * sigma_y
- # hoppings in y-directions
- sys[sys.possible_hoppings((0, 1), lat, lat)] = - t * sigma_0 + \
- 1j * alpha * sigma_x
-
- #### Define the leads. ####
- # left lead
- sym_lead0 = kwant.TranslationalSymmetry([lat.vec((-1, 0))])
- lead0 = kwant.Builder(sym_lead0)
-
- lead0[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z
- # hoppings in x-direction
- lead0[lead0.possible_hoppings((1, 0), lat, lat)] = - t * sigma_0 - \
- 1j * alpha * sigma_y
- # hoppings in y-directions
- lead0[lead0.possible_hoppings((0, 1), lat, lat)] = - t * sigma_0 + \
- 1j * alpha * sigma_x
-
- # Then the lead to the right
- # (again, obtained using reverse()
- lead1 = lead0.reversed()
-
- #### Attach the leads and return the finalized system. ####
- sys.attach_lead(lead0)
- sys.attach_lead(lead1)
-
- return sys
-
-def plot_conductance(sys, energies):
- # Compute conductance
- data = []
- for energy in energies:
- smatrix = kwant.solve(sys, energy)
- data.append(smatrix.transmission(1, 0))
-
- fig = pyplot.figure()
- pyplot.plot(energies, data)
- pyplot.xlabel("energy [in units of t]",
- fontsize=latex.mpl_label_size)
- pyplot.ylabel("conductance [in units of e^2/h]",
- fontsize=latex.mpl_label_size)
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("2-spin_orbit_result.pdf")
- fig.savefig("2-spin_orbit_result.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def main():
- sys = make_system()
-
- # Finalize the system.
- sys = sys.finalized()
-
- # We should see non-monotonic conductance steps.
- plot_conductance(sys, energies=[0.01 * i - 0.3 for i in xrange(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/images/2-spin_orbit.py.diff b/doc/source/images/2-spin_orbit.py.diff
new file mode 100644
index 00000000..fb74b9ce
--- /dev/null
+++ b/doc/source/images/2-spin_orbit.py.diff
@@ -0,0 +1,43 @@
+--- original
++++ modified
+@@ -17,6 +17,7 @@
+
+ # For matrix support
+ import numpy
++import latex, html
+
+ # define Pauli-matrices for convenience
+ sigma_0 = numpy.eye(2)
+@@ -72,19 +73,25 @@
+ smatrix = kwant.solve(sys, energy)
+ data.append(smatrix.transmission(1, 0))
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(energies, data)
+- pyplot.xlabel("energy [in units of t]")
+- pyplot.ylabel("conductance [in units of e^2/h]")
+- pyplot.show()
++ pyplot.xlabel("energy [in units of t]", fontsize=latex.mpl_label_size)
++ pyplot.ylabel("conductance [in units of e^2/h]",
++ fontsize=latex.mpl_label_size)
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("2-spin_orbit_result.pdf")
++ fig.savefig("2-spin_orbit_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def main():
+ sys = make_system()
+
+- # Check that the system looks as intended.
+- kwant.plot(sys)
+-
+ # Finalize the system.
