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

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.

References in corpus (21)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Magnetic-field-induced quantized anomalous Hall effect in intrinsic magnetic topological insulator MnBi${}_2$Te${}_4$
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Prediction and observation of the first antiferromagnetic topological insulator
• Intrinsic magnetic topological insulators in van der Waals layered MnBi${}_2$Te${}_4$-family materials
• Model Hamiltonian for Topological Insulators
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator
• Hexagonal Warping Effects in the Surface States of Topological Insulator Bi${}_2$Te${}_3$
• Experimental realization of an intrinsic magnetic topological insulator
• Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet $\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$ films
• Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes
• Variety of magnetic topological phases in the (MnBi${}_2$Te${}_4$)(Bi${}_2$Te${}_3$)${}_m$ family
• Topological insulators from the Perspective of first-principles calculations
• Large dynamical axion field in topological antiferromagnetic insulator Mn${}_2$Bi${}_2$Te${}_5$
• Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation
• Dynamical axion state with hidden pseudospin Chern numbers in MnBi${}_2$Te${}_4$-based heterostructures

Cited by in corpus (2)

• Floquet engineering of magnetic topological insulator MnBi${}_2$Te${}_4$ films
• MagneticKP: A package for quickly constructing $\mathbf{k}\cdot \mathbf{p}$ models of magnetic and non-magnetic crystals