The efficiencies/coefficients of performance of three-terminal devices, comprising two electronic terminals and a thermal one (e.g., a boson bath) are discussed. In particular, two procedures are analyzed. (a) One of the electronic terminals is coole
d by investing thermal power (from the thermal bath) and electric power (from voltage applied across the electronic junction); (b) The invested thermal power from the boson bath is exploited to cool one electronic terminal and to produce electric power. Rather surprisingly, the coefficient of performance of (b) can be enhanced as compared to that of (a).
We reanalyse the work of Cleuren et al., Phys. Rev. Lett. 109, 248902 (2012), in the light of Jiang et al. Phys. Rev. B 85, 075412 (2012). The condition for cooling enforces its rate to be exponentially small at low temperatures. Thus, the difficulty
with the dynamic version of the third law found by Levy et al., Phys. Rev. Lett. 109, 248901 (2012) and Allahverdyan et al., Phys. Rev. Lett. 109, 248903 (2012) is resolved.
The efficiency and cooling power of a two-terminal thermoelectric refrigerator are analyzed near the limit of vanishing dissipation (ideal system), where the optimal efficiency is the Carnot one, but the cooling power then unfortunately vanishes. Thi
s limit, where transport occurs only via a single sharp electronic energy, has been referred to as strong coupling or the best thermoelectric. It follows however, that parasitic effects that make the system deviate from the ideal limit, and reduce the efficiency from the Carnot limit, are crucial for the usefulness of the device. Among these parasitics, there are: parallel phonon conduction, finite width of the electrons transport band and more than a single energy transport channel. In terms of a small parameter characterizing the deviation from the ideal limit, the efficiency and power grow linearly, and the dissipation {em quadratically}. The results are generalized to the case of broken time-reversal symmetry, and the major nontrivial changes are discussed. Finally, the recent universal relation between the thermopower and the asymmetry of the dissipation between the two terminals is briefly discussed, including the small dissipation limit.
Two important features of mesoscopic Aharonov-Bohm (A-B) electronic interferometers are analyzed: decoherence due to coupling with other degrees of freedom and the coupled transport of charge and heat. We first review the principles of decoherence of
electronic interference. We then analyze the thermoelectric transport in a ring threaded by such a flux, with a molecular bridge on one of its arms. The charge carriers may also interact inelastically with the molecular vibrations. This nano-system is connected to three termi- nals; two of them are electric and thermal, held at slightly different chemical potentials and temperatures, and the third is purely thermal. For example, a phonon bath thermalizing the molecular vibrations. When this third terminal is held at a temperature different from those of the electronic reservoirs, both an electrical and a heat current are, in general, gen- erated between the latter. Likewise, a voltage and/or temperature difference between the electronic terminals leads to thermal current between the thermal and electronic terminals. The transport coefficients governing these
It is shown that for the hopping regime, the thermopowers in both finite two-terminal and three-terminal systems are governed by the edges of the samples. This is due to the fact that the energy transfer between a transport electron and a conducting
terminal is determined by the site most strongly coupled to that terminal. One-dimensional systems with both nearest-neighbor and variable-range transport as well as certain types of two-dimensional systems, are considered. For a given sample, the changes in the thermopowers due to modifying the bulk are quite limited, compared with those of the conductance. When the small thermopower changes exist, their average over a large ensemble of mesoscopic samples will vanish. We also obtain the distribution of the thermopower in such an ensemble and show that its width approaches a finite limit with increasing sample length. This contrasts with the distribution of conductances in such systems, whose width vanishes in the long sample limit. Finally, we find that the thermal conductances in the three-terminal case have a boundary-dominated contribution, due to non-percolating conduction paths. This contribution can become dominant when the usual conductance is small enough. All our theoretical statements are backed by numerical computations.
The interaction-induced orbital magnetic response of a nanoscale system, modeled by the persistent current in a ring geometry, is evaluated for a system which is a superconductor in the bulk. The interplay of the renormalized Coulomb and Fr{o}hlich i
nteractions is crucial. The diamagnetic response of the large superconductor may become paramagnetic when the finite-size-determined Thouless energy is larger than or on the order of the Debye energy.