+ sys = sys.finalized()
+
diff --git a/doc/source/images/3-band_structure.py b/doc/source/images/3-band_structure.py
deleted file mode 100644
index 1174523a..00000000
--- a/doc/source/images/3-band_structure.py
+++ /dev/null
@@ -1,73 +0,0 @@
-# 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 kwant
-
-from math import pi
-
-# For plotting
-from matplotlib import pyplot
-
-import latex, html
-
-
-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([lat.vec((-1, 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 xrange(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
-
-
-def plot_bandstructure(lead, momenta):
- # Use the method ``energies`` of the finalized lead to compute
- # the bandstructure
- energy_list = [lead.energies(k) for k in momenta]
-
- fig = pyplot.figure()
- pyplot.plot(momenta, energy_list)
- pyplot.xlabel("momentum [in units of (lattice constant)^-1]",
- fontsize=latex.mpl_label_size)
- pyplot.ylabel("energy [in units of t]",
- fontsize=latex.mpl_label_size)
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("3-band_structure_result.pdf")
- fig.savefig("3-band_structure_result.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def main():
- lead = make_lead().finalized()
-
- # list of momenta at which the bands should be computed
- momenta = [-pi + 0.02 * pi * i for i in xrange(101)]
-
- plot_bandstructure(lead, momenta)
-
-
-# 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/images/3-band_structure.py.diff b/doc/source/images/3-band_structure.py.diff
new file mode 100644
index 00000000..0ca2e45d
--- /dev/null
+++ b/doc/source/images/3-band_structure.py.diff
@@ -0,0 +1,35 @@
+--- original
++++ modified
+@@ -12,6 +12,7 @@
+
+ # For plotting
+ from matplotlib import pyplot
++import latex, html
+
+
+ def make_lead(a=1, t=1.0, W=10):
+@@ -39,11 +40,20 @@
+ # the bandstructure
+ energy_list = [lead.energies(k) for k in momenta]
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(momenta, energy_list)
+- pyplot.xlabel("momentum [in units of (lattice constant)^-1]")
+- pyplot.ylabel("energy [in units of t]")
+- pyplot.show()
++ pyplot.xlabel("momentum [in units of (lattice constant)^-1]",
++ fontsize=latex.mpl_label_size)
++ pyplot.ylabel("energy [in units of t]", fontsize=latex.mpl_label_size)
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("3-band_structure_result.pdf")
++ fig.savefig("3-band_structure_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def main():
diff --git a/doc/source/images/3-closed_system.py b/doc/source/images/3-closed_system.py
deleted file mode 100644
index 33a99297..00000000
--- a/doc/source/images/3-closed_system.py
+++ /dev/null
@@ -1,111 +0,0 @@
-# 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.
-
-
-from cmath import exp
-import kwant
-
-# For eigenvalue computation
-import scipy.linalg as la
-
-# For plotting
-from matplotlib import pyplot
-
-import latex, html
-
-
-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).
-
- lat = kwant.lattice.Square(a)
-
- sys = 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):
- # The magnetic field is controlled by the global variable B
- y = site1.pos[1]
- return - t * exp(-1j * B * y)
-
- sys[lat.shape(circle, (0, 0))] = 4 * t
- # hoppings in x-direction
- sys[sys.possible_hoppings((1, 0), lat, lat)] = hopx
- # hoppings in y-directions
- sys[sys.possible_hoppings((0, 1), lat, lat)] = - t
-
- # It's a closed system for a change, so no leads
- return sys
-
-
-def plot_spectrum(sys, Bfields):
- # global variable B controls the magnetic field
- global B
-
- # In the following, we compute the spectrum of the quantum dot
- # using dense matrix methods. This works in this toy example, as
- # the system is tiny. In a real example, one would want to use
- # sparse matrix methods
-
- energies = []
- for Bfield in Bfields:
- B = Bfield
-
- # Obtain the Hamiltonian as a dense matrix
- ham_mat = sys.hamiltonian_submatrix()
-
- ev = la.eigh(ham_mat, eigvals_only=True)
-
- # we only plot the 15 lowest eigenvalues
- energies.append(ev[:15])
-
- fig = pyplot.figure()
- pyplot.plot(Bfields, energies)
- pyplot.xlabel("magnetic field [some arbitrary units]",
- fontsize=latex.mpl_label_size)
- pyplot.ylabel("energy [in units of t]",
- fontsize=latex.mpl_label_size)
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("3-closed_system_result.pdf")
- fig.savefig("3-closed_system_result.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def main():
- sys = make_system()
-
- # Check that the system looks as intended.
