Electron cooling by diffusive normal metal - superconductor tunnel junctions

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.Comment: 9 pages, 4 figures, submitted to Phys. Rev.

Dissipative charge transport in diffusive superconducting double-barrier junctions

We solve the coherent multiple Andreev reflection (MAR) problem and calculate current-voltage characteristics (IVCs) for Josephson SINIS junctions, where S are local-equilibrium superconducting reservoirs, I denotes tunnel barriers, and N is a short diffusive normal wire, the length of which is much smaller than the coherence length, and the resistance is much smaller than the resistance of the tunnel barriers. The charge transport regime in such junctions qualitatively depends on a characteristic value \gamma = \Delta \tau_d of relative phase shifts between the electrons and retro-reflected holes accumulated during the dwell time \tau_d. In the limit of small electron-hole dephasing \gamma << 1, our solution recovers a known formula for a short mesoscopic connector extended to the MAR regime. At large dephasing, the subharmonic gap structure in the IVC scales with 1/ \gamma, which thus plays the role of an effective tunneling parameter. In this limit, the even gap subharmonics are resonantly enhanced, and the IVC exhibits portions with negative differential resistance.Comment: 8 pages, 3 figures, typos corrected, to be published in Phys. Rev.

Characteristics of the electric field accompanying a longitudinal acoustic wave in a metal. Anomaly in the superconducting phase

The temperature dependence of the amplitude and phase of the electric potential arising at a plane boundary of a conductor when a longitudinal acoustic wave is incident normally on it is investigated theoretically and experimentally. The surface potential is formed by two contributions, one of which is spatially periodic inside the sample, with the period of the acoustic field; the second is aperiodic and arises as a result of an additional nonuniformity of the electron distribution in a surface layer of the metal. In the nonlocal region the second contribution is dominant. The phases of these contributions are shifted by approximately \pi /2. For metals in the normal state the experiment is in qualitative agreement with the theory. The superconducting transition is accompanied by catastrophically rapid vanishing of the electric potential, in sharp contrast to the theoretical estimates, which predict behavior similar to the BCS dependence of the attenuation coefficient for a longitudinal sound.Comment: 9 pages, 6 figure

Loss of Andreev Backscattering in Superconducting Quantum Point Contacts

We study effects of magnetic field on the energy spectrum in a superconducting quantum point contact. The supercurrent induced by the magnetic field leads to intermode transitions between the electron waves that pass and do not pass through the constriction. The latter experience normal reflections which couple the states with opposite momenta inside the quantum channel and create a minigap in the energy spectrum that depends on the magnetic field

Nonequilibrium effects in tunnel Josephson junctions

We study nonequilibrium effects in current transport through voltage biased tunnel junction with long diffusive superconducting leads at low applied voltage, $eV \ll 2\Delta$, and finite temperatures. Due to a small value of the Josephson frequency, the quasiparticle spectrum adiabatically follows the time evolution of the superconducting phase difference, which results in the formation of oscillating bound states in the vicinity of the tunnel junction (Andreev band). The quasiparticles trapped by the Andreev band generate higher even harmonics of the Josephson ac current, and also, in the presence of inelastic scattering, a non-equilibrium dc current, which may considerably exceed the dc quasiparticle current given by the tunnel model. The distribution of travelling quasiparticles also deviates from the equilibrium due to the spectrum oscillations, which results in an additional contribution to the dc current, proportional to $\sqrt{V}$.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

Subgap current in superconducting tunnel junctions with diffusive electrodes

We calculate the subgap current in planar superconducting tunnel junctions with thin-film diffusive leads. It is found that the subharmonic gap structure of the tunnel current scales with an effective tunneling transparency which may exceed the junction transparency by up to two orders of magnitude depending on the junction geometry and the ratio between the coherence length and the elastic scattering length. These results provide an alternative explanation of anomalously high values of the subgap current in tunnelling experiments often ascribed to imperfection of the insulating layer. We also discuss the effect of finite lifetime of quasiparticles as the possible origin of additional enhancement of multiparticle tunnel currents.Comment: 4 pages, 4 figures, to be published in Phys. Rev.

IMAGE PROCESSING AT ELLIPSOIDAL PHOTOMETRY

Ellipsoidal photometry using Charge-Coupled Device (CCD photometry), as a new kind of optical diagnostics of scattering media in reflected and/or transmitted light, requires the development of specific principles of data analysis. The object of this work was substantiation the principles of ellipsoidal CCD photometry at implementation of a new data processing method of spatial distribution of scattered optical flux. Procedure of photometric analysis include the steps of determining the image significance, as well as the size, configuration and illuminance in its respective areas with regard to the criteria to optimize the shape and sensitivity of the zone. Zone analysis schemes of photometric images for media with a radially symmetric and directed scattering are developed. Recommended to use the method of comparison with etalon for studies the technical surfaces and turbid media to determine their roughness and optical characteristics, respectively. During the analysis of biological media, there is a possible of prognosis the spatial distribution of the brightness of the image by means of statistical modeling of optical radiation in the system «biological medium + ellipsoidal reflector». That confirmed by comparing results of the numerical (direct Monte Carlo simulation) and the real experiment for samples different thickness of muscle porcine tissue in vitro. Parameters of the optical radiation, which used as input data for the simulation, correspond to a laser wavelength of 632.8 nm with a Gaussian distribution profile of power of 2 mW. As a CCD detector was used monochrome camera DMK-21Au04.AS, and ellipsoidal reflector with an eccentricity of 0.66 and working aperture of 33.75 mm. Obtained results of zone distribution of illumination across the field in real experimental photometric images during biometrics showed correlation with the total transmission, absorption and diffuse scattering coefficients. This interdependence may be important part of improvement inverse methods of determination the optical parameters of biological media