Cooper Instability in the Occupation Dependent Hopping Hamiltonians

A generic Hamiltonian, which incorporates the effect of the orbital contraction on the hopping amplitude between the nearest sites, is studied both analytically at the weak coupling limit and numerically at the intermediate and strong coupling regimes for finite atomic cluster. The effect of the orbital contraction due to hole localization at atomic sites is specified with two coupling parameters V and W (multiplicative and additive contraction terms). The singularity of the vertex part of the two-particle Green's function determines the critical temperature Tc and the relaxation rate Gamma(T) of the order parameter at temperature above Tc. Unlike in conventional BCS superconductors, Gamma has a non-zero imaginary part which may influence the fluctuation conductivity of superconductor above Tc. We compute the ground state energy as a function of the particle number and magnetic flux through the cluster, and show the existence of the parity gap Delta appearing at the range of system parameters consistent with the appearance of Cooper instability. Numeric calculation of the Hubbard model (with U>0) at arbitrary occupation does not show any sign of superconductivity in small cluster.Comment: 13 pages, 12 figure

Non-adiabatic Josephson Dynamics in Junctions with in-Gap Quasiparticles

Conventional models of Josephson junction dynamics rely on the absence of low energy quasiparticle states due to a large superconducting gap. With this assumption the quasiparticle degrees of freedom become "frozen out" and the phase difference becomes the only free variable, acting as a fictitious particle in a local in time Josephson potential related to the adiabatic and non-dissipative supercurrent across the junction. In this article we develop a general framework to incorporate the effects of low energy quasiparticles interacting non-adiabatically with the phase degree of freedom. Such quasiparticle states exist generically in constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. Furthermore, recent experiments have revealed the existence of spurious low energy in-gap states in tunnel junctions of conventional superconductors - a system for which the adiabatic assumption typically is assumed to hold. We show that the resonant interaction with such low energy states rather than the Josephson potential defines nonlinear Josephson dynamics at small amplitudes.Comment: 9 pages, 1 figur

Transport and magnetization dynamics in a superconductor/single-molecule magnet/superconductor junction

We study dc-transport and magnetization dynamics in a junction of arbitrary transparency consisting of two spin-singlet superconducting leads connected via a single classical spin precessing at the frequency $\Omega$. The presence of the spin in the junction provides different transmission amplitudes for spin-up and spin-down quasiparticles as well as a time-dependent spin-flip transmission term. For a phase biased junction, we show that a steady-state superconducting charge current flows through the junction and that an out-of-equilibrium circularly polarized spin current, of frequency $\Omega$, is emitted in the leads. Detailed understanding of the charge and spin currents is obtained in the entire parameter range. In the adiabatic regime, $\hbar \Omega \ll 2\Delta$ where $\Delta$ is the superconducting gap, and for high transparencies of the junction, a strong suppression of the current takes place around \vp \approx 0 due to an abrupt change in the occupation of the Andreev bound-states. At higher values of the phase and/or precession frequency, extended (quasi-particle like) states compete with the bound-states in order to carry the current. Well below the superconducting transition, these results are shown to be weakly affected by the back-action of the spin current on the dynamics of the precessing spin. Indeed, we show that the Gilbert damping due to the quasi-particle spin current is strongly suppressed at low-temperatures, which goes along with a shift of the precession frequency due to the condensate. The results obtained may be of interest for on-going experiments in the field of molecular spintronics.Comment: 19 pages, 13 figures (v3) Minor modifications per referee's comments. No change in results. (v2) 2 authors added, 1 reference added (Ref. 25), no change in the text and result

Antilocalization in Coulomb Blockade

We study the effect of spin-orbit scattering on the statistics of the conductance of a quantum dot for Coulomb blockade peaks and valleys. We find the distribution function of the peak heights for strong spin-orbit scattering in the presence and absence of time reversal symmetry. We find that the application of a magnetic field suppresses the average peak height, similar to the antilocalizaion in the bulk systems. For the valleys, we consider the elastic cotunneling contribution to the conductance and calculate its moments at the crossover between ensembles of various symmetries.Comment: 4 pages, 2 figure

Quantum phase slips in the presence of finite-range disorder

To study the effect of disorder on quantum phase slips (QPS) in superconducting wires, we consider the plasmon-only model where disorder can be incorporated into a first-principles instanton calculation. We consider weak but general finite-range disorder and compute the formfactor in the QPS rate associated with momentum transfer. We find that the system maps onto dissipative quantum mechanics, with the dissipative coefficient controlled by the wave (plasmon) impedance Z of the wire and with a superconductor-insulator transition at Z=6.5 kOhm. We speculate that the system will remain in this universality class after resistive effects at the QPS core are taken into account.Comment: 4 pages, as accepted at Phys. Rev. Letter

Interaction of a Nanomagnet with a Weak Superconducting Link

We study electromagnetic interaction of a nanomagnet with a weak superconducting link. Equations that govern coupled dynamics of the two systems are derived and investigated numerically. We show that the presence of a small magnet in the proximity of a weak link may be detected through Shapiro-like steps caused by the precession of the magnetic moment. Despite very weak magnetic field generated by the weak link, a time-dependent bias voltage applied to the link can initiate a non-linear dynamics of the nanomagnet that leads to the reversal of its magnetic moment. We also consider quantum problem in which a nanomagnet interacting with a weak link is treated as a two-state spin system due to quantum tunneling between spin-up and spin-down states.Comment: 7 pages, 4 figure

Quantum phase slips in a confined geometry

We consider tunneling of vortices across a superconducting film that is both narrow and short (and connected to bulk superconducting leads at the ends). We find that in the superconducting state the resistance, at low values of the temperature (T) and current, does not follow the power-law dependence on T characteristic of longer samples but is exponential in 1/T. The coefficient of 1/T in the exponent depends on the length or, equivalently, the total normal-state resistance of the sample. These conclusions persist in the one-dimensional limit, which is similar to the problem of quantum phase slips in an ultra-narrow short wire.Comment: 14 pages, 1 figure; published in Phys. Rev.

Josephson current noise above Tc in superconducting tunnel junctions

Tunnel junction between two superconductors is considered in the vicinity of the critical temperature. Superconductive fluctuations above Tc give rise to the noise of the ac Josephson current although the current itself is zero in average. As a result of fluctuations, current noise spectrum is peaked at the Josephson frequency, which may be considered as precursor of superconductivity in the normal state. Temperature dependence and shape of the Josephson current noise resonance line is calculated for various junction configurations.Comment: 8 pages, 2 figure