Thermal Conductance and Seebeck Effect in Mesoscopic Systems

Abstract

In this work, thermoelectric transport through a saddle-point potential is discussed with an emphasis on the effects of the chemical potential and temperature. In particular, the thermal conductance and the Seebeck coefficient are calculated for two-dimensional systems of a constriction defined by a saddle-point potential. The solution as a function of temperature and chemical potential has been investigated. The Peltier coefficient and thermal transport in a quantum point contact (QPC), under the influence of external fields and different temperatures, are presented. Also, the oscillations of the Peltier coefficient in external fields are obtained. Numerical calculations of the Peltier coefficient are performed at different applied voltages, amplitudes, and temperatures. Moreover, a method is proposed for measuring the sub-band energies and spin-splitting energies in a bottle-neck of the constriction. For weak non-linearities, the charge and entropy currents across a QPC are expanded as a series in powers of the applied bias voltage and the temperature difference. Expansions of the Seebeck voltage in terms of the temperature difference and the Peltier heat in terms of the current are obtained.