Topology and edge states survive quantum criticality between topological insulators

TL;DR

This paper demonstrates that topological edge states can remain localized and stable at quantum critical points, even when the bulk gap closes, expanding the understanding of topological protection beyond energy gaps.

Contribution

It reveals that topological edge states persist at criticality if the topological index increases, generalizing the bulk-boundary correspondence to gapless transitions and introducing kinetic inversion.

Findings

Edge states remain localized at criticality despite gap closing.

Topological invariants at criticality can be half-integers, separating universality classes.

Edge states are stable to disorder, unlike in topological semi-metals.

Abstract

It is often thought that emergent phenomena in topological phases of matter are destroyed when tuning to a critical point. In particular, topologically protected edge states supposedly delocalize when the bulk correlation length diverges. We show that this is not true in general. Edge states of topological insulators or superconductors remain exponentially localized---despite a vanishing band gap---if the transition increases the topological index. This applies to all classes where the topological classification is larger than $Z_2$, notably including Chern insulators. Moreover, these edge states are stable to disorder, unlike in topological semi-metals. This new phenomenon is explained by generalizing band (or mass) inversion---a unifying perspective on topological insulators---to kinetic inversion. In the spirit of the bulk-boundary correspondence, we also identify topological invariants at criticality, which take half-integer values and separate topologically-distinct universality classes by a multi-critical point. This work enlarges the scope of topological protection and stability by showing that bulk energy gaps can be unnecessary. Experimental probes and stability to interactions are discussed.