The efficiency of a thermal engine working in the linear response regime in a multi-terminal configuration is discussed. For the generic three-terminal case, we provide a general definition of local and non-local transport coefficients: electrical and thermal conductances, and thermoelectric powers. Within the Onsager formalism, we derive analytical expressions for the efficiency at maximum power, which can be written in terms of generalized figures of merit. Furthermore, using two examples, we investigate numerically how a third terminal could improve the performance of a quantum system, and under which conditions non-local thermoelectric effects can be observed. , respectively) flowing from the corresponding reservoirs, which have to fulfill the constraints: J J 0 (energy conservation) , j Δ | | ≪ for j=1,2, and k B is the Boltzmann constant. Under these assumptions the relation between currents and biases can then be expressed through the Onsager matrix L of elements L ij via the identity: J J J J 2 Δ = are the generalized forces, and where J J J W J J J J T T J J ( ) J X J J X J X

We study the thermoelectric properties and heat-to-work conversion performance of an interacting, multilevel quantum dot (QD) weakly coupled to electronic reservoirs. We focus on the sequential tunneling regime. The dynamics of the charge in the QD is studied by means of master equations for the probabilities of occupation. From here we compute the charge and heat currents in the linear response regime. Assuming a generic multiterminal setup, and for low temperatures (quantum limit), we obtain analytical expressions for the transport coefficients which account for the interplay between interactions (charging energy) and level quantization. In the case of systems with two and three terminals we derive formulas for the power factor Q and the figure of merit ZT for a QD-based heat engine, identifying optimal working conditions which maximize output power and efficiency of heat-to-work conversion. Beyond the linear response we concentrate on the two-terminal setup. We first study the thermoelectric nonlinear coefficients assessing the consequences of large temperature and voltage biases, focusing on the breakdown of the Onsager reciprocal relation between thermopower and Peltier coefficient. We then investigate the conditions which optimize the performance of a heat engine, finding that in the quantum limit output power and efficiency at maximum power can almost be simultaneously maximized by choosing appropriate values of electrochemical potential and bias voltage. At last we study how energy level degeneracy can increase the output power

In a multi-terminal device the (electronic) heat and charge currents can follow different paths. In this paper we introduce and analyse a class of multi-terminal devices where this property is pushed to its extreme limits, with charge and heat currents flowing in different reservoirs. After introducing the main characteristics of such heat-charge current separation regime we show how to realise it in a multi-terminal device with normal and superconducting leads. We demonstrate that this regime allows to control independently heat and charge flows and to greatly enhance thermoelectric performances at low temperatures. We analyse in details a three-terminal setup involving a superconducting lead, a normal lead and a voltage probe. For a generic scattering region we show that in the regime of heat-charge current separation both the power factor and the figure of merit ZT are highly increased with respect to a standard two-terminal system. These results are confirmed for the specific case of a system consisting of three coupled quantum dots.

In a multi-terminal setup, when time-reversal symmetry is broken by a magnetic field, the heat flows can be managed by designing a device with programmable Boolean behavior. We show that such a device can be used to implement operations, such as on/off switching, reversal, selected splitting and swap of the heat currents. For each feature, the switching from one working condition to the other is obtained by inverting the magnetic field. This offers interesting opportunities for conceiving a programmable setup, whose operation is controlled by an external parameter (the magnetic field) without need to alter voltage and thermal biases applied to the system. Our results, generic within the framework of linear response, are illustrated by means of a three-terminal electronic interferometer model.

We demonstrate that, due to their spin-orbit interaction, carbon nanotube cross-junctions have attractive spin projective properties for transport. First, we show that the junction can be used as a versatile spin filter as a function of a backgate and a static external magnetic field. Switching between opposite spin filter directions can be achieved by small changes of the backgate potential, and a full polarization is generically obtained in an energy range close to the Dirac points. Second, we discuss how the spin filtering properties affect the noise correlators of entangled electron pairs, which allows us to obtain signatures of the type of entanglement that are different from the signatures in conventional semiconductor cross-junctions.