  We study the DC current generation in a periodically driven Bloch system
connected to a heat bath. Under a relaxation time approximation, the density
matrix for such a system is obtained, which is related to two equilibria: a
Floquet quasi-equilibrium where the density matrix is diagonal under the
Floquet-Bloch eigenbasis and an instantaneous Bloch thermal equilibrium. Then,
the current responses and their power features, i.e. the power input behavior,
are discussed in a unified manner, which reveals that there exist an intrinsic
current and an extrinsic correction. Remarkably, the intrinsic part consumes no
energy and corresponds to the Floquet quasi-equilibrium, while the extrinsic
part needs a sustained energy input and originates from a shift between two
equilibrium ensembles. We further investigate the role of the external driving
field strength finding that large DC currents can be generated under a
relatively strong but not too strong driving field.
