Non-Hermitian Floquet second order topological insulators in periodically quenched lattices

Higher-order topological phases are characterized by protected states localized at the corners or hinges of the system. By applying time-periodic quenches to a two-dimensional lattice with balanced gain and loss, we obtain a rich variety of non-Hermitian Floquet second order topological insulating phases. Each of the phases is characterized by a pair of integer topological invariants, which predict the numbers of Floquet corner modes at zero and $\pi$ quasienergies. We establish the topological phase diagram of the model, and find a series of non-Hermiticity induced transitions between different Floquet second order topological phases. We further generalize the mean chiral displacement to two-dimensional non-Hermitian systems, and use it to extract the topological invariants of our model dynamically. This work thus extend the study of higher-order topological matter to more generic nonequilibrium settings, in which the interplay between Floquet engineering and non-Hermiticity yields fascinating new phases.