- kwant.plot(sys, filename="3-closed_system_sys.pdf",
- width=latex.figwidth_pt)
- kwant.plot(sys, filename="3-closed_system_sys.png",
- width=html.figwidth_px)
-
- # Finalize the system.
- sys = sys.finalized()
-
- # We should observe energy levels that flow towards Landau
- # level energies with increasing magnetic field
- plot_spectrum(sys, [iB * 0.002 for iB in xrange(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/images/3-closed_system.py.diff b/doc/source/images/3-closed_system.py.diff
new file mode 100644
index 00000000..0bb1a9c1
--- /dev/null
+++ b/doc/source/images/3-closed_system.py.diff
@@ -0,0 +1,46 @@
+--- original
++++ modified
+@@ -17,6 +17,7 @@
+
+ # For plotting
+ from matplotlib import pyplot
++import latex, html
+
+
+ def make_system(a=1, t=1.0, r=10):
+@@ -69,18 +70,30 @@
+ # we only plot the 15 lowest eigenvalues
+ energies.append(ev[:15])
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(Bfields, energies)
+- pyplot.xlabel("magnetic field [some arbitrary units]")
+- pyplot.ylabel("energy [in units of t]")
+- pyplot.show()
++ pyplot.xlabel("magnetic field [some arbitrary units]",
++ fontsize=latex.mpl_label_size)
++ pyplot.ylabel("energy [in units of t]", fontsize=latex.mpl_label_size)
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("3-closed_system_result.pdf")
++ fig.savefig("3-closed_system_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def main():
+ sys = make_system()
+
+ # Check that the system looks as intended.
+- kwant.plot(sys)
++ kwant.plot(sys, filename="3-closed_system_sys.pdf",
++ width=latex.figwidth_pt)
++ kwant.plot(sys, filename="3-closed_system_sys.png",
++ width=html.figwidth_px)
+
+ # Finalize the system.
+ sys = sys.finalized()
diff --git a/doc/source/images/4-graphene.py b/doc/source/images/4-graphene.py
deleted file mode 100644
index 7eabb367..00000000
--- a/doc/source/images/4-graphene.py
+++ /dev/null
@@ -1,193 +0,0 @@
-# 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
-
-from __future__ import division # so that 1/2 == 0.5, and not 0
-from math import pi, sqrt, tanh
-
-import kwant
-
-# For computing eigenvalues
-import scipy.sparse.linalg as sla
-
-# For plotting
-from matplotlib import pyplot
-
-import latex, html
-
-# Define the graphene lattice
-sin_30, cos_30 = (1 / 2, sqrt(3) / 2)
-graphene = kwant.make_lattice([(1, 0), (sin_30, cos_30)],
- [(0, 0), (0, 1 / sqrt(3))])
-a, b = graphene.sublattices
-
-
-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
-
- sys = 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)
-
- sys[graphene.shape(circle, (0, 0))] = potential
-
- # specify the hoppings of the graphene lattice in the
- # format expected by possibe_hoppings()
- hoppings = (((0, 0), b, a), ((0, 1), b, a), ((-1, 1), b, a))
- for hopping in hoppings:
- sys[sys.possible_hoppings(*hopping)] = - 1
-
- # Modify the scattering region
- del sys[a(0, 0)]
- sys[a(-2, 1), b(2, 2)] = -1
-
- #### Define the leads. ####
- # left lead
- sym0 = kwant.TranslationalSymmetry([graphene.vec((-1, 0))])
-
- def lead0_shape(pos):
- x, y = pos
- return (-1 < x < 1) and (-0.4 * r < y < 0.4 * r)
-
- lead0 = kwant.Builder(sym0)
