The electrical conductance, thermal conductance, thermal power, and figure of merit (ZT) of semiconductor quantum dots (QDs) embedded into an insulator matrix connected with metallic electrodes are theoretically investigated in the Coulomb blockade regime. The multilevel Anderson model is used to simulate the multiple QDs junction system. The charge and heat currents in the sequential tunneling process are calculated by the Keldysh Green's function technique. In the linear-response regime the ZT values are still very impressive in the small tunneling rates case, although the effect of electron Coulomb interaction on ZT is significant. In the nonlinear-response regime, we have demonstrated that the thermal rectification behavior can be observed for the coupled QDs system, where the very strong asymmetrical coupling between the dots and electrodes, large energy-level separation between dots and strong interdot Coulomb interactions are required.

The charge transport of serially coupled quantum dots (SCQD) connected to the metallic electrodes is theoretically investigated in the Coulomb blockade regime. A closed-form expression for the tunneling current of SCQD in the weak interdot hopping limit is obtained by solving an extended two-site Hubbard model via the Green's function method. We use this expression to investigate spin current rectification, negative differential conductance, and coherent tunneling in the nonlinear response regime. The current rectification arising from the space symmetry breaking of SCQD is suppressed by increasing temperature. The calculation of SCQD is extended to the case of multiple parallel SCQDs for studying the charge ratchet effect and SCQD with multiple levels. In the linear response regime, the functionalities of spin filter and low-temperature current filter are demonstrated to coexist in this system. It is further demonstrated that two-electron spin-singlet and -triplet states can be readily resolved from the measurement of the Seebeck coefficient rather than that of electrical conductance.

It is theoretically demonstrated that the figure of merit ($ZT$) of quantum dot (QD) junctions can be significantly enhanced when the degree of degeneracy of the energy levels involved in electron transport is increased. The theory is based on the the Green-function approach in the Coulomb blockade regime by including all correlation functions resulting from electron-electron interactions associated with the degenerate levels ($L$). We found that electrical conductance ($G_e$) as well as electron thermal conductance (${\kappa }_e$) are highly dependent on the level degeneracy ($L$), whereas the Seebeck coefficient ($S$) is not. Therefore, the large enhancement of $ZT$ is mainly attributed to the increase of $G_e$ when the phonon thermal conductance (${\kappa }_{ph}$) dominates the heat transport of the QD junction system. In the serially coupled double-QD case, we also obtain a large enhancement of $ZT$ arising from higher $L$. Unlike $G_e$ and ${\kappa }_e, S$ is found almost independent on electron interdot hopping strength.

The transport and thermoelectric properties of finite textured graphene nanoribbons (t-GNRs) connected to electrodes with various coupling strengths are theoretically studied in the framework of the tight-binding model and Green’s function approach. Due to quantum constriction induced by the indented edges, such t-GNRs behave as serially coupled graphene quantum dots (SGQDs). These types of SGQDs can be formed by tailoring zigzag GNRs (ZGNRs) or armchair GNRs (AGNRs). Their bandwidths and gaps can be engineered by varying the size of the quantum dot and the neck width at indented edges. Effects of defects and junction contact on the electrical conductance, Seebeck coefficient, and electron thermal conductance of t-GNRs are calculated. When a defect occurs in the interior site of textured ZGNRs (t-ZGNRs), the maximum power factor within the central gap or near the band edges is found to be insensitive to the defect scattering. Furthermore, we found that SGQDs formed by t-ZGNRs have significantly better electrical power outputs than those of textured ANGRs due to the improved functional shape of the transmission coefficient in t-ZGNRs. With a proper design of contact, the maximum power factor (figure of merit) of t-ZGNRs could reach $90\%$ ($95\%$) of the theoretical limit.

Heat engines made of quantum dot (QD) superlattice nanowires (SLNWs) offer promising applications in energy harvesting due to the reduction in phonon thermal conductivity. In solid state electrical generators (refrigerators), one needs to generate (remove) a large amount of charge current (heat current). Consequently, a high QD SLNW density is required for realistic applications. This study theoretically investigated the properties of power factor and electron heat rectification for an SLNW array under the transition from a one-dimensional system to a two-dimensional system. The SLNW arrays show the functionality of heat diodes, which is mainly attributed to a transmission coefficient with a temperature-bias direction dependent characteristic.

: We have theoretically studied the thermoelectric properties of serially coupled quantum dots (SCQDs) embedded in an insulator connected to metallic electrodes. In the framework of Keldysh Green's function technique, the Landauer formula of transmission factor is obtained using the equation of motion method. Based on such analytical expressions of charge and heat currents, we calculate the electrical conductance, Seebeck coefficient, electron thermal conductance, and figure of merit (ZT) of SCQDs in the linear response regime. The effects of interdot hopping and electron Coulomb interactions on ZT are analyzed. We demonstrate that ZT is not a monotonic increasing function of interdot electron hopping strength (tc). We also show that in the absence of phonon thermal conductance, SCQD can reach the Carnot efficiency as tcapproaches zero.