# Universal driving protocol for symmetry-protected Floquet topological phases

## TL;DR

This paper introduces a universal driving protocol for realizing and controlling symmetry-protected topological phases in 2+1D Floquet systems, enabling switching between trivial and non-trivial phases via parameter variation.

## Contribution

It presents a universal protocol for symmetry-protected Floquet topological phases, identifying key symmetries and demonstrating controllable topological boundary states.

## Key findings

- Existence of symmetry-protected copropagating boundary states
- Ability to switch between trivial and non-trivial phases
- Universal protocol applicable to various symmetry classes

## Abstract

Universal driving protocol for symmetry-protected Floquet topological phasesWe propose a universal driving protocol for the realization of symmetry-protected topological phases in $2+1$ dimensional Floquet systems. Our proposal is based on the theoretical analysis of the possible symmetries of a square lattice model with pairwise nearest-neighbor coupling terms. Among the eight possible symmetry operators we identify the two relevant choices for topological phases with either time-reversal, chiral, or particle-hole symmetry. From the corresponding symmetry conditions on the protocol parameters, we obtain the universal driving protocol where each of the symmetries can be realized or broken individually. We provide specific parameter values for the different cases, and demonstrate the existence of symmetry-protected copropagating and counterpropagating topological boundary states. The driving protocol especially allows us to switch between bosonic and fermionic time-reversal symmetry, and thus between a trivial and non-trivial symmetry-protected topological phase, through continuous variation of a parameter.