- lead0[graphene.shape(lead0_shape, (0, 0))] = - pot
- for hopping in hoppings:
- lead0[lead0.possible_hoppings(*hopping)] = - 1
-
- # The second lead, going to the top right
- sym1 = kwant.TranslationalSymmetry([graphene.vec((0, 1))])
-
- def lead1_shape(pos):
- x, y = pos
- u = x * sin_30 + y * cos_30
- v = y * sin_30 - x * cos_30
- return (-1 < u < 1) and (-0.4 * r < v < 0.4 * r)
-
- lead1 = kwant.Builder(sym1)
- lead1[graphene.shape(lead1_shape, (0, 0))] = pot
- for hopping in hoppings:
- lead1[lead1.possible_hoppings(*hopping)] = - 1
-
- return sys, [lead0, lead1]
-
-
-def compute_evs(sys):
- # Compute some eigenvalues of the closed system
- sparse_mat = sys.hamiltonian_submatrix(sparse=True)
-
- try:
- # This requires scipy version >= 0.9.0
- # Failure (i.e. insufficient scipy version) is not critical
- # for the remainder of the tutorial, hence the try-block
- evs = sla.eigs(sparse_mat, 2)[0]
- print evs
- except:
- pass
-
-
-def plot_conductance(sys, energies):
- # Compute transmission as a function of energy
- data = []
- for energy in energies:
- smatrix = kwant.solve(sys, energy)
- data.append(smatrix.transmission(0, 1))
-
- fig = pyplot.figure()
- pyplot.plot(energies, data)
- pyplot.xlabel("energy [in units of t]",
- fontsize=latex.mpl_label_size)
- pyplot.ylabel("conductance [in units of e^2/h]",
- fontsize=latex.mpl_label_size)
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("4-graphene_result.pdf")
- fig.savefig("4-graphene_result.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def plot_bandstructure(flead, momenta):
- # Use the method ``energies`` of the finalized lead to compute
- # the bandstructure
- energy_list = [flead.energies(k) for k in momenta]
-
- fig = pyplot.figure()
- pyplot.plot(momenta, energy_list)
- pyplot.xlabel("momentum [in untis of (lattice constant)^-1]",
- fontsize=latex.mpl_label_size)
- pyplot.ylabel("energy [in units of t]",
- fontsize=latex.mpl_label_size)
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("4-graphene_bs.pdf")
- fig.savefig("4-graphene_bs.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def main():
- pot = 0.1
- sys, 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:
- plotter_symbols = {a: kwant.plotter.Circle(r=0.3),
- b: kwant.plotter.Circle(r=0.3,
- fcol=kwant.plotter.white,
- lcol=kwant.plotter.black)}
-
- # Plot the closed system without leads.
- kwant.plot(sys, symbols=plotter_symbols,
- filename="4-graphene_sys1.pdf", width=latex.figwidth_pt)
- kwant.plot(sys, symbols=plotter_symbols,
- filename="4-graphene_sys1.png", width=html.figwidth_px)
-
- # Compute some eigenvalues.
- compute_evs(sys.finalized())
-
- # Attach the leads to the system.
- for lead in leads:
- sys.attach_lead(lead)
-
- # Then, plot the system with leads.
- kwant.plot(sys, symbols=plotter_symbols,
- filename="4-graphene_sys2.pdf", width=latex.figwidth_pt)
- kwant.plot(sys, symbols=plotter_symbols,
- filename="4-graphene_sys2.png", width=html.figwidth_px)
-
- # Finalize the system.
- sys = sys.finalized()
-
- # Compute the band structure of lead 0.
- momenta = [-pi + 0.02 * pi * i for i in xrange(101)]
- plot_bandstructure(sys.leads[0], momenta)
-
- # Plot conductance.
