Anomalous Floquet topological crystalline insulators

TL;DR

This paper introduces an anomalous Floquet topological crystalline insulator with tunable surface states, characterized by a new topological invariant derived from the scattering matrix, despite trivial bulk mirror Chern numbers.

Contribution

It presents a novel class of Floquet topological crystalline insulators with robust surface Dirac cones governed by new invariants, expanding understanding of topological phases in driven systems.

Findings

Surface Dirac cones are tunable and robust.

Surface state count is determined by a new scattering matrix invariant.

Dirac cone positions are controlled by an additional invariant related to particle-hole symmetry.

Abstract

Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected topological crystalline insulators, obtained as a stack of weakly-coupled two-dimensional layers. The system has tunable and robust surface Dirac cones even though the mirror Chern numbers of the Floquet bulk bands vanish. The number of surface Dirac cones is given by a new topological invariant determined from the scattering matrix of the system. Further, we find that due to particle-hole symmetry, the positions of Dirac cones in the surface Brillouin zone are controlled by an additional invariant, counting the parity of modes present at high symmetry points.