Unoccupied Topological Surface State in MnBi$_2$Te$_4$

TL;DR

This paper predicts and proposes methods to observe a previously unrecognized unoccupied topological surface state in MnBi$_2$Te$_4$, expanding understanding of its electronic structure and optical properties.

Contribution

It uncovers a second unoccupied topological surface state in MnBi$_2$Te$_4$ and suggests optical techniques for its experimental detection.

Findings

Identification of a second unoccupied topological surface state at 1.6 eV above the occupied state.

Proposal of optical detection methods including Kerr effect and terahertz-sideband generation.

Prediction of observable optical phenomena linked to the unoccupied surface state.

Abstract

The unoccupied part of the band structure in the magnetic topological insulator MnBi$_2$Te$_4$ is studied by first-principles calculations. We find a second, unoccupied topological surface state with similar electronic structure to the celebrated occupied topological surface state. This state is energetically located approximate $1.6$ eV above the occupied Dirac surface state around $\Gamma$ point, which permit it to be directly observed by the two-photon angle-resolved photoemission spectroscopy. We propose a unified effective model for the occupied and unoccupied surface states. Due to the direct optical coupling between these two surface states, we further propose two optical effects to detect the unoccupied surface state. One is the polar Kerr effect in odd layer from nonvanishing ac Hall conductance $\sigma_{xy}(\omega)$, and the other is higher-order terahertz-sideband generation in even layer, where the non-vanishining Berry curvature of the unoccupied surface state is directly observed from the giant Faraday rotation of optical emission.