- energies = [-2 * pot + 4. / 50. * pot * i for i in xrange(51)]
- plot_conductance(sys, 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/images/4-graphene.py.diff b/doc/source/images/4-graphene.py.diff
new file mode 100644
index 00000000..b2e31cb2
--- /dev/null
+++ b/doc/source/images/4-graphene.py.diff
@@ -0,0 +1,97 @@
+--- original
++++ modified
+@@ -17,6 +17,7 @@
+
+ # For plotting
+ from matplotlib import pyplot
++import latex, html
+
+
+ # Define the graphene lattice
+@@ -63,7 +64,7 @@
+ return (-1 < x < 1) and (-0.4 * r < y < 0.4 * r)
+
+ lead0 = kwant.Builder(sym0)
+- lead0[graphene.shape(lead0_shape, (0, 0))] = -pot
++ lead0[graphene.shape(lead0_shape, (0, 0))] = - pot
+ for hopping in hoppings:
+ lead0[lead0.possible_hoppings(*hopping)] = -1
+
+@@ -105,11 +106,21 @@
+ smatrix = kwant.solve(sys, energy)
+ data.append(smatrix.transmission(0, 1))
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(energies, data)
+- pyplot.xlabel("energy [in units of t]")
+- pyplot.ylabel("conductance [in units of e^2/h]")
+- pyplot.show()
++ pyplot.xlabel("energy [in units of t]",
++ fontsize=latex.mpl_label_size)
++ pyplot.ylabel("conductance [in units of e^2/h]",
++ fontsize=latex.mpl_label_size)
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("4-graphene_result.pdf")
++ fig.savefig("4-graphene_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def plot_bandstructure(flead, momenta):
+@@ -117,11 +128,21 @@
+ # the bandstructure
+ energy_list = [flead.energies(k) for k in momenta]
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(momenta, energy_list)
+- pyplot.xlabel("momentum [in untis of (lattice constant)^-1]")
+- pyplot.ylabel("energy [in units of t]")
+- pyplot.show()
++ pyplot.xlabel("momentum [in untis of (lattice constant)^-1]",
++ fontsize=latex.mpl_label_size)
++ pyplot.ylabel("energy [in units of t]",
++ fontsize=latex.mpl_label_size)
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("4-graphene_bs.pdf")
++ fig.savefig("4-graphene_bs.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def main():
+@@ -136,17 +157,20 @@
+ lcol=kwant.plotter.black)}
+
+ # Plot the closed system without leads.
+- kwant.plot(sys, symbols=plotter_symbols)
+-
+- # Compute some eigenvalues.
+- compute_evs(sys.finalized())
++ kwant.plot(sys, symbols=plotter_symbols,
++ filename="4-graphene_sys1.pdf", width=latex.figwidth_pt)
++ kwant.plot(sys, symbols=plotter_symbols,
++ filename="4-graphene_sys1.png", width=html.figwidth_px)
+
+ # Attach the leads to the system.
+ for lead in leads:
+ sys.attach_lead(lead)
+
+ # Then, plot the system with leads.
+- kwant.plot(sys, symbols=plotter_symbols)
++ kwant.plot(sys, symbols=plotter_symbols,
++ filename="4-graphene_sys2.pdf", width=latex.figwidth_pt)
++ kwant.plot(sys, symbols=plotter_symbols,
++ filename="4-graphene_sys2.png", width=html.figwidth_px)
+
+ # Finalize the system.
+ sys = sys.finalized()
diff --git a/doc/source/images/5-superconductor_band_structure.py b/doc/source/images/5-superconductor_band_structure.py
deleted file mode 100644
index d2bc3276..00000000
--- a/doc/source/images/5-superconductor_band_structure.py
+++ /dev/null
@@ -1,81 +0,0 @@
-# Physics background
-# ------------------
-# band structure of a superconducting quantum wire in tight-binding
-# approximation
-#
-# Kwant features highlighted
-# --------------------------
-# - Repetition of previously used concepts (band structure calculations,
-# matrices as values in Builder).
