  We discuss the geometric phase of Wanner-Stark ladders generated by
periodically driven clock states in alkaline-earth(-like) atoms. Using
$^{171}$Yb atoms as a concrete example, we show that clock states driven by two
detuned clock lasers can be mapped to two-band Wannier-Stark ladders, where
dynamics of the system along the ladder is mapped to Bloch oscillations in a
one-dimensional topological lattice. When the adiabatic condition is satisfied,
the geometric phase accumulated in one period of the oscillation is quantized,
and reveals the change of band topology as the laser parameters are tuned. We
show how the geometric phase can be experimentally detected through
interference between different nuclear spin states. Our study sheds light on
the engineering of exotic band structures in Floquet dynamics.
