Quantum transport simulations made easy
=======================================
**Update 15 Dec 2014**: Kwant is going to be one of the main tools in a massive open online course on `topology in condensed matter <http://tiny.cc/topocm>`_. The course will start in February, sign up!
Kwant is a `free (open source) <http://git.kwant-project.org/kwant>`_ Python
package for numerical calculations on tight-binding models with a strong focus
on quantum transport. It is designed to be flexible and easy to use. Thanks to
the use of innovative algorithms, Kwant is often faster than other available
codes, even those entirely written in the low level FORTRAN and C/C++ languages.
Tight-binding models can describe a vast variety of systems and phenomena in
quantum physics. Therefore, Kwant can be used to simulate metals, graphene,
topological insulators, quantum Hall effect, superconductivity, spintronics,
molecular electronics, any combination of the above, and many other things.
Kwant does not use the traditional input files often found in scientific
software packages. Instead, one writes short programs in the powerful yet
easy-to-learn Python language. These programs define a system and calculate its
quantum properties (conductance, density of states, etc). This workflow can be
summarized as follows:
.. raw:: html
<object type="image/svg+xml" data="kwant-workflow.svgz" width="100%">kwant-workflow.svgz</object>
Kwant was designed to be easy to use: Section 2 of the `Kwant paper
<http://downloads.kwant-project.org/doc/kwant-paper.pdf>`_ contains a
line-by-line walkthrough of a program very similar to the one used to generate
the above image. That complete Python script is 26 lines long (including
comments).
Examples of Kwant usage
-----------------------
The following examples are meant to give an overview of what is possible with
Kwant. The tutorial section of `Kwant documentation <doc/1.0/>`_ and the
`Kwant paper`_ each contain several pedagogical examples with line-by-line
explanations (`zipfile of all examples
<http://downloads.kwant-project.org/examples/kwant-examples-1.0.0.zip>`_).
Graphene flake
..............
.. container:: rightside
.. raw:: html
<object type="image/svg+xml" data="graphene-edgestate.svgz" style="width: 15em;">graphene-edgestate.svgz</object>
The complete code that constructs the graphene flake shown on the right side
is::
def disk(pos):
x, y = pos
return x**2 + y**2 < 8**2
lat = kwant.lattice.honeycomb()
sys = kwant.Builder()
sys[lat.shape(disk, (0, 0))] = 0
sys[lat.neighbors()] = -1
In addition to the flake itself, the image also shows the wave function of a
low energy eigenstate. The size of each circle is proportional to the wave
function probability amplitude on that site. It can be clearly seen that the
wave function is peaked near the zigzag segments of the boundary, as `expected
<http://arxiv.org/abs/1003.4602>`_ for graphene quantum dots.
Taken from the Kwant `plotting tutorial <doc/1.0/tutorial/tutorial6.html>`_.
Quantum Hall effect
...................
.. container:: rightside
.. raw:: html
<object type="image/svg+xml" data="qhe-edgestate.svgz" style="width: 15em;">qhe-edgestate.svgz</object>
.. container:: leftside
.. raw:: html
<object type="image/svg+xml" data="qhe-plateaus.svgz" style="width: 15em;">qhe-plateaus.svgz</object>
One of the most common applications of Kwant is to calculate the conductance of
a nanoelectronic system. The plot on the left shows the conductance through a
2-d electron gas as a function of magnetic flux. The quantization of
conductance that is visible (plateaus) is the hallmark of the quantum Hall
effect. The third plateau does not develop due to a constriction in the system
that leads to backscattering. The scattering wave function from the left lead
at magnetic field strength corresponding to the middle of the third QHE plateau
is shown on the right.
Taken from example 6 of the `Kwant paper
<http://downloads.kwant-project.org/doc/kwant-paper.pdf>`_.
3-d system: Majorana states
...........................
.. container:: rightside
.. image:: quantum-wire.png
Kwant allows systems of any dimensionality, for example three-dimensional ones.
This image shows a 3-d model of a semiconducting quantum wire (gray cylinder).
The red region is a tunnel barrier, used to measure tunneling conductance, the
blue region is a superconducting electrode. In this simulated device, a
Majorana bound state appears close to the superconducting-normal interface.
Taken from an unpublished work by S. Mi, A. R. Akhmerov, and M. Wimmer.
Numerical experiment: flying qubit
..................................
.. container:: rightside
.. image:: flying-qubit.png
Numerical simulations and experimental results for a flying qubit sample made in
a GaAs/GaAlAs heterostrucutre. The Kwant simulations were performed with
particular attention to a realistic model of the confining potential seen by the
electrons. This allows for rather subtle aspects of the experiment could be
reproduced. Such "numerical experiments" can not only be used to interpret the
experimental data but also can help to design the sample geometry and in to
choose the right materials.
Taken from an unpublished work by T. Bautze et al. See Yamamoto et al., `Nature
Nanotechnology 7, 247 (2012) <http://dx.doi.org/doi:10.1038/nnano.2012.28>`_ for
details about the experiment.
Conductance of a Corbino disk in a quantum Hall regime
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.. container:: leftside
.. raw:: html
<object type="image/svg+xml" data="corbino-layout.svgz" style="width: 15em;">corbino-layout.svgz</object>
.. container:: rightside
.. image:: corbino-conductance.png
Transport properties of a Corbino disk across a quantum Hall transition. Left:
geometry of the sample consisting of a ring-shaped two-dimensional electron gas
(grey) in a perpendicular magnetic field. Right: conductance across the
transition, showing quantized conductance peaks.
Taken from I. C. Fulga, F. Hassler, A. R. Akhmerov, C. W. J. Beenakker,
`Phys. Rev. B 84, 245447 (2011)
<http://link.aps.org/doi/10.1103/PhysRevB.84.245447>`_; `arXiv:1110.4280
<http://arxiv.org/abs/1110.4280>`_.
Anton Akhmerov
authored