Thermoelectric efficiency of three-terminal quantum thermal machines

Abstract

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

Quantum thermodynamics

“…Dynamically, QTMs can be classified as those that operate in discrete strokes, and those that operate as continuous devices, where the steady state of the continuous time device operates as a QTM. Furthermore, such continuous engines can be further classified as those that employ linear response techniques [14] and those that employ dynamical equation techniques [24]. These models of quantum engines are in contrast with biological motors, that extract work from fluctuations and have been studied extensively [154].…”

“…For example, the study of thermalisation has been approached by quantum information theory from the standpoint of typicality and entanglement, and by many-body physics with a dynamical approach. Likewise, the recent study of quantum thermal machines, originally approached from a quantum optics perspective [10][11][12], has since received significant input from many-body physics, fluctuation relations, and linear response approaches [13,14]. These designs further contrast with studies on thermal machines based on quantum information theoretic approaches [15][16][17][18][19][20].…”

From Thermal Rectifiers to Thermoelectric Devices

“…First investigations for a generic three-terminal system have shown that in some instances the coupling to a third terminal can improve both the extracted power and the efficiency of a thermoelectric device [96]. Moreover, with three terminals one can separate the currents, with charge and heat flowing to different reservoirs.…”

Nanowire-based thermoelectric ratchet in the hopping regime

“…We define a nonlocal thermopower [9] quantifying the voltage (δμ/e, e < 0 electron charge) between the electronic reservoirs L and R due to the temperature difference (δT P ) with the phonon bath P , in the absence of a temperature bias between the two electrodes (δT = 0):…”