Driven superconductors with anomalous Floquet higher-order topology

In this work, we classify periodically driven class D superconductors in two dimensions with higher-order topologies that are statically impossible. While hosting trivial Floquet Bogoliubov-de Gennes (BdG) bands in the bulk, such an anomalous Floquet higher-order topological superconductor (AFHOTSC) features corner Majorana zero and π modes that are protected by crystalline symmetries. Unlike its static counterpart, the presence of corner Majorana modes in an AFHOTSC is indicated by robust nodal structures in the eigenspectrum of the time-evolution operator. By proposing a set of higher-order topological indices, we achieve a systematic classification of all 2D AFHOTSCs protected by rotation group symmetries in class D. Concrete lattice models of AFHOTSCs are constructed to demonstrate applications of our theory. Experimental realizations and detections of AFHOTSCs are also discussed.