A detailed investigation of the non-equilibrium steady-state electric and thermoelectric transport properties of a quantum dot coupled to the normal metallic and s-wave superconducting reservoirs (N-QD-S) are provided within the Coulomb blockade regime. Using non-equilibrium Keldysh Green’s function formalism, initially, various model parameter dependence of thermoelectric transport properties are analysed within the linear response regime. It is observed that the single-particle tunnelling close to the superconducting gap edge can generate a relatively large thermopower and figure of merit. Moreover, the Andreev tunnelling plays a significant role in the suppression of thermopower and figure of merit within the gap region. Further, within the non-linear regime, we discuss two different situations, i.e., the finite voltage biasing between isothermal reservoirs and the finite thermal gradient in the context of thermoelectric heat engine. In the former case, it is shown that the sub-gap Andreev heat current can become finite beyond the linear response regime and play a vital role in asymmetric heat dissipation and thermal rectification effect for low voltage biasing. The rectification of heat current is enhanced for strong on-dot Coulomb interaction and at low background thermal energy. In the latter case, we study the variation of thermovoltage, thermopower, maximum power output, and corresponding efficiency with the applied thermal gradient. These results illustrate that hybrid superconductor-quantum dot nanostructures are a promising candidate for low-temperature thermal applications.

We study the influence of superconductivity on the formation of the localized magnetic moment for a single-level quantum impurity embedded in an s-wave Bardeen–Cooper–Schrieffer (BCS) superconducting medium, modeled by single-impurity Anderson Hamiltonian. We have combined Bogoliubov transformation with Green’s function method within self-consistent Hartree–Fock mean field approximation to analyze the conditions necessary in metal (in the superconducting) for the formation of the magnetic moment at the impurity site for the low-frequency limit |ω| ≪ Δsc as well as for the finite superconducting gap Δsc. We have compared these results with other theoretical results and with the single-level quantum impurity embedded in the normal metallic host. Further, we analyze the spectral density of the quantum impurity embedded in a superconducting host to study the sub-gap states as a function of impurity parameters.

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Herein, an analytical study of a strongly correlated quantum dot‐based thermoelectric particle‐exchange heat engine for both finite and infinite on‐dot Coulomb interaction is presented. Employing Keldysh's nonequilibrium Green's function formalism for different decoupling schemes in the equation of motion, the thermoelectric properties within the nonlinear transport regime have been analyzed. Initially, Hubbard‐I approximation has been used to study the quantum dot level position (), thermal gradient (), and on‐dot Coulomb interaction (U) dependence of the thermoelectric properties. Furthermore, as a natural extension, a decoupling beyond Hubbard‐I (Lacroix approximation) with infinite‐U limit (strong on‐dot Coulomb repulsion) has been used to provide additional insight into the operation of a more practical quantum dot heat engine. Within this infinite‐U limit, the role of the symmetric dot‐reservoir tunneling (Γ) and external serial load resistance (R) in optimizing the performance of the strongly correlated quantum dot heat engine is examined. The infinite‐U results show a good quantitative agreement with recent experimental data for a quantum dot coupled to two metallic reservoirs.

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