Floquet higher-order topological phases in momentum space

TL;DR

This paper introduces a new class of Floquet higher-order topological phases in momentum space within a driven quantum system, revealing novel corner modes and topological invariants that extend HOTP concepts.

Contribution

It demonstrates the existence of Floquet HOTPs in momentum space, protected by chiral symmetry, characterized by large integer topological invariants, and reveals their measurable dynamical signatures.

Findings

Multiple Floquet corner modes with zero and π quasienergies emerge.

Topological invariants can be measured from wave packet dynamics.

Bulk-corner correspondence relates topological invariants to corner modes.

Abstract

Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers can also be measured from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and $\pi$ quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in continuum. The numbers of these corner modes are further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study HOTPs to momentum-space lattices, and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet driven systems.