anjishnubose / tightbindingtoolkit.jl

Tools for general Tight Binding systems

TightBindingToolkit

TightBindingToolkit.jl is a Julia package meant for constructing, and obtaining useful properties of generic tight-binding models. It supports any lattice structure, with any user-defined bonds on that lattice. It also has support for any spin of the particle hopping on the lattice.

Install

In the Julia REPL, Push "]" to enter the package mode.

add TightBindingToolkit

Or equivalently

using Pkg
Pkg.add("TightBindingToolkit")

Features

Currently supported :

• Custom Unit Cell Construction. (v1.3) : now also supports construction in dimensions upto d=3. Can change primitives, or expand unit cell on the go.

  Honeycomb Model with 1st, 2nd and 3rd neighbour hoppings.

• Corresponding Brillouin Zone Construction. (v1.3) : now also supports construction in dimensions upto d=3.
• Hamiltonian, given a Unit Cell and a Brillouin Zone. (v1.3) : now also support BdG Hamiltonians.
• Diagonalizing the Hamiltonian in momentum space to get band structures and wavefunctions.

  Band structure for a triangular lattice with 1st, 2nd and 3rd neighbour hopping.

• Density of State

  Density of state of graphene.

• Filling the model at given chemical potential, and calculating gaps. (v1.3) : also supported for BdG systems.

  Band structure of the Kitaev Chain in 1-d.

• Fermi surfaces of systems

  Fermi surface for a triangular lattice with 1st, 2nd and 3rd neighbour hopping.

• Getting correlation functionsin momentum space and real space. (v1.3) : also supported for BdG systems.
• Getting Berry curvature and Chern numbers. Also workjs for topological superconductors.

  Chern numbers in a spin-ful Haldane model as a function of t2.

• Getting magnetic susceptibility in any direction, at any momentum, and energy.

  imaginary part of zero-energy susceptibility for a triangular lattice with 1st, 2nd and 3rd neighbour hopping.

• Real-sapce lattice construction with arbitrary boundary condition. (v2.1)

Documentation

For more details, please see Documentation

tightbindingtoolkit.jl's Issues

Kubo Calculation

1. Add formula to compute Hall conductance for partial filling. Ideally we would also add the explicit Berry curvature calculation that computes only filled non-Abelian Berry curvature.
2. Integrate IsBandGapped() into the Chern number calculation to prevent calculating Chern number separately for degenerate bands.

Proposed Plot Changes

Things We'd Like to add to the Plotting

1. keyword arguments to turn off legends
2. keyword arguments to change band structure colors

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