Superconductors with anomalous Floquet higher-order topology

DinhDuy Vu; Rui-Xing Zhang; Zhi-Cheng Yang; S. Das Sarma

doi:10.1103/PhysRevB.104.L140502

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Superconductors with anomalous Floquet higher-order topology

DinhDuy Vu, Rui-Xing Zhang, Zhi-Cheng Yang, S. Das Sarma

DOI 10.1103/PhysRevB.104.L140502 · Physical Review B

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Abstract

We develop a general theory for two-dimensional (2D) anomalous Floquet higher-order topological superconductors (AFHOTSCs), which are dynamical Majorana-carrying phases of matter with no static counterpart. Despite the triviality of its bulk Floquet bands, an AFHOTSC generically features the simultaneous presence of corner-localized Majorana modes at both zero and π/T quasienergies, a phenomenon beyond the scope of any static topological band theory. We show that the key to AFHOTSCs is their unavoidable singular behavior in the phase spectrum of the bulk time-evolution operator. By mapping such evolution-phase singularities to the stroboscopic boundary signatures, we classify 2D AFHOTSCs that are protected by a rotation group symmetry in symmetry class D. We further extract a higher-order topological index for unambiguously predicting the presence of Floquet corner Majorana modes, which we confirm numerically. Our theory serves as a milestone towards a dynamical topological theory for Floquet superconducting systems.