Transformations RS42(3){RS}_4^2(3) of the Ranks ≤4\leq4 and Algebraic Solutions of the Sixth Painlev\'e Equation

Compositions of rational transformations of independent variables of linear matrix ordinary differential equations (ODEs) with the Schlesinger transformations ($RS$-transformations) are used to construct algebraic solutions of the sixth Painlev\'e equation. $RS$-Transformations of the ranks 3 and 4 of $2\times2$ matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified.Comment: 26 page

Hydrodynamic description of transport in strongly correlated electron systems

We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, $\kappa$. This is in striking contrast with the Stokes flow, in which the resistance is independent of $\kappa$ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magnetoresistance

Andreev tunneling through a double quantum-dot system coupled to a ferromagnet and a superconductor: effects of mean field electronic correlations

We study the transport properties of a hybrid nanostructure composed of a ferromagnet, two quantum dots, and a superconductor connected in series. By using the non-equilibrium Green's function approach, we have calculated the electric current, the differential conductance and the transmittance for energies within the superconductor gap. In this regime, the mechanism of charge transmission is the Andreev reflection, which allows for a control of the current through the ferromagnet polarization. We have also included interdot and intradot interactions, and have analyzed their influence through a mean field approximation. In the presence of interactions, Coulomb blockade tend to localized the electrons at the double-dot system, leading to an asymmetric pattern for the density of states at the dots, and thus reducing the transmission probability through the device. In particular, for non-zero polarization, the intradot interaction splits the spin degeneracy, reducing the maximum value of the current due to different spin-up and spin-down densities of states. Negative differential conductance (NDC) appears for some regions of the voltage bias, as a result of the interplay of the Andreev scattering with electronic correlations. By applying a gate voltage at the dots, one can tune the effect, changing the voltage region where this novel phenomenon appears. This mechanism to control the current may be of importance in technological applications.Comment: 12 pages, 11 figure

Re-entrant localization of single particle transport in disordered Andreev wires

We study effects of disorder on the low energy single particle transport in a normal wire surrounded by a superconductor. We show that the heat conductance includes the Andreev diffusion decreasing with increase in the mean free path $\ell$ and the diffusive drift produced by a small particle-hole asymmetry, which increases with increasing $\ell$. The conductance thus has a minimum as a function of $\ell$ which leads to a peculiar re-entrant localization as a function of the mean free path.Comment: 4 pages, 2 figure

Simple theory of extremely overdoped HTS

We demonstrate the existence of a simple physical picture of superconductivity for extremely overdoped CuO2 planes. It possesses all characteristic features of HTS, such as a high superconducting transition temperature, the $d_{x^2 - y^2}$ symmetry of order parameter, and the coexistence of a single electron Fermi surface and a pseudogap in the normal state. Values of pseudogap are calculated for different doping levels. An orbital paramagnetism of preformed pairs is predicted.Comment: 7 pages, 1 figur

Nonlocal Andreev reflection at high transmissions

We analyze non-local effects in electron transport across three-terminal normal-superconducting-normal (NSN) structures. Subgap electrons entering S-electrode from one N-metal may form Cooper pairs with their counterparts penetrating from another N-metal. This phenomenon of crossed Andreev reflection -- combined with normal scattering at SN interfaces -- yields two different contributions to non-local conductance which we evaluate non-perturbatively at arbitrary interface transmissions. Both these contributions reach their maximum values at fully transmitting interfaces and demonstrate interesting features which can be tested in future experiments.Comment: 4 pages, 4 figure

Spin resolved Andreev reflection in ferromagnet-superconductor junctions with Zeeman splitting

Andreev reflection in ferromagnet-superconductor junctions is derived in a regime in which Zeeman splitting dominates the response of the superconductor to an applied magnetic field. Spin-up and spin-down Andreev reflections are shown to be resolved as voltage is increased. In the metallic limit, the transition from Andreev to tunnel conductivity in the spin-up channels has a non trivial behavior when spin polarization is increased. The conductance is asymmetric in a voltage reversal.Comment: RevTex. 13 pages. 3 figures include