  The generation of thermopower in a miniaturized device modeled as a channel
connected to reservoirs/contacts maintained at different temperatures is
studied in this work. The left reservoir is also coupled to a periodic THz
driving source leading to a rearrangement of its internal energy levels. The
modified levels are determined using Floquet theory that governs the dynamics
of a periodic Hamiltonian. The starting point for the presented thermopower
calculations (mirrored in the related thermal gradient controlled current) is
the Landauer formula rooted in the transmission formalism. Primarily, we show
that while thermally activated electrons can be pumped from the hot reservoir
into the cold side as a straightforward manifestation of the Seebeck effect
through a difference in their respective Fermi levels, the quantum of charge
flow increases in presence of the periodic perturbation. We explain this
phenomenon by noting how the periodic driving makes available a greater number
of states in the left reservoir that are able to inject electrons into the
channel. The calculations also uncover a useful feature whereby the strength of
such a thermally-pumped current is amenable through a joint control of the
amplitude and frequency of the signal, offering an additional
experimentally-adjustable tool to regulate their flow. The calculated results
are shown for two classes of materials defined by prototypical linear and
quadratic dispersion, with the former capable of furnishing a larger current by
virtue of higher available density-of-modes. We close by pointing out possible
improvements to the calculation by accounting for dissipative effects in the
channel.
