Parametric optimization designs of a thermoelectric refrigeration device existing Zeeman and Coulomb effects

A general class of quantum dot refrigeration devices, which is consisting of a single orbital interacting quantum dot and two metal leads with different temperatures and chemical potentials, is established. In the model, not only the Zeeman splitting of energy levels resulting from an external magnetic field but also the effect of a linear fade of the Coulomb energy caused by the splitting are taken into account simultaneously. Based on the quantum master equation, the occupation probabilities of quantum states for the electron are determined under the steady state condition. The general expressions of the particle fluxes, heat flows, power input, cooling rate and the coefficient of performance (COP) are derived. The influences of the energy level and external magnetic field on the performance of the refrigerator are discussed in detail. By applying numerical simulations, three-dimensional diagrams of the cooling rate and COP varying with the magnetic field and energy level are given. The maximum COP and the optimal values of corresponding parameters as well as the maximum cooling rate are obtained. The optimal regions of the magnetic field and the energy level are determined. The optimized scopes of the COP and cooling rate are provided. Some important conclusions in the previous literatures can be directly deduced from the current model under the different extreme conditions.