Superconductors with anomalous Floquet higher-order topology

TL;DR

This paper introduces a comprehensive theory for 2D anomalous Floquet higher-order topological superconductors, revealing their unique corner Majorana modes at zero and π/T energies, driven by phase spectrum singularities.

Contribution

It develops a classification and topological index for AFHOTSC, a novel dynamical phase with no static counterpart, and confirms predictions through numerical simulations.

Findings

Identification of corner Majorana modes at zero and π/T energies

Classification of AFHOTSC protected by rotation symmetry

Numerical validation of topological index predictions

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.