Charge imbalance and Josephson effects in superconductor-normal metal mesoscopic structures

We consider a $SBS$ Josephson junction the superconducting electrodes $S$ of which are in contact with normal metal reservoirs ($B$ means a barrier). For temperatures near $T_{c}$ we calculate an effective critical current $I_{c}^{\ast}$ and the resistance of the system at the currents $I<$ $I_{c}^{\ast}$ and $I>>I_{c}^{\ast}$. It is found that the charge imbalance, which arises due to injection of quasiparticles from the $N$ reservoirs into the $S$ wire, affects essentially the characteristics of the structure. The effective critical current $I_{c}^{\ast}$ is always larger than the critical current $I_{c}$ in the absence of the normal reservoirs and increases with decreasing the ratio of the length of the $S$ wire $2L$ to the charge imbalance relaxation length $l_{Q}$. It is shown that a series of peaks arises on the $I-V$ characteristics due to excitation of the Carlson-Goldman collective modes. We find the position of Shapiro steps which deviates from that given by the Josephson relation.Comment: 12 pages, 4 figures; accepted for publication in Phys. Rev.

Intrinsic Josephson Effect and Violation of the Josephson Relation in Layered Superconductors

Equations describing the resistive state of a layered superconductor with anisotropic pairing are derived. The similarity with a stack of Josephson junctions is found at small voltages only, when current density in the direction perpendicular to the layers can be interpreted as a sum of the Josephson superconducting, the Ohmic dissipative and the interference currents. In the spatially uniform state differential conductivity at higher voltages becomes negative. Nonuniformity of the current distribution generates the branch imbalance and violates the Josephson relation between frequency and voltage.Comment: 11 pages, no figures, revtex, to be published in Phys. Rev. Let

Subharmonic gap structure in short ballistic graphene junctions

We present a theoretical analysis of the current-voltage characteristics of a ballistic superconductor-normal-superconductor (SNS) junction, in which a strip of graphene is coupled to two superconducting electrodes. We focus in the short-junction regime, where the length of the strip is much smaller than superconducting coherence length. We show that the differential conductance exhibits a very rich subharmonic gap structure which can be modulated by means of a gate voltage. On approaching the Dirac point the conductance normalized by the normal-state conductance is identical to that of a short diffusive SNS junction.Comment: revtex4, 4 pages, 4 figure

Character of electron reflection at a normal metal-Peierls semiconductor boundary

The reflection of electrons incident from a normal metal on the boundary of the metal with a quasi-one-dimensional conductor containing a charge-density wave (CDW) is investigated theoretically. It is shown that the reflection is not of an Andreev character, as it was suggested earlier, but rather of a Bragg character. This is due to the fact that the CDW is actually an electronic crystal, and its wave vector is a reciprocal lattice vector of the electronic crystal. The ratio of the intensities of the standard and Bragg reflection depends on the phase of the CDW.Comment: 9 pages, no figures, revte

On Effect of Equilibrium Fluctuations on Superfluid Density in Layered Superconductors

We calculate suppression of inter- and intralayer superconducting currents due to equilibrium phase fluctuations and find that, in contrast to a recent prediction, the effect of thermal fluctuations cannot account for linear temperature dependence of the superfluid density in high-Tc superconductors at low temperatures. Quantum fluctuations are found to dominate over thermal fluctuations at low temperatures due to hardening of their spectrum caused by the Josephson plasma resonance. Near Tc sizeable thermal fluctuations are found to suppress the critical current in the stack direction stronger, than in the direction along the layers. Fluctuations of quasiparticle branch imbalance make the spectral density of voltage fluctuations at small frequencies non zero, in contrast to what may be expected from a naive interpretation of Nyquist formula.Comment: 5 pages, LaTeX, RevTeX, Submitted to PR

Linear response and collective oscillations in superconductors with d-wave pairing

Simple and physically transparent equations for the linear response of layered superconductors with d-wave symmetry of the order parameter are derived by means of the quasiclassic kinetic theory of superconductivity. Responses to solenoidal and potential electric fields have different frequency dependencies. The conductivity describing the response to the solenoidal field is limited by the momentum relaxation, like in a normal metal. The response to the potential electric field depends, in addition, on the branch imbalance relaxation rate. The damping of plasma oscillations of superconducting electrons is determined by dielectric relaxation and is small. Relaxation of branch imbalance determined by elastic scattering is large enough to make the Carlson-Goldman mode in d-wave superconductors overdamped.Comment: 11 pages, latex, no figures, submitted to Physical Review