  We present an analytical study of a strongly correlated quantum dot-based
thermoelectric particle-exchange heat engine for both finite and infinite
on-dot Coulomb interaction. Employing Keldysh's non-equilibrium Green's
function formalism for different decoupling schemes in the equation of motion,
we have analyzed the thermoelectric properties within the non-linear transport
regime. As the simplest mean-field approximation is insufficient for analyzing
thermoelectric properties in the Coulomb blockade regime, one needs to employ a
higher-order approximation to study strongly correlated QD-based heat engines.
Therefore initially, we have used the Hubbard-\Romannum{1} approximation to
study the quantum dot level position ($\epsilon_d$), thermal gradient ($\Delta
T$), and on-dot Coulomb interaction ($U$) dependence of the thermoelectric
properties. Furthermore, as a natural extension, we have used an approximation
beyond Hubbard-\Romannum{1} in the infinite-$U$ limit (strong on-dot Coulomb
repulsion) to provide additional insight into the operation of a more practical
quantum dot heat engine. Within this infinite-$U$ limit, we examine the role of
the symmetric dot-reservoir tunneling ($\Gamma$) and external serial load
resistance ($R$) in optimizing the performance of the strongly correlated
quantum dot heat engine. Our infinite-$U$ results show a good quantitative
agreement with recent experimental data for a quantum dot coupled to two
metallic reservoirs.
