Linear response of the Chern insulator MnBi₂Te₄: A Wannier function approach

We calculate the topological properties and linear response of MnBi₂Te₄ thin films using recently derived expressions from a microscopic theory of polarization and magnetization. In this formalism, the linear response of a Chern insulator to an external finite-frequency electric field separates into a Kubo term associated with the finite-frequency response and with a term describing the quantum anomalous Hall effect. Using ab initio methods such as density functional theory and exponentially localized Wannier functions, we numerically compute both contributions in thin films of one, four, and five septuple layers of MnBi₂Te₄, which have been experimentally demonstrated to realize a topologically trivial insulator, axion insulator, and a Chern insulator phase, respectively. Furthermore, we examine topological signatures in these systems, such as the Chern invariants and band inversions in the band structure that typically arise from strong spin-orbit coupling.