Berlin 2018 – wissenschaftliches Programm
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HL: Fachverband Halbleiterphysik
HL 7: Topological insulators I (joint session HL/TT)
HL 7.7: Vortrag
Montag, 12. März 2018, 11:00–11:15, A 151
Microscopic theory of the surface anomalous Hall conductivity — •Tomáš Rauch1, Thomas Olsen2, David Vanderbilt3, and Ivo Souza1,4 — 1Centro de Física de Materiales, San Sebastián, Spain — 2Technical University of Denmark, Kongens Lyngby, Denmark — 3Rutgers University, Piscataway, New Jersey, USA — 4Ikerbasque Foundation, Bilbao, Spain
The dimensionless axion coupling θ describes the isotropic part of the linear magnetoelectric tensor. In a bulk crystal θ is only defined modulo 2 π, and only its space-time gradients enter Maxwell’s equations. At surfaces, the spatial gradient of θ gives rise to a surface anomalous Hall conductivity (AHC). In this work, we derive a microscopic expression for the AHC of an insulating surface. We find that in general it comprises not only a geometric contribution that is a property of the occupied states, but also a non-geometric “cross-gap” term that is absent from the expression for the intrinsic AHC of a free-standing film or slab. By constructing tight-binding models in a slab geometry, we numerically test our analytical results and explore the connection between the surface AHC and the bulk axion coupling. In particular, we illustrate how different insulating surfaces of the same bulk crystal can have AHCs that differ by an integer multiple of e2/h, and that this difference resides in the geometric term alone.