Slow quenches in two-dimensional time-reversal symmetric Z2 topological insulators

TL;DR

This paper investigates the effects of slow quenches on the topological and transport properties of 2D Z2 topological insulators modeled by the BHZ Hamiltonian, revealing invariant preservation, Kibble-Zurek scaling, and symmetry-breaking effects.

Contribution

It provides a detailed analysis of how slow quenches influence topological invariants and transport in 2D Z2 insulators, including symmetry considerations and scaling laws.

Findings

The Z2 invariant remains unchanged during symmetry-preserving quenches.

Bulk spin Hall conductivity approaches the final ground state value over time.

Breaking time-reversal symmetry restores the invariant-transport correspondence.

Abstract

We study the topological properties and transport in the Bernevig-Hughes-Zhang (BHZ) model undergoing a slow quench between different topological regimes. Due to the closing of the band gap during the quench, the system ends up in an excited state. For quenches governed by a Hamiltonian that preserves the symmetries present in the BHZ model (time-reversal, inversion, and conservation of spin projection), the $\mathbb{Z}_2$ invariant remains equal to the one evaluated in the initial state. The bulk spin Hall conductivity does change and its time average approaches that of the ground state of the final Hamiltonian. The deviations from the ground-state spin Hall conductivity as a function of the quench time follow the Kibble-Zurek scaling. We also consider the breaking of the time-reversal symmetry, which restores the correspondence between the bulk invariant and the transport properties after the quench.