  We study the effects of periodic driving on a variant of the
Bernevig-Hughes-Zhang (BHZ) model defined on a square lattice. In the absence
of driving, the model has both topological and nontopological phases depending
on the different parameter values. We also study the anisotropic BHZ model and
show that, unlike the isotropic model, it has a nontopological phase which has
states localized on only two of the four edges of a finite-sized square. When
an appropriate term is added, the edge states get gapped and gapless states
appear at the four corners of a square; we have shown that these corner states
can be labeled by the eigenvalues of a certain operator. When the system is
driven periodically by a sequence of two pulses, multiple corner states may
appear depending on the driving frequency and other parameters. We discuss to
what extent the system can be characterized by topological invariants such as
the Chern number and a diagonal winding number. We have shown that the
locations of the jumps in these invariants can be understood in terms of the
Floquet operator at both the time-reversal invariant momenta and other momenta
which have no special symmetries.
