Gapless higher-order topology and corner states in Floquet systems

TL;DR

This paper uncovers a new form of higher-order topology in Floquet systems induced by periodic driving at phase transition points, revealing unique corner states that exist beyond equilibrium conditions.

Contribution

It introduces a novel type of Floquet higher-order topological phase at critical points, with analytical and numerical analysis of corner modes in driven lattice models.

Findings

Identification of zero and π corner modes at Floquet topological transitions

Proposal of a bulk-corner correspondence scheme for Floquet HOTPs

Demonstration of topological transitions with corner states surviving in Floquet systems

Abstract

Higher-order topological phases (HOTPs) possess localized and symmetry-protected eigenmodes at corners and along hinges in two and three dimensional lattices. The numbers of these topological boundary modes will undergo quantized changes at the critical points between different HOTPs. In this work, we reveal unique higher-order topology induced by time-periodic driving at the critical points of topological phase transitions, which has no equilibrium counterparts and also goes beyond the description of gapped topological matter. Using an alternately coupled Creutz ladder and its Floquet-driven descendants as illustrative examples, we analytically characterize and numerically demonstrate the zero and $\pi$ corner modes that could emerge at the critical points between different Floquet HOTPs. Moreover, we propose a unified scheme of bulk-corner correspondence for both gapless and gapped Floquet HOTPs protected by chiral symmetry in two dimensions. Our work reveals the possibility of corner modes surviving topological transitions in Floquet systems and initializes the study of higher-order Floquet topology at quantum criticality.