Quantum annealing and non-equilibrium dynamics of Floquet Chern insulators

TL;DR

This paper explores how periodic driving induces topological transitions in materials, highlighting the challenges of adiabatic state preparation due to small energy gaps and demonstrating control over edge currents in graphene-like systems.

Contribution

It reveals the non-adiabatic dynamics and edge-state population in Floquet topological insulators under slow driving, with a focus on non-equilibrium effects and local topological markers.

Findings

Edge currents flow only at edges after time-averaging.

Bulk undergoes a non-equilibrium topological transition.

Adiabatic preparation is hindered by small energy gaps.

Abstract

Inducing topological transitions by a time-periodic perturbation offers a route to controlling the properties of materials. Here we show that the adiabatic preparation of a non-trivial state involves a selective population of edge-states, due to exponentially-small gaps preventing adiabaticity. We illustrate this by studying graphene-like ribbons with hopping's phases of slowly increasing amplitude, as for, e.g., a circularly polarized laser slowly turned-on. The induced currents have large periodic oscillations, but flow solely at the edges upon time-averaging, and can be controlled by focusing the laser on either edge. The bulk undergoes a non-equilibrium topological transition, as signaled by the local Chern marker introduced by Bianco & Resta in equilibrium. The failure of the adiabatic picture in presence of intraband resonances is discussed.