Green's functions for the electrodynamics of topological insulators: formalities and applications

Alberto Martín-Ruiz (ICN-UNAM)

Most states of quantum matter are described by the symmetries they break. However, topological states of quantum matter evade traditional symmetry-breaking classification schemes. Instead they are described in the low-energy limit by topological field theories. Recently, topological insulators have attracted great attention in condensed matter physics. These materials, among other unique electronic properties, display nontrivial topological order and are characterized by a fully insulating bulk and gapless edge or surface states, which are protected by time-reversal symmetry. In addition to their interesting electronic properties, topological insulators also exhibit interesting properties in terms of their interaction with electromagnetic sources and fields, in contrast to ordinary insulators or conductors. In this talk we present a general technique to analyze the classical interaction between ideal topological insulators and electromagnetic sources and fields. For inhomogeneous permittivity and permeability, the problem of finding the Green’s function must be solved in an ad hoc manner. Our results, satisfactorily reproduce previously existing ones and also generalize some others. The method here elaborated can be exploited to determine the electromagnetic fields for more general configurations aiming to measure the interaction between real 3D topological insulators and electromagnetic fields.