A Programmable k · p Hamiltonian Method and Application to Magnetic Topological Insulator MnBi₂Te₄

Abstract

In the band theory, first-principles calculations, the tight-binding method and the effective k · p model are usually employed to investigate electronic structures of condensed matters. The effective k · 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 · p model and first-principles calculations to explore topological materials. However, the traditional method to derive the k · p Hamiltonian is complicated and time-consuming by hand. We independently developed a programmable algorithm to construct effective k · p Hamiltonians for condensed matters. Symmetries and orbitals are used as the input information to produce the one-/two-/three-dimensional k · p Hamiltonian in our method, and the open-source code can be directly downloaded online. At last, we also demonstrated the application to MnBi2Te4-family magnetic topological materials.

MagneticKP: A package for quickly constructing $\boldsymbol{k}\cdot\boldsymbol{p}$ models of magnetic and non-magnetic crystals

“…In practice, a k•p model is usually constructed from symmetry constraint. The input information include the symmetry group of at the expansion point K and the symmetry information of the target band states at K. Depending on the needs, the output model is expanded to a specified cutoff power of k. At present, there already exist a few packages, including kdotp-symmetry [20], Qsymm [21], kdotp-generator (based on kdotpsymmetry) [22] and Model-Hamiltonian [23], which can construct k • p Hamiltonians. All these packages are written in Python and use a similar algorithm, namely, the direct-product decomposition algorithm (DDA).…”