Topological edge states at Floquet quantum criticality

TL;DR

This paper demonstrates that Floquet quantum criticality in driven Majorana chains can host topological edge states at phase boundaries, including Majorana π modes, expanding understanding of nonequilibrium topological phases.

Contribution

It reveals that topological edge states can exist at Floquet phase boundaries and provides a bulk-edge correspondence formula for predicting these modes.

Findings

Edge states appear at Floquet phase boundaries.

Majorana π modes can be stabilized at criticality.

A bulk-edge correspondence formula is established.

Abstract

Topologically protected edge states exactly at topological phase boundaries challenge the conventional belief that topological states must be associated with a bulk energy gap. Because periodically driven (Floquet) systems host unusually intricate topological phase boundaries, topological edge states can be prolific at such Floquet quantum criticality. Working on a class of chiral-symmetric, Floquet-driven Majorana fermion chains, we analytically and computationally show that the precise boundaries between different Floquet topological gapped phases can accommodate topological edge modes, including the so-called Majorana $\pi$ modes. We also identify a general bulk-edge correspondence formula to predict and understand the emergence of topological edge modes at Floquet quantum criticality. Of direct interest to quantum simulation experiments, our results break new grounds for studies of nonequilibrium topological phases of matter undergoing topological phase transitions.