Abstract:
We discuss the theoretical framework to describe quasiparticle electric and heat currents in NIS tunnel junctions in the dirty limit. The approach is based on quasiclassical Keldysh-Usadel equations. We apply this theory to diffusive NIS'S tunnel junctions. Here N and S are respectively normal metal and superconductor reservoirs, I is an insulator layer and S' is a nonequilibrium superconducting lead. We calculate the quasiparticle electric and heat currents in such structures and consider the effect of inelastic relaxation in the S' lead. We find that in the absence of strong relaxation the electric current and the cooling power for voltages $eV < \Delta$ are suppressed. The value of this suppression scales with the diffusive transparency parameter. We ascribe this suppression to the effect of backtunneling of nonequilibrium quasiparticles into the normal metal.

Abstract:
We consider a model NISIN system with two junctions in series, where N is a normal metal, S is a superconductor and I is an insulator. We assume that the resistance of the first junction is high, while the resistance of the second one is low. In this case the first junction cools the left normal electrode, while the second junction partially removes excited quasiparticles from the superconductor. We consider cooling properties of this double junction structure. It is shown that the cooling power depends strongly on the ratio of the resistances of the two junctions. In conclusion, we derive a generalized expression for the cooling power of a NIS tunnel junction taking into account charge imbalance effects.

Abstract:
Spatially resolved relaxation of non-equilibrium quasiparticles in a superconductor at ultra-low temperatures was experimentally studied. It was found that the quasiparticle injection through a tunnel junction results in modification of the shape of I-V characteristic of a remote `detector' junction. The effect depends on temperature, injection current and proximity to the injector. The phenomena can be understood in terms of creation of quasiparticle charge and energy disequilibrium characterized by two different length scales $\Lambda_{Q^{\ast}}$ $\sim5$ $\mu$m and $\Lambda_{T^{\ast}}\sim$ $40$ $\mu$m. The findings are in good agreement with existing phenomenological models, while more elaborated microscopic theory is mandatory for detailed quantitative comparison with experiment. The results are of fundamental importance for understanding electron transport phenomena in various nanoelectronic circuits.

Abstract:
We study the thermoelectric transport of a small metallic island weakly coupled to two electrodes by tunnel junctions. In the Coulomb blockade regime, in the case when the ground state of the system corresponds to an even number of electrons on the island, the main mechanism of electron transport at lowest temperatures is elastic cotunneling. In this regime, the transport coefficients strongly depend on the realization of the random impurity potential or the shape of the island. Using the random-matrix theory, we calculate the thermopower and the thermoelectric kinetic coefficient and study the statistics of their mesoscopic fluctuations in the elastic cotunneling regime. The fluctuations of the thermopower turn out to be much larger than the average value.

Abstract:
We investigate superconductor/insulator/ferromagnet/superconductor (SIFS) tunnel Josephson junctions in the dirty limit, using the quasiclassical theory. We consider the case of a strong tunnel barrier such that the left S layer and the right FS bilayer are decoupled. We calculate quantitatively the density of states (DOS) in the FS bilayer for arbitrary length of the ferromagnetic layer, using a self-consistent numerical method. We compare these results with a known analytical DOS approximation, which is valid when the ferromagnetic layer is long enough. Finally we calculate quantitatively the current-voltage characteristics of a SIFS junction.

Abstract:
We investigate superconductor/insulator/ferromagnet/superconductor (SIFS) tunnel Josephson junctions in the dirty limit, using the quasiclassical theory. We formulate a quantitative model describing the oscillations of critical current as a function of thickness of the ferromagnetic layer and use this model to fit recent experimental data. We also calculate quantitatively the density of states (DOS) in this type of junctions and compare DOS oscillations with those of the critical current.

Abstract:
We investigate heat and charge transport through a diffusive SIF1F2N tunnel junction, where N (S) is a normal (superconducting) electrode, I is an insulator layer and F1,2 are two ferromagnets with arbitrary direction of magnetization. The flow of an electric current in such structures at subgap bias is accompanied by a heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We demonstrate that the refrigeration efficiency depends on the strength of the ferromagnetic exchange field h and the angle {\alpha} between the magnetizations of the two F layers. As expected, for values of h much larger than the superconducting order parameter \Delta, the proximity effect is suppressed and the efficiency of refrigeration increases with respect to a NIS junction. However, for h \sim \Delta the cooling power (i.e. the heat flow out of the normal metal reservoir) has a non-monotonic behavior as a function of h showing a minimum at h \approx \Delta. We also determine the dependence of the cooling power on the lengths of the ferromagnetic layers, the bias voltage, the temperature, the transmission of the tunneling barrier and the magnetization misalignment angle {\alpha}.

Abstract:
We investigate the subgap transport properties of a S-F-Ne structure. Here S (Ne) is a superconducting (normal) electrode, and F is either a ferromagnet or a normal wire in the presence of an exchange or a spin- splitting Zeeman field respectively. By solving the quasiclassical equations we first analyze the behavior of the subgap current, known as the Andreev current, as a function of the field strength for different values of the voltage, temperature and length of the junction. We show that there is a critical value of the bias voltage V * above which the Andreev current is enhanced by the spin-splitting field. This unexpected behavior can be explained as the competition between two-particle tunneling processes and decoherence mechanisms originated from the temperature, voltage and exchange field respectively. We also show that at finite temperature the Andreev current has a peak for values of the exchange field close to the superconducting gap. Finally, we compute the differential conductance and show that its measurement can be used as an accurate way of determining the strength of spin-splitting fields smaller than the superconducting gap.

Abstract:
The Andreev current and the subgap conductance in a superconductor/ insulator/ ferromagnet (SIF) structure in the presence of a small spin-splitting field show novel interesting features (A. Ozaeta et al., Phys. Rev. B 86, 060509(R), 2012). For example, the Andreev current at zero temperature can be enhanced by a spin-splitting field h, smaller than the superconducting gap, as has been recently reported by the authors. Also at finite temperatures the Andreev current has a peak for values of the spin-splitting field close to the superconducting gap. Finally, the differential subgap conductance at low temperatures shows a peak at the bias voltage eV = h. In this paper we investigate the Andreev current and the subgap conductance in SFF structures with arbitrary direction of magnetization of the F layers. We show that all aforementioned features occur now at the value of the "effective field", which is the field acting on the Cooper pairs in the multi-domain ferromagnetic region, averaged over the decay length of the superconducting condensate into a ferromagnet. We also briefly discuss the heat transport and electron cooling in the considered structures.

Abstract:
We investigate heat and charge transport in NN'IS tunnel junctions in the diffusive limit. Here N and S are massive normal and superconducting electrodes (reservoirs), N' is a normal metal strip, and I is an insulator. The flow of electric current in such structures at subgap bias is accompanied by heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We show that the two-particle current due to Andreev reflection generates Joule heating, which is deposited in the N electrode and dominates over the single-particle cooling at low enough temperatures. This results in the existence of a limiting temperature for refrigeration. We consider different geometries of the contact: one-dimensional and planar, which is commonly used in the experiments. We also discuss the applicability of our results to a double-barrier SINIS microcooler.