A programmable $k\cdot p$ Hamiltonian method and application to magnetic topological insulator MnBi$_2$Te$_4$

TL;DR

This paper introduces a programmable algorithm for efficiently constructing effective $k ext{ extperiodcentered}p$ Hamiltonians, combining symmetry and orbital information, with an application to magnetic topological insulator MnBi$_2$Te$_4$.

Contribution

The authors develop an open-source, programmable method to derive $k ext{ extperiodcentered}p$ Hamiltonians, simplifying and accelerating the process compared to traditional manual derivations.

Findings

The method successfully constructs $k ext{ extperiodcentered}p$ Hamiltonians for various dimensions.

Application to MnBi$_2$Te$_4$ demonstrates the method's effectiveness in magnetic topological materials.

Open-source code is available for broad use in the community.

Abstract

In the band theory, first-principles calculations, the tight-binding method and the effective $k\cdot p$ model are usually employed to investigate the electronic structure of condensed matters. The effective $k\cdot p$ model has a compact form with a clear physical picture, and first-principles calculations can give more accurate results. Nowadays, it has been widely recognized to combine the $k\cdot p$ model and first-principles calculations to explore topological materials. However, the traditional method to derive the $k\cdot p$ Hamiltonian is complicated and time-consuming by hand. In this work, we independently develop a programmable algorithm to construct effective $k\cdot p$ Hamiltonians. Symmetries and orbitals are used as the input information to produce the one-/two-/three-dimension $k\cdot p$ Hamiltonian in our method, and the open-source code can be directly downloaded online. At last, we also demonstrate the application to MnBi$_2$Te$_4$-family magnetic topological materials.