Engineering Floquet Higher Order Topological Insulator by Periodic Driving

We theoretically investigate periodically driven two dimentional semimetal in high frequency regime and demonstrate
the possibility of realizing both Floquet Topological Insulator featuring Floquet edge states and Floquet higher
order topological insulating phase, accommodating topological corner modes. Topological phase transition
takes place with the external drive where Chern number changes from +1 to -1 with the change of drive amplitude
in case with broken time-reversal symmetry (T ) due to circularly polarized light. When discreet four-fold rotation
symmetry (C_4 ) is broken by adding a mass perturbation alongwith broken T, the quadrupolar moment Q_xy is
found to have a quantized value 0.5 and topological corner modes arise in the system which is characterization of
second order topological insulator. The nature of the Floquet corner modes with the increase of external drive
is examined.