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We study the effects of periodic driving on a variant of theBernevig-Hughes-Zhang (BHZ) model defined on a square lattice. In the absenceof driving, the model has both topological and nontopological phases dependingon the different parameter values. We also study the anisotropic BHZ model andshow that, unlike the isotropic model, it has a nontopological phase which hasstates localized on only two of the four edges of a finite-sized square. Whenan appropriate term is added, the edge states get gapped and gapless statesappear at the four corners of a square; we have shown that these corner statescan be labeled by the eigenvalues of a certain operator. When the system isdriven periodically by a sequence of two pulses, multiple corner states mayappear depending on the driving frequency and other parameters. We discuss towhat extent the system can be characterized by topological invariants such asthe Chern number and a diagonal winding number. We have shown that thelocations of the jumps in these invariants can be understood in terms of theFloquet operator at both the time-reversal invariant momenta and other momentawhich have no special symmetries.

Generating a second-order topological insulator with multiple corner states by periodic driving