From 9eb71bb30d9706eff79b16c6eb4b573c91035a69 Mon Sep 17 00:00:00 2001
From: Joseph Weston <joseph@weston.cloud>
Date: Thu, 9 May 2019 13:41:40 +0200
Subject: [PATCH] add parameter declarations to the start of some tutorials
---
doc/source/tutorial/spin_potential_shape.rst | 63 ++++++++------------
doc/source/tutorial/superconductors.rst | 9 +--
2 files changed, 29 insertions(+), 43 deletions(-)
diff --git a/doc/source/tutorial/spin_potential_shape.rst b/doc/source/tutorial/spin_potential_shape.rst
index bc3b1cdc..9107f701 100644
--- a/doc/source/tutorial/spin_potential_shape.rst
+++ b/doc/source/tutorial/spin_potential_shape.rst
@@ -84,6 +84,15 @@ unit matrix):
sigma_y = tinyarray.array([[0, -1j], [1j, 0]])
sigma_z = tinyarray.array([[1, 0], [0, -1]])
+and we also define some other parameters useful for constructing our system:
+
+.. jupyter-execute::
+
+ t = 1.0
+ alpha = 0.5
+ e_z = 0.08
+ W, L = 10, 30
+
Previously, we used numbers as the values of our matrix elements.
However, `~kwant.builder.Builder` also accepts matrices as values, and
we can simply write:
@@ -91,18 +100,9 @@ we can simply write:
.. jupyter-execute::
:hide-code:
- # 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()
- t = 1.0
- alpha = 0.5
- e_z = 0.08
- W, L = 10, 30
-
-
.. jupyter-execute::
#### Define the scattering region. ####
@@ -260,22 +260,9 @@ Instead, we use a python *function* to define the onsite energies. We
define the potential profile of a quantum well as:
.. jupyter-execute::
- :hide-code:
- a = 1
- t = 1.0
W, L, L_well = 10, 30, 10
-.. jupyter-execute::
-
- # 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:
@@ -293,9 +280,15 @@ Kwant now allows us to pass a function as a value to
.. jupyter-execute::
+ a = 1
+ t = 1.0
+
def onsite(site, pot):
return 4 * t + potential(site, pot)
+ lat = kwant.lattice.square(a)
+ syst = kwant.Builder()
+
syst[(lat(x, y) for x in range(L) for y in range(W))] = onsite
syst[lat.neighbors()] = -t
@@ -429,24 +422,9 @@ that returns ``True`` whenever a point is inside the shape, and
``False`` otherwise:
.. jupyter-execute::
- :hide-code:
- a = 1
- t = 1.0
- W = 10
r1, r2 = 10, 20
-.. jupyter-execute::
-
- # 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
@@ -461,7 +439,12 @@ provided by the lattice:
.. jupyter-execute::
- # and add the corresponding lattice points using the `shape`-function
+ a = 1
+ t = 1.0
+
+ lat = kwant.lattice.square(a)
+ syst = kwant.Builder()
+
syst[lat.shape(ring, (0, r1 + 1))] = 4 * t
syst[lat.neighbors()] = -t
@@ -515,10 +498,12 @@ For the leads, we can also use the ``lat.shape``-functionality:
.. jupyter-execute::
#### Define the leads. ####
- # left lead
+ W = 10
+
sym_lead = kwant.TranslationalSymmetry((-a, 0))
lead = kwant.Builder(sym_lead)
+
def lead_shape(pos):
(x, y) = pos
return (-W / 2 < y < W / 2)
diff --git a/doc/source/tutorial/superconductors.rst b/doc/source/tutorial/superconductors.rst
index 0c1c3739..56f5a849 100644
--- a/doc/source/tutorial/superconductors.rst
+++ b/doc/source/tutorial/superconductors.rst
@@ -85,11 +85,10 @@ a superconductor on the right, and a tunnel barrier in between:
We implement the BdG Hamiltonian in Kwant using a 2x2 matrix structure
for all Hamiltonian matrix elements, as we did
-previously in the :ref:`spin example <tutorial_spinorbit>`. We declare
-the square lattice and construct the scattering region with the following:
+previously in the :ref:`spin example <tutorial_spinorbit>`.
+We start by declaring some parameters that will be used in the following code:
.. jupyter-execute::
- :hide-code:
a = 1
W, L = 10, 10
@@ -97,9 +96,11 @@ the square lattice and construct the scattering region with the following:
barrierpos = (3, 4)
mu = 0.4
Delta = 0.1
- Deltapos=4
+ Deltapos = 4
t = 1.0
+and we declare the square lattice and construct the scattering region with the following:
+
.. jupyter-execute::
# Start with an empty tight-binding system. On each site, there
--
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