Theory of the thermopower of a quantum dot

TLDR

The authors develop a linear‑response theory for the thermopower of a small‑capacitance quantum dot. In the classical regime (kT ≫ ΔE) the thermopower oscillates in a sawtooth pattern around zero versus Fermi energy, provided kT ≪ e²/C. The oscillation period matches that of Coulomb‑blockade conductance oscillations and is set by ground‑state energy differences, while in the quantum resonant‑tunneling regime a finer structure appears whose period reflects the excitation spectrum at fixed electron number.

Abstract

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 \ensuremath{\Delta}E), 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\ensuremath{\ll}\ensuremath{\Delta}E), 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.