Graduate Lunch Talk: Judith Hoeller, Yale University, “Topological Bloch oscillations”

We propose a new way to characterize symmetry-protected transport in Fermionic and Bosonic insulators. In the simplest case of an insulator exposed to an electric field with no transitions to states above the energy gap, all observables oscillate with an integer multiple of the usual Bloch period. This integer is protected by spatial symmetries, divides n for n-fold rotationally symmetric insulators and therefore we call these topological Bloch oscillations (remember Bloch’s theorem: states in translation-invariant systems are functions of a parameter on a torus!). I will explain the origin of topological Bloch oscillations from two dual perspectives: from symmetric parallel transport of Bloch states on the torus, and from the phase accumulation of localized functions in a tilted lattice potential. If time permits, I will discuss to what extend topological Bloch oscillations survive if transitions to states above the energy gap are included.