Josephson dynamics and Shapiro steps at high transmissions: current bias regime.

We investigate Josephson dynamics of highly transparent superconducting nanojunctions at subgap voltages and temperatures. In this limit, intrinsic dissipation in such junctions turns out to be sub-Ohmic, which yields a linear dependence of the average voltage on the bias current slightly exceeding the critical one . We demonstrate a strong impact of intrinsic sub-Ohmic dissipation on integer Shapiro steps appearing on the - curve in the presence of external microwave radiation.

Cooper pair splitting controlled by a temperature gradient.

Electrons in two different normal metallic electrodes attached to a sufficiently thin superconducting island may become entangled due to the effect of Cooper pair splitting. This phenomenon is of fundamental importance and may also have serious implications for developing quantum communication technologies. One way to identify Cooper pair splitting is to analyze long-range cross correlations of fluctuating currents in three-terminal hybrid normal-superconducting-normal nanostructures.

Plasma modes in capacitively coupled superconducting nanowires.

We investigate plasma oscillations in long electromagnetically coupled superconducting nanowires. We demonstrate that in the presence of inter-wire coupling plasma modes in each of the wires get split into two "new" modes propagating with different velocities across the system. These plasma modes form an effective dissipative quantum environment interacting with electrons inside both wires and causing a number of significant implications for the low-temperature behavior of the systems under consideration.

Superconductor-insulator transition in capacitively coupled superconducting nanowires.

We investigate superconductor-insulator quantum phase transitions in ultrathin capacitively coupled superconducting nanowires with proliferating quantum phase slips. We derive a set of coupled Berezinskii-Kosterlitz-Thouless-like renormalization group equations demonstrating that interaction between quantum phase slips in one of the wires gets modified due to the effect of plasma modes propagating in another wire. As a result, the superconductor-insulator phase transition in each of the wires is controlled not only by its own parameters but also by those of the neighboring wire as well as by mutual capacitance.

Interplay between Josephson and Aharonov-Bohm effects in Andreev interferometers.

Proximity induced quantum coherence of electrons in multi-terminal voltage-driven hybrid normal-superconducting nanostructures may result in a non-trivial interplay between topology-dependent Josephson and Aharonov-Bohm effects. We elucidate a trade-off between stimulation of the voltage-dependent Josephson current due to non-equilibrium effects and quantum dephasing of quasiparticles causing reduction of both Josephson and Aharonov-Bohm currents. We also predict phase-shifted quantum coherent oscillations of the induced electrostatic potential as a function of the externally applied magnetic flux.

Theory of a large thermoelectric effect in superconductors doped with magnetic impurities.

We argue that parametrically strong enhancement of a thermoelectric current can be observed in conventional superconductors doped by magnetic impurities. This effect is caused by the violation of the symmetry between electronlike and holelike excitations due to formation of subgap bound Andreev states in the vicinity of magnetic impurities. We develop a quantitative theory of this effect and demonstrate that it can be detected in modern experiments.

Triplet superconductivity in a ferromagnetic vortex.

We argue that triplet superconductivity can be conveniently realized in hybrid superconductor-ferromagnet (S-F) structures with a ferromagnetic vortex. We demonstrate that due to proximity-induced long-range triplet pairing such S-F-S junctions can sustain appreciable supercurrent which can be directly measured in experiments. Depending on the contact geometry either zero- or π-junction regime can be realized in the system under consideration.

Crossed Andreev reflection and charge imbalance in diffusive normal-superconducting-normal structures.

We formulate a microscopic theory of nonlocal electron transport in three-terminal diffusive normal-superconducting-normal (NSN) structures with arbitrary interface transmissions. At low energies epsilon, we predict strong enhancement of nonlocal spectral conductance g_{12} proportional, variant1/epsilon due to quantum interference of electrons in disordered N terminals. In contrast, nonlocal resistance R_{12} remains smooth at small epsilon and, furthermore, is found to depend neither on parameters of normal-superconducting interfaces nor on those of N terminals.