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 ($\mathcal{T}$) due to circularly polarized light. When the discrete fourfold rotational symmetry (${\mathcal{C}}_4$) is also broken by adding a Wilson mass term along with broken $\mathcal{T}$, 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.

• Received 28 November 2019
• Accepted 20 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.235403