Floquet topological phase of nondriven $p$-wave nonequilibrium excitonic insulators

The nontrivial topology of {\it p}-wave superfluids make these systems attractive candidate in information technology. In this work we report on the topological state of a {\it p}-wave nonequilibrium excitonic insulator (NEQ-EI) and show how to steer a nontopological band-insulator with bright $p$-excitons toward this state by a suitable laser pulse, thus achieving a dynamical topological phase transition. The underlying mechanism behind the transition is the broken gauge-symmetry of the NEQ-EI which causes self-sustained persistent oscillations of the excitonic condensate and hence a Floquet topological state for high enough exciton densities. We show the formation of Floquet Majorana modes at the boundaries of the open system and discuss topological spectral signatures for ARPES experiments. We emphasize that the topological properties of a {\it p}-wave NEQ-EI arise exclusively from the electron-hole Coulomb interaction as the system is not driven by external fields.