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 are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.
Highlights
Driving fields could induce symmetries and phase transitions that are unique to Floquet systems [104,105], yielding Floquet Higher-order topological phases (HOTPs) with topological properties that go beyond any static counterparts [82,93]
This is different from the situations usually observed in 2D static and Floquet HOTPs, where corner modes are separated from bulk states by spectral gaps
We find rich Floquet second-order topological phases in a two-dimensional extension of the on-resonance double kicked rotor
Summary
Higher-order topological phases (HOTPs) in D spatial dimensions are characterized by symmetry-protected states localized along its ( D − n)-dimensional boundaries, where. In one-dimensional (1D) descendant models of Equation (7), rich first-order Floquet topological phases have been discovered, which are characterized by large Chern (winding numbers), multiple chiral (dispersionless) edge modes and topologically quantized acceleration in momentum space [107,120,121,122,123]. These discoveries further motivate us to explore HOTPs in the 2D on-resonance double-kicked lattice model. We construct the bulk topological invariants for Floquet HOTPs in the 2D on-resonance double kicked lattice based on these analysis and establish the bulk topological phase diagram of the system
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