Stability of Periodically Driven Topological Phases against Disorder

TL;DR

This paper develops a universal effective theory to predict the existence and phase transition of periodically driven topological phases in disordered systems, validated by numerical simulations.

Contribution

It introduces a novel analytical framework combining free probability and random matrix theory to analyze topological phases under disorder at finite driving frequencies.

Findings

Predicts the critical disorder strength for topological-trivial transition.

Provides critical exponents for the phase transition.

Shows excellent agreement with numerical diagonalizations.

Abstract

In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder similar to equilibrium topological phases. However, proving the existence of such topological phases in a general setting is an open problem. We propose a universal effective theory that leverages on modern free probability theory and ideas in random matrices to analytically predict the existence of the topological phase for finite driving frequencies and across a range of disorder. We find that, depending on the strength of disorder, such systems may be topological or trivial and that there is a transition between the two. In particular, the theory predicts the critical point for the transition between the two phases and provides the critical exponents. We corroborate our results by comparing them to exact diagonalizations for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang models and find excellent agreement. This Letter may guide the experimental efforts for exploring topological phases.