-# - Main motivation is to contrast to the implementation of superconductivity
-# in tutorial5b.py
-
-import kwant
-
-import numpy as np
-from math import pi
-
-# For plotting
-from matplotlib import pyplot
-
-import latex, html
-
-tau_x = np.array([[0, 1], [1, 0]])
-tau_z = np.array([[1, 0], [0, -1]])
-
-
-def make_lead(a=1, t=1.0, mu=0.7, Delta=0.1, W=10):
- # Start with an empty lead with a single square lattice
- lat = kwant.lattice.Square(a)
-
- sym_lead = kwant.TranslationalSymmetry([lat.vec((-1, 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 xrange(W):
- lead[lat(0, j)] = (4 * t - mu) * tau_z + Delta * tau_x
-
- if j > 0:
- lead[lat(0, j), lat(0, j - 1)] = - t * tau_z
-
- lead[lat(1, j), lat(0, j)] = - t * tau_z
-
- return lead
-
-
-def plot_bandstructure(lead, momenta):
- # Use the method ``energies`` of the finalized lead to compute
- # the bandstructure
- energy_list = [lead.energies(k) for k in momenta]
-
- fig = pyplot.figure()
- pyplot.plot(momenta, energy_list)
- pyplot.xlabel("momentum [in untis of (lattice constant)^-1]")
- pyplot.ylabel("energy [in units of t]")
- pyplot.ylim([-0.8, 0.8])
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("5-superconductor_band_structure_result.pdf")
- fig.savefig("5-superconductor_band_structure_result.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def main():
- # Make system and finalize it right away.
- lead = make_lead().finalized()
-
- # list of momenta at which the bands should be computed
- momenta = np.linspace(-1.5, 1.5, 201)
-
- plot_bandstructure(lead, momenta)
-
-
-# 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/images/5-superconductor_band_structure.py.diff b/doc/source/images/5-superconductor_band_structure.py.diff
new file mode 100644
index 00000000..8b8d6e5a
--- /dev/null
+++ b/doc/source/images/5-superconductor_band_structure.py.diff
@@ -0,0 +1,33 @@
+--- original
++++ modified
+@@ -17,6 +17,7 @@
+
+ # For plotting
+ from matplotlib import pyplot
++import latex, html
+
+ tau_x = np.array([[0, 1], [1, 0]])
+ tau_z = np.array([[1, 0], [0, -1]])
+@@ -47,12 +48,20 @@
+ # the bandstructure
+ energy_list = [lead.energies(k) for k in momenta]
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(momenta, energy_list)
+ pyplot.xlabel("momentum [in untis of (lattice constant)^-1]")
+ pyplot.ylabel("energy [in units of t]")
+ pyplot.ylim([-0.8, 0.8])
+- pyplot.show()
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("5-superconductor_band_structure_result.pdf")
++ fig.savefig("5-superconductor_band_structure_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def main():
diff --git a/doc/source/images/5-superconductor_transport.py b/doc/source/images/5-superconductor_transport.py
deleted file mode 100644
index b9a90a61..00000000
--- a/doc/source/images/5-superconductor_transport.py
+++ /dev/null
@@ -1,126 +0,0 @@
-# Physics background
-# ------------------
-# - conductance of a NS-junction (Andreev reflection, superconducting gap)
-#
-# Kwant features highlighted
-# --------------------------
-# - Implementing electron and hole ("orbital") degrees of freedom
-# using different lattices
-
-import kwant
-
-# For plotting
-from matplotlib import pyplot
-
-import latex, html
-
-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 and two square lattices,
- # corresponding to electron and hole degree of freedom
- lat_e = kwant.lattice.Square(a)
