Theory of topologically induced properties of surfaces and interfaces

I will discuss several examples of systems in which the bulk topology of the material plays a central role in determining the properties of surfaces or interfaces. First I will review our recent proposal for topological switching in antiferroelectrics [1], in which we computationally identified materials that are predicted to be in a topological insulator (TI) phase in the polar state, but topologically trivial in the antipolar state. This raises the possibility of electric-field induced switching between TI and non-TI behavior, although there is a potential question whether such switching is really possible in view of the topologically protected metallic states that should exist at antipolar-polar domain walls. Second, I will describe our work in which we construct simple tight-binding models of axion insulators, in which the topological index is protected by inversion rather than TR symmetry. I will discuss the conditions under which a half-integer quantized anomalous Hall conductivity should be present at the surface, and how the surface termination determines its sign. If time permits, I will also discuss the bulk-boundary correspondence for topological crystalline insulators and its consequences for surface and interface properties of such materials.
This work was done in collaboration with Bartomeu Monserrat, Nicodemos Varnava, and Jinwoong Kim.
[1] B. Monserrat and D. Vanderbilt, Phys. Rev. Lett. 119, 036802 (2017).