Dynamical Buildup of a Quantized Hall Response from Non-Topological States

TL;DR

This paper investigates how a non-topological state can develop a quantized Hall response through dynamical processes, with coherence and dephasing playing key roles, revealing new ways to realize topological phenomena.

Contribution

It demonstrates that a quantized Hall response can emerge dynamically from trivial states during non-adiabatic ramps, even without a change in the Chern number, and explores the effects of dephasing.

Findings

Non-equilibrium Hall response approaches quantized value with slow ramps.

Dephasing stabilizes the Hall response despite loss of topological invariants.

The phenomena are explained via time-dependent Berry curvature.

Abstract

We consider a two-dimensional system initialized in a topologically trivial state before its Hamiltonian is ramped through a phase transition into a Chern insulator regime. This scenario is motivated by current experiments with ultracold atomic gases aimed at realizing time-dependent dynamics in topological insulators. Our main findings are twofold. First, considering coherent dynamics, the non-equilibrium Hall response is found to approach a topologically quantized time averaged value in the limit of slow but non-adiabatic parameter ramps, even though the Chern number of the state remains trivial. Second, adding dephasing, the destruction of quantum coherence is found to stabilize this Hall response, while the Chern number generically becomes undefined. We provide a geometric picture of this phenomenology in terms of the time-dependent Berry curvature.