  Time-periodic (Floquet) topological phases of matter exhibit bulk-edge
relationships that are more complex than static topological insulators and
superconductors. Finding the edge modes unique to driven systems usually
requires numerics. Here we present a minimal two-band model of Floquet
topological insulators and semimetals in two dimensions where all the bulk and
edge properties can be obtained analytically. It is based on the extended
Harper model of quantum Hall effect at flux one half. We show that periodical
driving gives rise to a series of phases characterized by a pair of integers.
The model has a most striking feature: the spectrum of the edge modes is always
given by a single cosine function, $\omega(k_y)\propto \cos k_y$ where $k_y$ is
the wave number along the edge, as if it is freely dispersing and completely
decoupled from the bulk. The cosine mode is robust against the change in
driving parameters and persists even to semi-metallic phases with Dirac points.
The localization length of the cosine mode is found to contain an integer and
in this sense quantized.
