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).
The interaction-induced orbital magnetic response of a nanoscale ring is evaluated for a diffusive system which is a superconductor in the bulk. The interplay of the renormalized Coulomb and Fr{o}hlich interactions is crucial. The magnetic susceptibi
lity which results from the fluctuations of the uniform superconducting order parameter is diamagnetic (paramagnetic) when the renormalized combined interaction is attractive (repulsive). Above the transition temperature of the bulk the total magnetic susceptibility has contributions from many wave-vector- and (Matsubara) frequency-dependent order parameter fluctuations. Each of these contributions results from a different renormalization of the relevant coupling energy, when one integrates out the fermionic degrees of freedom. The total diamagnetic response of the large superconductor may become paramagnetic when the systems size decreases.
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 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.
Following a short discussion of the granular model for an inhomogeneous superconductor, we review the Uemura and Homes correlations and show how both follow in two limits of a simple granular superconductor model. Definite expressions are given for t
he almost universal coefficients appearing in these relationships in terms of known constants.
