  We study Floquet topological phases in periodically driven systems that are
protected by "time glide symmetry", a combination of reflection and half time
period translation. Time glide symmetry is an analog of glide symmetry with
partial time translation replacing the partial space translation, and hence, is
an intrinsically dynamical symmetry which may be engineered in periodically
driven systems by exploiting the controllability of driving. We present lattice
models of time glide symmetric Floquet topological insulators in two and three
dimensions. The topological numbers characterizing those Floquet topological
phases are derived from the half period time evolution operator along with time
glide operator. Moreover, we classify Floquet topological phases protected by
time glide symmetry in general dimensions using a Clifford algebra approach.
The obtained classification table is similar to that for topological
crystalline insulators protected by static reflection symmetry, but shows
nontrivial entries in different combination of symmetries, which clarifies that
time glide symmetric Floquet topological phases are a distinct set of
topological phases from topological crystalline insulators. We also classify
Floquet topological phases with "time screw symmetry," defined as a two-fold
spatial rotation accompanied by half-period time translation.
