Python Tight Binding (PythTB)

PythTB is a software package providing a Python implementation of the tight-binding approximation. It can be used to construct and solve tight-binding models of the electronic structure of systems of arbitrary dimensionality (crystals, slabs, ribbons, clusters, etc.), and is rich with features for computing Berry phases and related properties.

• About
• Installation
• Examples
• Formalism
• Usage
• Resources

Quick installation

Type in terminal:

pip install pythtb --upgrade

or if you need more assistance follow these instructions.

Quick example

This is a simple example showing how to define graphene tight-binding model with first neighbour hopping only. Below is the source code and plot of the resulting band structure. Here you can find more examples.

from pythtb import * # lattice vectors and orbital positions lat=[[1.0, 0.0], [0.5, np.sqrt(3.0)/2.0]] orb=[[1./3., 1./3.], [2./3., 2./3.]] # two-dimensional tight-binding model gra=tb_model(2, 2, lat, orb) # define hopping between orbitals gra.set_hop(-1.0, 0, 1, [ 0, 0]) gra.set_hop(-1.0, 1, 0, [ 1, 0]) gra.set_hop(-1.0, 1, 0, [ 0, 1]) # solve model on a path in k-space k=[[0.0, 0.0],[1./3., 2./3.],[0.5,0.5]] (k_vec,k_dist,k_node)=gra.k_path(k, 100) evals=gra.solve_all(k_vec) # plot bandstructure import matplotlib.pyplot as plt fig, ax = plt.subplots() ax.plot(k_dist,evals[0,:]) ax.plot(k_dist,evals[1,:]) ax.set_xticks(k_node) ax.set_xticklabels(["$\Gamma$","K","M"]) ax.set_xlim(k_node[0],k_node[-1]) fig.savefig("band.png")