Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
Dr. Perry Mahon, Dept. of Physics, The University of Texas at Austin
In the 1980s a paradigm shift in condensed matter physics occurred when it was discovered that the electronic ground state of a crystalline band insulator encodes a manifold that is characterized by topological invariants and that (some of) these invariants can be directly accessed via the material’s linear susceptibilities. A prototypical example is the quantum anomalous Hall effect (QAHE), which occurs in two-dimensional band insulators that break time-reversal symmetry (TRS) and manifests through the Hall conductivity which is proportional to the insulator’s Z-valued first Chern invariant. More recently it has been proposed on theoretical grounds that three-dimensional (3D) band insulators with TRS can exhibit a topological magnetoelectric response related to a Z2-valued topological invariant. In contrast to the QAHE, for which the symmetry and topological arguments are immediately consistent, a delicate tension complicates the relationship between the topological magnetoelectric effect (TME) and TRS. TRS underlies a particular Z2 topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear-response theory but, according to standard symmetry arguments, simultaneously forbids a nonzero magnetoelectric coefficient in any physical finite-size system.
In this talk I will use explicit calculations for simple models of finite sized and bulk systems to demonstrate these subtleties, in particular, that in nonmagnetic Z2 topological insulators the TME is activated by magnetic surface dopants, and conjecture a type of microscopic bulk-boundary correspondence based on analytical results. Finally, I will present an experimental proposal for the direct measurement of the TME, which has remained elusive since its prediction over a decade ago.
