Commit c691d182 authored by Joseph Weston's avatar Joseph Weston
Browse files

add 2-band model example and include links in whatsnew

parent 33c7d839
--- original
+++ modified
@@ -11,6 +11,7 @@
# + 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
@@ -60,7 +61,10 @@
psi = kwant.wave_function(syst, energy=params['m'], params=params)(0)
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)
if __name__ == '__main__':
......@@ -24,9 +24,18 @@ with continuum models and for discretizing them into tight-binding models. It
aims at providing a handy interface to convert symbolic Hamiltonians into a
builder with N-D translational symmetry that can be use to calculate
tight-binding band structures or construct systems with different/lower
symmetry.
symmetry. For example in just a few lines we can construct a two-band model that exhibits
a quantum anomalous spin Hall phase:
See :doc:`../../tutorial/discretize`
.. literalinclude:: ../../tutorial/plot_qahe.py
:start-after: HIDDEN_BEGIN_model
:end-before: HIDDEN_END_model
From: :download:`QAHE example script <../../tutorial/plot_qahe.py>`
See the tutorial: :doc:`../../tutorial/discretize`
See the reference documentation: :doc:`../../reference/kwant.continuum`
Calculating charges and currents using the operator module
----------------------------------------------------------
......@@ -57,10 +66,17 @@ Quantities defined on system hoppings (e.g. currents calculated using
`~kwant.operator.current`) can be directly plotted as a streamplot over the
system using `kwant.plotter.current`. This is similar to how
`kwant.plotter.map` can be used to plot quantities defined on sites.
The example below shows edge states of a quantum anomalous Hall phase
of the two-band model shown in the `above section
<#tools-for-continuum-hamiltonians>`_:
.. literalinclude:: ../../tutorial/plot_qahe.py
:start-after: HIDDEN_BEGIN_current
:end-before: HIDDEN_END_current
See :doc:`../../tutorial/plotting`
.. image:: ../../images/plot_qahe_current.*
.. image:: ../../images/plot_qpc_current.*
From: :download:`QAHE example script <../../tutorial/plot_qahe.py>`
Scattering states with discrete symmetries and conservation laws
----------------------------------------------------------------
......
# 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 math
import matplotlib.pyplot
import kwant
# 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_spacing=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)
#HIDDEN_END_current
if __name__ == '__main__':
main()
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