An Example of Time Reversal Invariant Kerr Effect

Abstract

Here we describe how certain classes of two dimensional topological insulators, including the CdTe$/$HgTe quantum wells, display a new type of optical activity in two dimensions similar to the magneto-optical Kerr effect in the quantum Hall effect. This optical activity is characterized by a genuine Kerr angle and it is compatible with time reversal symmetry, being thus fundamentally different to other known types of time reversal invariant optical activity. The term responsible of such optical activity, having the form of $(\mathbf{E}\cdot\partial\mathbf{B}/\partial t-\mathbf{B}\cdot\partial\mathbf{E}/\partial t)$, can be considered a time reversal invariant counterpart of the magneto-electric term $\mathbf{E}\cdot\mathbf{B}$. The microscopical origin of this response is a chiral non-minimal coupling between electrons and the external electromagnetic field. This optical activity constitutes a proof of principle that there is possible to find systems that are time reversal invariant displaying a genuine Kerr effect.