Superconductors with anomalous Floquet higher-order topology

Abstract

We develop a general theory for two-dimensional (2D) anomalous Floquet higher-order topological superconductors (AFHOTSC), 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 $\pi /T$ quasi-energies, a phenomenon beyond the scope of any static topological band theory. We show that the key to AFHOTSC is its 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 all 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.

6 pages, 4 figures

References in corpus (3)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures

Cited by in corpus (6)

• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Floquet higher-order Weyl and nexus semimetals
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Dynamical Symmetry Indicators for Floquet Crystals