From 50804c6e58b2feb42d9467a01cd4ab8ec4c1d82a Mon Sep 17 00:00:00 2001
From: Joseph Weston <joseph@weston.cloud>
Date: Fri, 26 Apr 2019 11:06:23 +0200
Subject: [PATCH] convert band structure example to jupyter-sphinx
---
doc/source/tutorial/spectrum.rst | 66 ++++++++++++++++++++++++++++----
1 file changed, 58 insertions(+), 8 deletions(-)
diff --git a/doc/source/tutorial/spectrum.rst b/doc/source/tutorial/spectrum.rst
index 734f5a1d..acd99d7f 100644
--- a/doc/source/tutorial/spectrum.rst
+++ b/doc/source/tutorial/spectrum.rst
@@ -6,7 +6,29 @@ Band structure calculations
.. seealso::
The complete source code of this example can be found in
- :download:`band_structure.py </code/download/band_structure.py>`
+ :jupyter-download:script:`band_structure`
+
+.. jupyter-kernel::
+ :id: band_structure
+
+.. jupyter-execute::
+ :hide-code:
+
+ # 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 kwant
+
+ # For plotting
+ from matplotlib import pyplot
When doing transport simulations, one also often needs to know the band
structure of the leads, i.e. the energies of the propagating plane waves in the
@@ -19,9 +41,26 @@ tight-binding wire.
Computing band structures in Kwant is easy. Just define a lead in the
usual way:
-.. literalinclude:: /code/include/band_structure.py
- :start-after: #HIDDEN_BEGIN_zxip
- :end-before: #HIDDEN_END_zxip
+.. jupyter-execute::
+
+ 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
"Usual way" means defining a translational symmetry vector, as well
as one unit cell of the lead, and the hoppings to neighboring
@@ -42,13 +81,24 @@ do something more profound with the dispersion relation these energies may be
calculated directly using `~kwant.physics.Bands`. For now we just plot the
bandstructure:
-.. literalinclude:: /code/include/band_structure.py
- :start-after: #HIDDEN_BEGIN_pejz
- :end-before: #HIDDEN_END_pejz
+.. jupyter-execute::
+
+ def main():
+ lead = make_lead().finalized()
+ kwant.plotter.bands(lead, show=False)
+ pyplot.xlabel("momentum [(lattice constant)^-1]")
+ pyplot.ylabel("energy [t]")
+ pyplot.show()
This gives the result:
-.. image:: /code/figure/band_structure_result.*
+.. jupyter-execute::
+ :hide-code:
+
+ # 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()
where we observe the cosine-like dispersion of the square lattice. Close
to ``k=0`` this agrees well with the quadratic dispersion this tight-binding
--
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