Scheme to Equilibrate the Quantized Hall Response of Topological Systems from Coherent Dynamics

TL;DR

This paper presents a novel scheme to achieve equilibration of the quantized Hall response in topological systems through pure coherent dynamics, avoiding the need for engineered noise, and applies it to Weyl semimetals.

Contribution

The authors introduce a new method for equilibrating the Hall response in topological insulators using coherent dynamics, enabling observation of topological phase transitions without noise.

Findings

Successfully equilibrated Hall response in 2D topological insulators.

Demonstrated equilibration in Weyl semimetals despite gapless bands.

Identified key factors affecting the equilibration process.

Abstract

Two-dimensional topologically distinct insulators are separated by topological gapless points, which exist as Weyl points in three-dimensional momentum space. Slowly varying parameters in the two-dimensional Hamiltonian across two distinct phases therefore necessarily experiences the gap closing process, which prevents the intrinsic physical observable, the Hall response, from equilibrating. To equilibrate the Hall response, engineered laser noises were introduced at the price of destroying the quantum coherence. Here we demonstrate a new scheme to equilibrate the quantized Hall response from pure coherent dynamics as the Hamiltonian is slowly tuned from the topologically trivial to nontrivial regimes. We show the elements that affect the process of equilibration including the sequence when the electric field is switched on, its strength and the band dispersion of the final Hamiltonian. We further apply our method to Weyl semimetals in three dimensions and find the equilibrated Hall response despite the underlying gapless band structure. Our finding not only lays the theoretical foundation for observing the two-dimensional topological phase transition but also for observing and controlling Weyl semimetals in ultracold atomic gases.