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

Stability of dynamic coherent states in intrinsic Josephson-junction stacks near internal cavity resonance

Stacks of intrinsic Josephson junctions in the resistive state can by efficiently synchronized by the internal cavity mode resonantly excited by the Josephson oscillations. We study the stability of dynamic coherent states near the resonance with respect to small perturbations. Three states are considered: the homogeneous and alternating-kink states in zero magnetic field and the homogeneous state in the magnetic field near the value corresponding to half flux quantum per junction. We found two possible instabilities related to the short-scale and long-scale perturbations. The homogeneous state in modulated junction is typically unstable with respect to the short-scale alternating phase deformations unless the Josephson current is completely suppressed in one half of the stack. The kink state is stable with respect to such deformations and homogeneous state in the magnetic field is only stable within a certain range of frequencies and fields. Stability with respect to the long-range deformations is controlled by resonance excitations of fast modes at finite wave vectors and typically leads to unstable range of the wave-vectors. This range shrinks with approaching the resonance and increasing the in-plane dissipation. As a consequence, in finite-height stacks the stability frequency range near the resonance increases with decreasing the height.Comment: 15 pages, 8 figures, to appear in Phys. Rev.

Josephson effect in mesoscopic graphene strips with finite width

We study Josephson effect in a ballistic graphene strip of length $L$ smaller than the superconducting coherence length and arbitrary width $W$. We find that the dependence of the critical supercurrent $I_{c}$ on $W$ is drastically different for different types of the edges. For \textit{smooth} and \textit{armchair} edges at low concentration of the carriers $I_{c}$ decreases monotonically with decreasing $W/L$ and tends to a constant minimum for a narrow strip $W/L\lesssim1$. The minimum supercurrent is zero for smooth edges but has a finite value $e\Delta_{0}/\hbar$ for the armchair edges. At higher concentration of the carriers, in addition to this overall monotonic variation, the critical current undergoes a series of peaks with varying $W$. On the other hand in a strip with \textit{zigzag} edges the supercurrent is half-integer quantized to $(n+1/2)4e\Delta_{0}/\hbar$, showing a step-wise variation with $W$.Comment: 4 pages, 3 figure

Josephson effect in ballistic graphene

We solve the Dirac-Bogoliubov-De-Gennes equation in an impurity-free superconductor-normal-superconductor (SNS) junction, to determine the maximal supercurrent that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result is determined by the superconducting gap and by the aspect ratio of the junction (length L, small relative to the width W and to the superconducting coherence length). Moving away from the Dirac point of zero doping, we recover the usual ballistic result in which the Fermi wave length takes over from L. The product of critical current and normal-state resistance retains its universal value (up to a numerical prefactor) on approaching the Dirac point.Comment: 4 pages, 2 figure

Phase diagram of geometric d-wave superconductor Josephson junctions

We show that a constriction-type Josephson junction realized by an epitactic thin film of a d-wave superconductor with an appropriate boundary geometry exhibits intrinsic phase differences between 0 and pi depending on geometric parameters and temperature. Based on microscopic Eilenberger theory, we provide a general derivation of the relation between the change of the free energy of the junction and the current-phase relation. From the change of the free energy, we calculate phase diagrams and discuss transitions driven by geometric parameters and temperature.Comment: 9 pages, 11 figures. Phys. Rev. B, accepte

Electron-electron interactions in antidot-based Aharonov-Bohm interferometers

We present a microscopic picture of quantum transport in quantum antidots in the quantum Hall regime taking electron interactions into account. We discuss the edge state structure, energy level evolution, charge quantization and linear-response conductance as the magnetic field or gate voltage is varied. Particular attention is given to the conductance oscillations due to Aharonov-Bohm interference and their unexpected periodicity. To explain the latter we propose the mechanisms of scattering by point defects and Coulomb blockade tunneling. They are supported by self-consistent calculations in the Hartree approximation, which indicate pinning and correlation of the single-particle states at the Fermi energy as well as charge oscillation when antidot-bound states depopulate. We have also found interesting phenomena of anti-resonance reflection of the Fano type.Comment: 12 pages, 8 figure

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