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

Persistent Currents in Helical Structures

Recent discovery of mesoscopic electronic structures, in particular the carbon nanotubes, made necessary an investigation of what effect may helical symmetry of the conductor (metal or semiconductor) have on the persistent current oscillations. We investigate persistent currents in helical structures which are non-decaying in time, not requiring a voltage bias, dissipationless stationary flow of electrons in a normal-metallic or semiconducting cylinder or circular wire of mesoscopic dimension. In the presence of magnetic flux along the toroidal structure, helical symmetry couples circular and longitudinal currents to each other. Our calculations suggest that circular persistent currents in these structures have two components with periods $\Phi_0$ and $\Phi_0/s$ ($s$ is an integer specific to any geometry). However, resultant circular persistent current oscillations have $\Phi_0$ period. \pacs{PACS:}PACS:73.23.-bComment: 4 pages, 2 figures. Submitted to PR

Spin Current in p-wave Superconducting Rings

A formula of the spin current in mesoscopic superconductors is derived from the mean-field theory of superconductivity. The spin flow is generated by the spatial fluctuations of $\vec{d}$ which represents a spin state of spin-triplet superconductors. We discuss a possibility of the circulating spin current in isolated p-wave superconducting rings at the zero magnetic field. The direction of the spin current depends on topological numbers which characterize the spatial configuration of $\vec{d}$ on the ring.Comment: 4page

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