Unoccupied topological surface state in MnBi2Te4

The unoccupied part of the band structure in the magnetic topological insulator MnBi2Te4 is studied by first-principles calculations. We propose a possible second, unoccupied topological surface state with a similar electronic structure to the celebrated occupied topological surface state. The conventional density functional theory method employed here may not describe excited state properties precisely, and therefore the calculations for the current study can be considered as model simulations. This unoccupied topological surface state is energetically located approximate 1.5 eV above the occupied massive Dirac surface state around the Gamma point, which permits it to be directly observed by 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 if it exists. One is the polar Kerr effect in odd layers from nonvanishing ac Hall conductance sigma(xy)(omega), and the other is higher-order terahertz-sideband generation in even layers, where the nonvanishing Berry curvature of the unoccupied surface state is directly observed from the giant Faraday rotation of optical emission.