  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 promising candidatess for
low-temperature thermal applications.
