Theory of the thermopower of a quantum dot

A linear-response theory is presented for the thermopower of a quantum dot of small capacitance. In the classical regime (thermal energy kT much greater than the level spacing ΔE), the thermopower oscillates around zero in a sawtooth fashion as a function of Fermi energy (as long as kT is small compared to the charged energy ${\mathit{e}}^2$/C). The periodicity of the oscillations is the same as that of the previously studied Coulomb-blockade oscillations in the conductance, and is determined by the difference in ground-state energies on addition of a single electron to the quantum dot. In the quantum regime of resonant tunneling (kT≪ΔE), a fine structure is predicted to develop on the oscillations. Unlike the Coulomb-blockade oscillations, the periodicity of the fine structure is determined by the excitation spectrum at a constant number of electrons on the quantum dot.