Excitation spectrum of a 2D long-range Bose-liquid with a supersymmetry

We have studied excitation spectrum of the specfic 2D model of strongly interacting Bose particles via mapping of the many-body Schrodinger equation in imaginary time to the classical stochastic dynamics. In a broad range of coupling strength $\alpha$ a roton-like spectrum is found, with the roton gap being extremely small in natural units. A single quantum phase transition between strongly correlated supefluid and quantum Berezinsky crystal is found.Comment: 6 pages, 6 figure

Mean field theory for driven domain walls in disordered environments

We study the mean field equation of motion for driven domain walls in random media. We discuss the two cases of an external constant as well as an oscillating driving force. Our main focus lies on the critical dynamics close to the depinning transition, which we study by analytical and numerical methods. We find power-law scaling for the velocity as well as the hysteresis loop area.Comment: 16 pages, 19 figures, submitted to Phys. Rev.

Proximity-induced superconductivity in graphene

We propose a way of making graphene superconductive by putting on it small superconductive islands which cover a tiny fraction of graphene area. We show that the critical temperature, T_c, can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, T<<T_c, and zero magnetic field, the density of states is characterized by a small gap E_g<T_c resulting from the collective proximity effect. Transverse magnetic field H_g(T) E_g is expected to destroy the spectral gap driving graphene layer to a kind of a superconductive glass state. Melting of the glass state into a metal occurs at a higher field H_{g2}(T).Comment: 4 pages, 3 figure

Coherent transport in Josephson-Junction rhombi chain with quenched disorder

We consider a chain of Josephson-junction rhombi (proposed originally by Doucot and Vidal) in quantum regime. In a regular chain with no disorder in the maximally frustrated case when magnetic flux through each rhombi \Phi_r is equal to one half of superconductive flux quantum \Phi_0, Josephson current is due to correlated transport of pairs of Cooper pairs, i.e. charge is quantized in units of $4e$. Sufficiently strong deviation \delta\Phi =|\Phi_r-\Phi_0/2| > \delta\Phi^c from the maximally frustrated point brings the system back to usual $2e$-quantized supercurrent. For a regular chain \delta\Phi^c was calculated by us previously. Here we present detailed analysis of the effect of quenched disorder (random stray charges and random fluxes piercing rhombi) on the pairing effect.Comment: 21 pages, 5 figure

Universal and non-universal tails of distribution functions in the directed polymer and KPZ problems

The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(F) for an elastic string (of a large but finite length L) interacting with a quenched random potential. A further modification of this approach is proposed which takes into account the renormalization effects and allows one to study the most close (universal) parts of the tails. The problem is analyzed for different dimensions of a space in which the polymer is imbedded. In terms the stochastic growth problem, the same distribution function describes the distribution of heights in the regime of a non-stationary growth in a situation when an interface starts to grow from a flat configuration.Comment: 17 pages, 2 figures, the final version, two paragraphs added to the conclusio

Coulomb Blockade of Proximity Effect at Large Conductance

We consider the proximity effect in a normal dot coupled to a bulk superconducting reservoir by the tunnel contact with large normal conductance. Coulomb interaction in the dot suppresses the proximity minigap induced in the normal part of the system. We find exact expressions for the thermodynamic and tunneling minigaps as functions of the junction's capacitance. The tunneling minigap interpolates between its proximity-induced value in the regime of weak Coulomb interaction to the Coulomb gap in the regime of strong interaction. In the intermediate case a non-universal two-step structure of the tunneling density of states is predicted. The charge quantization in the dot is also studied.Comment: 4 pages (RevTeX), 3 figures. Version 2: minor corrections, a figure and two references adde

Eigenfunction fractality and pseudogap state near superconductor-insulator transition

We develop a theory of a pseudogap state appearing near the superconductor-insulator transition in strongly disordered metals with attractive interaction. We show that such an interaction combined with the fractal nature of the single particle wave functions near the mobility edge leads to an anomalously large single particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem

Josephson Effect in a Coulomb-blockaded SINIS Junction

The problem of Josephson current through Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as phase bias changes from 0 to pi. In the broad range of Coulomb strength the current-phase relation is substantially non-sinusoidal and qualitatively different from the case of semi-ballistic SNS junctions. Coulomb interaction leads to appearance of a local minimum in the current at some intermediate value of phase difference applied to the junction.Comment: 5 pages, 2 EPS figures, JETP Letters style file include

Theory of 4e versus 2e supercurrent in frustrated Josepshon-junction rhombi chain

We consider a chain of Josepshon-junction rhombi (proposed originally in \cite{Doucot}) in quantum regime, and in the realistic case when charging effects are determined by junction capacitances. In the maximally frustrated case when magnetic flux through each rhombi $\Phi_r$ is equal to one half of superconductive flux quantum $\Phi_0$, Josepshon current is due to correlated transport of {\em pairs of Cooper pairs}, i.e. charge is quantized in units of $4e$. Sufficiently strong deviation $\delta\Phi \equiv |\Phi_r-\Phi_0/2| > \delta\Phi^c$ from the maximally frustrated point brings the system back to usual $2e$-quantized supercurrent. We present detailed analysis of Josepshon current in the fluctuation-dominated regime (sufficiently long chains) as function of the chain length, $E_J/E_C$ ratio and flux deviation $\delta\Phi$. We provide estimates for the set of parameters optimized for the observation of $4e$-supercurrent.Comment: 23 pages, 9 figure

Order and Creep in Flux Lattices and CDWs Pinned by Planar Defects

The influence of randomly distributed point impurities \emph{and} planar defects on the order and transport in type-II superconductors and related systems is considered theoretically. For planar defects of identical orientation the flux line lattice exhibits a new glassy phase dominated by the planar defects with a finite compressibility, a transverse Meissner effect, large sample to sample fuctuations of the susceptibility and an exponential decay of translational long range order. The flux creep resistivity for currents $J$ parallel to the defects is $\rho(J)\sim \exp-(J_0/J)^{3/2}$ . Strong disorder enforces an array of dislocations to relax shear strain