Magneto-electric response and Quantum Anomalous Hall Effect in Topological Antiferromagnets

I will discuss the magneto-electric and transport properties of thin films formed from bulk normal and antiferromagnetic topological insulators. In the thick film limit, both systems have the quantized magneto-electric response properties (QTME) that are characteristic of topological insulators. In non-magnetic case, thin films with surface magnetism exhibit a quantized anomalous Hall effect when the magnetizations on the top and bottom surfaces are parallel, and a QTME response when the magnetizations have opposite orientations and the films are sufficiently thick. I will present a unified picture [1] of both effects that associates finite thickness corrections to the QTME with non-locality in the side-wall current response function, emphasizing that the side-wall response is non-zero only near the surface. In the magnetic case, the anomalous Hall effect vanishes when the product of time-reversal and inversion is a good quantum number [2,3], and the magneto-electric response then has both surface and bulk contributions that are quantized only when summed [4]. Quantum anomalous Hall effects occur in many configurations of magnetic topological insulator thin films [5], including in some collinear configurations in which the total spin magnetization vanishes [6].