Recent breakthroughs in quantum-dot circuit-quantum-electrodynamics (circuit-QED) systems are important both from a fundamental perspective and from the point of view of quantum photonic devices. However, understanding the applications of such setups as potential thermoelectric diodes and transistors has been missing. In this paper, via the Keldysh nonequilibrium Green's function approach, we show that cavity-coupled double quantum-dots can serve as excellent quantum thermoelectric diodes and transistors. Using an enhanced perturbation approach based on polarontransformations, we find non-monotonic dependences of thermoelectric transport properties on the electron-photon interaction. Strong light-matter interaction leads to pronounced rectification effects for both charge and heat, as well as thermal transistor effects in the linear transport regime, which opens up a cutting-edge frontier for quantum thermoelectric devices.

A B S T R A C TThe energy efficiency and power of a three-terminal thermoelectric nanodevice are studied by considering elastic tunneling through a single quantum dot. Facilitated by the three-terminal geometry, the nanodevice is able to generate simultaneously two electrical powers by utilizing only one temperature bias. These two electrical powers can add up constructively or destructively, depending on their signs. It is demonstrated that the constructive addition leads to the enhancement of both energy efficiency and output power for various system parameters. In fact, such enhancement, dubbed as thermoelectric cooperative effect, can lead to maximum efficiency and power no less than when only one of the electrical power is harvested. IntroductionThermoelectric phenomena at nanoscales have attracted a lot of research interest because of fundamental physics and application impacts on renewable energy devices with high performance 1-16 . Theory and experiments have shown that nanostructured materials can have high thermoelectric efficiency and power 13,14,[17][18][19][20][21][22] . Up till now, most of the theories for thermoelectricity is based on elastic (or quasi-elastic) transport theory, where energy-dependent conductivity is commonly involved 11,23-29 . In particularly, Mahan and Sofo proposed that the "best thermoelectrics" can be realized in narrow band conductors, where the thermopower and the electronic heat current are balanced and optmized to yield a high energy efficiency (characterized by a large thermoelectric figure of merit, ZT) 30 . However, recent studies show that if phonon parasitic heat conduction is taken into account the bandwidth of the carrier should be much 2 / 13 enlarged and the figure of merit is significantly reduced 11,31 . These findings reveal the intrinsic entanglement of the Seebeck coefficient, electrical conductivity, and the heat conductivity, which may impede future improvement of thermoelectric performance.Recently, to go beyond such an obstacle, the concept of inelastic thermoelectric transport is proposed 5,11,13,14,32,33 . A typical inelastic thermoelectric device involve three terminals (see Fig.1a):two electrodes (the source and the drain), and a boson bath (e.g., a phonon bat). The boson bath provides the energy (in the form of, e.g., phonons) to assist the inelastic transport between the source and the drain. This picture is essentially similar to a solar cell, but with much lower energy scales. In the situation of phonon-assisted hopping transport, the figure of merit is limited by the average frequency and bandwidth of the phonons involved in the inelastic transport 16 . High figure of merit can be achieved with large average frequency and small bandwidth 11,31 , which do not conflict with electrical conductivity if the electron-phonon interaction is strong (e.g., electronphonon interaction near the Debye frequency in ionic crystals) 5,34 . Thus high thermoelectric efficiency and power may be achieved without requiring narrow electronic bands. Such a paradigm ...

The three-terminal heat device that consists of an electronic cavity and couples to a heat bath is studied both as a heat engine and as a refrigerator. We investigate the characteristic performance in the linear and nonlinear regime for both setups. It is our focus here to analyze how the efficiency of the heat engine and coefficient of performance of the refrigerator are affected by the nonlinear transport. With such considerations, the maximum efficiency and power are then optimized for various energy levels, temperatures and other parameters.

Graphene-hexagonal-boron-nitride-InSb near-field structures are designed and optimized to enhance the output power and energy efficiency of the thermophotovoltaic systems working in the temperature range of common industrial waste heat, 400 K ∼ 800 K, which is also the working temperature range for conventional thermoelectric devices. We show that the optimal output electric power can reach 3.5 × 10 4 W/m 2 for the system with a graphene-hexagonal-boron-nitride heterostructure emitter and a graphene-covered InSb cell, whereas the best efficiency is achieved by the system with the heterostructure emitter and an uncovered InSb cell (reaching to 27% of the Carnot efficiency). These results show that the performances of near-field thermophotovoltaic systems can be comparable with or even superior than the state-of-art thermoelectric devices. The underlying physics for the significant enhancement of the thermophotovoltaic performance is understood as due to the resonant coupling between the emitter and the cell, where the surface plasmons in graphene and surface phonon-polaritons in boron-nitride play important roles. Our study provides a stepping stone for future high-performance thermophotovoltaic systems.

We establish a theory of optimal efficiency and power for three-terminal thermoelectric engines which have two independent output electric currents and one input heat current. This set-up goes beyond the conventional heat engines with only one output electric current. For such a set-up, we derive the optimal efficiency and power and their trade-off for three-terminal heat engines with and without time-reversal symmetry. The formalism goes beyond the known optimal efficiency and power for systems with or without time-reversal symmetry, showing interesting features that have not been revealed before. A concrete example of quantum-dot heat engine is studied to show that the current set-up can have much improved efficiency and power compared with previous set-ups with only one output electric current. Our analytical results also apply for thermoelectric heat engines with multiple output electric currents, providing an alternative scheme toward future highperformance thermoelectric materials.