Current-voltage characteristics of asymmetric double-barrier Josephson junctions

We develop a theory for the current-voltage characteristics of diffusive superconductor-normal metal-superconductor Josephson junctions with resistive interfaces and the distance between the electrodes smaller than the superconducting coherence length. The theory allows for a quantitative analytical and numerical analysis in the whole range of the interface transparencies and asymmetry. We focus on the regime of large interface resistance compared to the resistance of the normal region, when the electron-hole dephasing in the normal region is significant and the finite length of the junction plays a role. In the limit of strong asymmetry we find pronounced current structures at the combination subharmonics of $\Delta+\Delta_g$, where $\Delta_g$ is the proximity minigap in the normal region, in addition to the subharmonics of the energy gap $2\Delta$ in the electrodes. In the limit of rather transparent interfaces, our theory recovers a known formula for the current in a short mesoscopic connector - a convolution of the current through a single-channel point contact with the transparency distribution for an asymmetric double-barrier potential.Comment: 10 pages, 3 figure

Scattering theory of superconductive tunneling in quantum junctions

We present a consistent theory of superconductive tunneling in single-mode junctions within a scattering formulation of Bogoliubov-de Gennes quantum mechanics. Both dc Josephson effect and dc quasiparticle transport in voltage biased junctions are considered. Elastic quasiparticle scattering by the junction determines equilibrium Josephson current. We discuss the origin of Andreev bound states in tunnel junctions and their role in equilibrium Josephson transport. In contrast, quasiparticle tunneling in voltage biased junctions is determined by inelastic scattering. We derive a general expression for inelastic scattering amplitudes and calculate the quasiparticle current at all voltages with emphasis on a discussion of the properties of subgap tunnel current and the nature of subharmonic gap structure.Comment: 47 pages, 9 figures, [preprint,eqsecnum,aps]{revtex

Dissipative charge transport in diffusive superconducting double-barrier junctions

We solve the coherent multiple Andreev reflection (MAR) problem and calculate current-voltage characteristics (IVCs) for Josephson SINIS junctions, where S are local-equilibrium superconducting reservoirs, I denotes tunnel barriers, and N is a short diffusive normal wire, the length of which is much smaller than the coherence length, and the resistance is much smaller than the resistance of the tunnel barriers. The charge transport regime in such junctions qualitatively depends on a characteristic value \gamma = \Delta \tau_d of relative phase shifts between the electrons and retro-reflected holes accumulated during the dwell time \tau_d. In the limit of small electron-hole dephasing \gamma << 1, our solution recovers a known formula for a short mesoscopic connector extended to the MAR regime. At large dephasing, the subharmonic gap structure in the IVC scales with 1/ \gamma, which thus plays the role of an effective tunneling parameter. In this limit, the even gap subharmonics are resonantly enhanced, and the IVC exhibits portions with negative differential resistance.Comment: 8 pages, 3 figures, typos corrected, to be published in Phys. Rev.

Multiple Andreev reflections and enhanced shot noise in diffusive SNS junctions

We study the dc conductance and current fluctuations in diffusive voltage biased SNS junctions with a tunnel barrier inside the mesoscopic normal region. We find that at subgap voltages, eV<2Delta/n, the current associated with the chain of n Andreev reflections is mapped onto the quasiparticle flow through a structure of n+1 voltage biased barriers connected by diffusive conductors. As a result, the current-voltage characteristic of a long SNINS structure obeys Ohm's law, in spite of the complex multiparticle transport process. At the same time, nonequilibrium heating of subgap electrons produces giant shot noise with pronounced subharmonic gap structure which corresponds to stepwise growth of the effective transferred charge. At eV\to 0, the shot noise approaches the magnitude of the Johnson-Nyquist noise with the effective temperature T^*=Delta/3, and the effective charge increases as (e/3)(1 + 2Delta/eV), with the universal ``one third suppression'' factor. We analyse the role of inelastic scattering and present a criterion of strong nonequilibrium.Comment: 4 pages, 2 figure

On the theory of Josephson effect in a diffusive tunnel junction

Specific features of the equilibrium current-carrying state of a Josephson tunnel junction between diffusive superconductors are studied theoretically in the 1D geometry. It is found that the Josephson current induces localized states of electron excitations in the vicinity of the tunnel barrier, which are a continuous analog of Andreev levels in a ballistic junction. The depth of the corresponding ``potential well'' is much greater than the separation between an Andreev level and the continuous energy spectrum boundary for the same transmissivity of the barrier. In contrast to a ballistic junction in which the Josephson current is transported completely by localized excitations, the contribution to current in a diffusive junction comes from whole spectral region near the energy gap boundary, where the density of states differs considerably from its unperturbed value. The correction to the Josephson current in the second order of the barrier transmissivity, which contains the second harmonic of the phase jump, is calculated and it is found that the true expansion parameter of the perturbation theory for a diffusive junction is not the tunneling probability $\Gamma$ itself, but a much larger parameter $W = (3\xi_0/4l)\Gamma$.Comment: 8 pages, 5 Postscript figures, submitted to Low Temp. Phy

Superconducting d-wave junctions: The disappearance of the odd ac components

We study voltage-biased superconducting planar d-wave junctions for arbitrary transmission and arbitrary orientation of the order parameters of the superconductors. For a certain orientation of the superconductors the odd ac components disappear, resulting in a doubling of the Josephson frequency. We study the sensitivity of this disappearance to orientation and compare with experiments on grain boundary junctions. We also discuss the possibility of a current flow parallel to the junction.Comment: 5 pages, 3 figure

Resonant multiple Andreev reflections in mesoscopic superconducting junctions

We investigate the properties of subharmonic gap structure (SGS) in superconducting quantum contacts with normal-electron resonances. We find two distinct new features of the SGS in resonant junctions which distinguish them from non-resonant point contacts: (i) The odd-order structures on the current-voltage characteristics of resonant junctions are strongly enhanced and have pronounced peaks, while the even-order structures are suppressed, in the case of a normal electron resonance being close to the Fermi level. (ii) Tremendous current peaks develop at $eV=\pm 2E_0$ where $E_0$ indicates a distance of the resonance to the Fermi level. These properties are determined by the effect of narrowing of the resonance during multiple Andreev reflections and by overlap of electron and hole resonances.Comment: 13 pages, 10 figure

Subgap current in superconducting tunnel junctions with diffusive electrodes

We calculate the subgap current in planar superconducting tunnel junctions with thin-film diffusive leads. It is found that the subharmonic gap structure of the tunnel current scales with an effective tunneling transparency which may exceed the junction transparency by up to two orders of magnitude depending on the junction geometry and the ratio between the coherence length and the elastic scattering length. These results provide an alternative explanation of anomalously high values of the subgap current in tunnelling experiments often ascribed to imperfection of the insulating layer. We also discuss the effect of finite lifetime of quasiparticles as the possible origin of additional enhancement of multiparticle tunnel currents.Comment: 4 pages, 4 figures, to be published in Phys. Rev.

Andreev Level Qubit

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf-SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and read out of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits, and discuss the relevant SQUID parameters for qubit operation and read out.Comment: 4 pages, 1 figur