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2. Tutorial: learning Kwant through examples
¶
2.1. Introduction
Quantum transport
The Python programming language
Kwant
2.2. First steps: setting up a simple system and computing conductance
Discretization of a Schrödinger Hamiltonian
Transport through a quantum wire
Building the same system with less code
2.3. More interesting systems: spin, potential, shape
Matrix structure of on-site and hopping elements
Spatially dependent values through functions
Nontrivial shapes
2.4. Beyond transport: Band structure and closed systems
Band structure calculations
Closed systems
2.5. Beyond square lattices: graphene
2.6. Superconductors: orbital degrees of freedom, conservation laws and symmetries
2.7. Computing local quantities: densities and currents
Introduction
Local densities
Local currents
Spatially varying operators
Defining operators over parts of a system
Density of states in a circle
Current flowing through a cut
Advanced Topics
Using
bind
for speed
2.8. Plotting Kwant systems and data in various styles
2D example: graphene quantum dot
3D example: zincblende structure
2.9. Calculating spectral density with the kernel polynomial method
Introduction
Calculating the density of states
Increasing the accuracy of the approximation
Calculating the spectral density of an operator
Advanced topics
Custom distributions for random vectors
Reproducible calculations
Defining operators as sesquilinear maps
2.10. Discretizing continuous Hamiltonians
Introduction
Discretizing by hand
Using
discretize
to obtain a template
Building a Kwant system from the template
Models with more structure: Bernevig-Hughes-Zhang
Limitations of discretization
Advanced topics
2.11. Frequently asked questions
What is a system, and what is a builder?
What is a site?
What is a hopping?
What is a site family, and what is a tag?
What is a lattice?
When plotting, how to color the different sublattices differently?
How to create many similar hoppings in one go?
How to set the hoppings between adjacent sites?
How to make a hole in a system?
How to access a system’s sites?
How to use different lattices for the scattering region and a lead?
How to cut a finite system out of a system with translational symmetries?
How does Kwant order the propagating modes of a lead?
How does Kwant order scattering states?
How does Kwant order components of an individual wavefunction?
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