- lat_h = kwant.lattice.Square(a)
-
- sys = kwant.Builder()
-
- #### Define the scattering region. ####
- sys[(lat_e(x, y) for x in range(L) for y in range(W))] = 4 * t - mu
- sys[(lat_h(x, y) for x in range(L) for y in range(W))] = mu - 4 * t
-
- # the tunnel barrier
- sys[(lat_e(x, y) for x in range(barrierpos[0], barrierpos[1])
- for y in range(W))] = 4 * t + barrier - mu
- sys[(lat_h(x, y) for x in range(barrierpos[0], barrierpos[1])
- for y in range(W))] = mu - 4 * t - barrier
-
- # hoppings in x and y-directions, for both electrons and holes
- sys[sys.possible_hoppings((1, 0), lat_e, lat_e)] = - t
- sys[sys.possible_hoppings((0, 1), lat_e, lat_e)] = - t
- sys[sys.possible_hoppings((1, 0), lat_h, lat_h)] = t
- sys[sys.possible_hoppings((0, 1), lat_h, lat_h)] = t
-
- # Superconducting order parameter enters as hopping between
- # electrons and holes
- sys[((lat_e(x, y), lat_h(x, y)) for x in range(Deltapos, L)
- for y in range(W))] = Delta
-
- #### Define the leads. ####
- # left electron lead
- sym_lead0 = kwant.TranslationalSymmetry([lat_e.vec((-1, 0))])
- lead0 = kwant.Builder(sym_lead0)
-
- lead0[(lat_e(0, j) for j in xrange(W))] = 4 * t - mu
- # hoppings in x and y-direction
- lead0[lead0.possible_hoppings((1, 0), lat_e, lat_e)] = - t
- lead0[lead0.possible_hoppings((0, 1), lat_e, lat_e)] = - t
-
- # left hole lead
- sym_lead1 = kwant.TranslationalSymmetry([lat_h.vec((-1, 0))])
- lead1 = kwant.Builder(sym_lead1)
-
- lead1[(lat_h(0, j) for j in xrange(W))] = mu - 4 * t
- # hoppings in x and y-direction
- lead1[lead1.possible_hoppings((1, 0), lat_h, lat_h)] = t
- lead1[lead1.possible_hoppings((0, 1), lat_h, lat_h)] = t
-
- # Then the lead to the right
- # this one is superconducting and thus is comprised of electrons
- # AND holes
- sym_lead2 = kwant.TranslationalSymmetry([lat_e.vec((1, 0))])
- lead2 = kwant.Builder(sym_lead2)
-
- lead2[(lat_e(0, j) for j in xrange(W))] = 4 * t - mu
- lead2[(lat_h(0, j) for j in xrange(W))] = mu - 4 * t
- # hoppings in x and y-direction
- lead2[lead2.possible_hoppings((1, 0), lat_e, lat_e)] = - t
- lead2[lead2.possible_hoppings((0, 1), lat_e, lat_e)] = - t
- lead2[lead2.possible_hoppings((1, 0), lat_h, lat_h)] = t
- lead2[lead2.possible_hoppings((0, 1), lat_h, lat_h)] = t
- lead2[((lat_e(0, j), lat_h(0, j)) for j in xrange(W))] = Delta
-
- #### Attach the leads and return the system. ####
- sys.attach_lead(lead0)
- sys.attach_lead(lead1)
- sys.attach_lead(lead2)
-
- return sys
-
-
-def plot_conductance(sys, energies):
- # Compute conductance
- data = []
- for energy in energies:
- smatrix = kwant.solve(sys, energy)
- # Conductance is N - R_ee + R_he
- data.append(smatrix.submatrix(0, 0).shape[0] -
- smatrix.transmission(0, 0) +
- smatrix.transmission(1, 0))
-
- fig = pyplot.figure()
- pyplot.plot(energies, data)
- pyplot.xlabel("energy [in units of t]")
- pyplot.ylabel("conductance [in units of e^2/h]")
- pyplot.setp(fig.get_axes()[0].get_xticklabels(),
- fontsize=latex.mpl_tick_size)
- pyplot.setp(fig.get_axes()[0].get_yticklabels(),
- fontsize=latex.mpl_tick_size)
- fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
- fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
- fig.savefig("5-superconductor_transport_result.pdf")
- fig.savefig("5-superconductor_transport_result.png",
- dpi=(html.figwidth_px/latex.mpl_width_in))
-
-
-def main():
- sys = make_system()
-
- # Finalize the system.
