A Programmable k$\cdot$p Hamiltonian Method and Application to Magnetic Topological Insulator MnBi$_2$Te$_4$
Guohui Zhan1†, Minji Shi1†, Zhilong Yang1, and Haijun Zhang1,2*
1National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China 2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
Abstract：In the band theory, first-principles calculations, the tight-binding method and the effective $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ model are usually employed to investigate electronic structures of condensed matters. The effective $\boldsymbol{k}$$\cdot$$\boldsymbol{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 $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ model and first-principles calculations to explore topological materials. However, the traditional method to derive the $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonian is complicated and time-consuming by hand. We independently developed a programmable algorithm to construct effective $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonians for condensed matters. Symmetries and orbitals are used as the input information to produce the one-/two-/three-dimensional $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonian in our method, and the open-source code can be directly downloaded online. At last, we also demonstrated the application to MnBi$_2$Te$_4$-family magnetic topological materials.
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2021, Vol. 38 
