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.
PythTB package is intended to set up and solve tight-binding
models for the electronic structure of
1D chains and ladders
2D layers (square lattice, hexagonal lattice, honeycomb lattice, etc.)
clusters, ribbons, slabs, etc., cut from higher-dimensional crystals
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.
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
anomalous Hall conductivity
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.
PythTB package was written in Python for several reasons,
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.
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
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.
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.
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.
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-10-05838 and DMR-14-08838. 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.