- sys = sys.finalized()
-
- plot_conductance(sys, energies=[0.002 * i for i in xrange(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/images/5-superconductor_transport.py.diff b/doc/source/images/5-superconductor_transport.py.diff
new file mode 100644
index 00000000..241d417d
--- /dev/null
+++ b/doc/source/images/5-superconductor_transport.py.diff
@@ -0,0 +1,40 @@
+--- original
++++ modified
+@@ -11,6 +11,7 @@
+
+ # For plotting
+ from matplotlib import pyplot
++import latex, html
+
+
+ def make_system(a=1, W=10, L=10, barrier=1.5, barrierpos=(3, 4),
+@@ -95,19 +96,24 @@
+ smatrix.transmission(0, 0) +
+ smatrix.transmission(1, 0))
+
+- pyplot.figure()
++ fig = pyplot.figure()
+ pyplot.plot(energies, data)
+ pyplot.xlabel("energy [in units of t]")
+ pyplot.ylabel("conductance [in units of e^2/h]")
+- pyplot.show()
++ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
++ fontsize=latex.mpl_tick_size)
++ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
++ fontsize=latex.mpl_tick_size)
++ fig.set_size_inches(latex.mpl_width_in, latex.mpl_width_in*3./4.)
++ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
++ fig.savefig("5-superconductor_transport_result.pdf")
++ fig.savefig("5-superconductor_transport_result.png",
++ dpi=(html.figwidth_px/latex.mpl_width_in))
+
+
+ def main():
+ sys = make_system()
+
+- # Check that the system looks as intended.
+- kwant.plot(sys)
+-
+ # Finalize the system.
+ sys = sys.finalized()
+
diff --git a/doc/source/images/generate-diffs.sh b/doc/source/images/generate-diffs.sh
new file mode 100755
index 00000000..e68cacef
--- /dev/null
+++ b/doc/source/images/generate-diffs.sh
@@ -0,0 +1,10 @@
+# !/bin/sh
+
+# This script regenerates the .diff files in this directory. It's these files
+# that are kept under vesion control instead of the scripts themselves.
+
+for f in [0-9]-*.py; do
+ # We use custom labels to suppress the time stamps which are unnecessary
+ # here and would only lead to noise in version control.
+ diff -u --label original --label modified ../../../tutorial/$f $f >$f.diff
+done
diff --git a/tutorial/3-closed_system.py b/tutorial/3-closed_system.py
index 2cb44f58..82361ebe 100644
--- a/tutorial/3-closed_system.py
+++ b/tutorial/3-closed_system.py
@@ -36,7 +36,7 @@ def make_system(a=1, t=1.0, r=10):
def hopx(site1, site2):
# The magnetic field is controlled by the global variable B
y = site1.pos[1]
- return - t * exp(-1j * B * y)
+ return -t * exp(-1j * B * y)
sys[lat.shape(circle, (0, 0))] = 4 * t
# hoppings in x-direction
diff --git a/tutorial/README b/tutorial/README
new file mode 100644
index 00000000..d77eef72
--- /dev/null
+++ b/tutorial/README
@@ -0,0 +1,14 @@
+This directory contains the example scripts of the tutorial.
+
+
+Note for kwant developers
+-------------------------
+
+Say you have modified SCRIPT.py in this directory. Make sure that the tutorial
+image generation patches still apply by deleting doc/source/images/SCRIPT.py
+and running ``make doc/source/images/SCRIPT.py`` in doc. Now examine the newly
+created doc/source/images/SCRIPT.py. If you do not like the result or the
+patch did not apply, edit doc/source/images/SCRIPT.py until you like it. You
+can run `make html` during your edits to check things. Finally, even if you
+did not edit the script, execute generate-diffs.sh in doc/source/images. If
+the patches applied cleanly the diff files will usually stay unchanged.
--
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