# About

The “Python Tight Binding” (`PythTB`) code was developed and is maintained by Sinisa Coh (University of California at Riverside) and David Vanderbilt (Rutgers University) with assistance from many other individuals.

The primary location for this package is at http://www.physics.rutgers.edu/pythtb where the most up-to-date releases and information can be found.

## Motivations and capabilities

The tight binding method is an approximate approach for solving for the electronic wave functions for electrons in solids assuming a basis of localized atomic-like orbitals. We assume here that the orbitals are orthonormal, and focus on the “empirical tight binding” approach in which the Hamiltonian matrix elements are simply parametrized, as opposed to being computed ab-initio.

The `PythTB` package is intended to set up and solve tight-binding models for the electronic structure of

- 0D clusters

- 1D chains and ladders

- 2D layers (square lattice, hexagonal lattice, honeycomb lattice, etc.)

- 3D crystals

- clusters, ribbons, slabs, etc., cut from higher-dimensional crystals

- etc.

As currently written, it is not intended to handle realistic chemical interactions. So for example, the Slater-Koster forms for interactions between s, p and d orbitals are not currently coded, although the addition of such features could be considered for a future release.

The `PythTB` package includes capabilities for

- computing electron eigenvalues and eigenvectors at selected k-points or on a mesh of k-points

- generating band-structure plots

- generating density-of-states plots

It can also calculate Berry phases, connections and curvatures in ways that are useful for calculations of

- adiabatic charge transport

- electric polarization

- anomalous Hall conductivity

- topological indices

- etc.

Finally, it provides tools for setting up more complicated tight-binding models, e.g., by “cutting” a cluster, ribbon, or slab out of a higher-dimensional crystal, and for visualizing the connectivity of a tight-binding model once it has been constructed. You can get an idea of the capabilities of the package by browsing the PythTB examples.

The code is intended for pedagogical as well as research purposes. For example, it should be suitable for use in an undergraduate- or graduate-level solid-state physics course as a tool for illustrating the calculation of electronic band structructures, and it is simple enough that it can be considered for use in homework sets or special projects in such a course.

The `PythTB` package was written in Python for several reasons, including

- The ease of learning and using Python

- The wide availability of Python in the community

- The flexibility with which Python can be interfaced with graphics and visualization modules

- In general, the easy extensibility of Python programs

On the other hand, please note that Python is not a computationally efficient platform when applied to large systems requiring heavy computation.

## Getting started

The best way to explore the capabilities of `PythTB` and to get started in using it is to read through the installation instructions and PythTB examples.

If you are unfamiliar with Python or are not sure whether Python and the needed Python modules are installed on your system, see our python introduction and installation instructions.

Note that the `PythTB` code is freely distributed under the terms of the `GNU GPL public license`. You may use it for your own research and educational purposes, or pass it on to others for similar use. However, the code is not guaranteed to be bug-free, and we do not promise active support for the package.

## Wannier90 interface

Starting with Version 1.7, `PythTB` also provides an interface to the Wannier90 code, which can be used to take the output of a first-principles density-functional calculation and construct from it a tight-binding model, in the basis of Wannier functions, that accurately reproduces the first-principles bandstructure. See usage.

## History

This code package had its origins in a simpler package that was developed for use in a special-topics course on “Berry Phases in Solid State Physics” offered by D. Vanderbilt in Fall 2010 at Rutgers University. The students were asked to use the code as provided, or to make extensions on their own as needed, in order to compute properties of simple systems, such as a 2D honeycomb model of graphene, in the tight-binding (TB) approximation.

From the beginning, Sinisa Coh, who was a PhD student with Vanderbilt at the time, has been the primary developer of the package. However, many other individuals made contributions to this code, including Wenshuo Liu, Victor Alexandrov, Tahir Yusufaly, and Maryam Taherinejad.

## Feedback

Please send comments or suggestions for improvement to these email addresses.

## Acknowledgments and Disclaimer

This Web page is based in part upon work supported by the US National Science Foundation under Grants DMR-1005838, DMR-1408838, DMR-1954856, and DMR-2421895. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.