Higher order topological insulator via periodic driving

We theoretically investigate a periodically driven semimetal based on a square lattice. The possibility of engineering both a Floquet topological insulator featuring Floquet edge states and a Floquet higher order topological insulating phase accommodating topological corner modes has been demonstrated starting from the semimetal phase, based on a Floquet Hamiltonian picture. A topological phase transition takes place in the bulk quasienergy spectrum with the variation of the drive amplitude where the Chern number changes signs from +1 to -1. This can be attributed to broken time-reversal invariance (T) due to circularly polarized light. When the discrete fourfold rotational symmetry (C-4) is also broken by adding a Wilson mass term along with broken T, a higher order topological insulator (HOTI), hosting in-gap modes at all the corners, can be realized. The Floquet quadrupolar moment, calculated with the Floquet states, exhibits a quantized value of 0.5 (modulo 1), identifying the HOTI phase. We also show the emergence of the dressed corner modes at quasienergy omega/2 (remnants of zero modes in the quasistatic high frequency limit), where omega is the driving frequency, in the intermediate frequency regime.