E. V. Bezuglyi

Circuit theory of multiple Andreev reflections in diffusive SNS junctions: The incoherent case

The incoherent regime of multiple Andreev reflections ~MAR! is studied in long diffusive SNS junctions at applied voltages larger than the Thouless energy. Incoherent MAR are treated as a transport problem in energy space by means of a circuit theory for an equivalent electrical network. The current through NS interfaces is explained in terms of diffusion flows of electrons and holes through ‘‘tunnel’’ and ‘‘Andreev’’ resistors. These resistors in diffusive junctions play roles analogous to the normal and Andreev reflection coefficients in Octavio-Tinkham-Blonder-Klapwijk theory for ballistic junctions. The theory is applied to the subharmonic gap structure ~SGS!; simple analytical results are obtained for the distribution function and current spectral density for the limiting cases of resistive and transparent NS interfaces. In the general case, the exact solution is found in terms of chain fractions, and the current is calculated numerically. SGS shows qualitatively different behavior for even and odd subharmonic numbers n52D/eV, and the maximum slopes of the differential resistance correspond to the gap subharmonics, eV52D/n. The influence of inelastic scattering on the subgap anomalies of the differential resistance is analyzed.

Current noise in long diffusive SNS junctions in the incoherent multiple Andreev reflections regime

Spectral density of current fluctuations at zero frequency is calculated for a long diffusive SNS junction with low-resistive interfaces. At low temperature, T << Delta, the subgap shot noise approaches linear voltage dependence, S=(2/ 3R)(eV + 2Delta), which is the sum of the shot noise of the normal conductor and voltage independent excess noise. This result can also be interpreted as the 1/3-suppressed Poisson noise for the effective charge q = e(1+2Delta/eV) transferred by incoherent multiple Andreev reflections (MAR). At higher temperatures, anomalies of the current noise develop at the gap subharmonics, eV = 2Delta/n. The crossover to the hot electron regime from the MAR regime is analyzed in the limit of small applied voltages.

Nonequilibrium effects in tunnel Josephson junctions

We study nonequilibrium effects in current transport through voltage biased tunnel junction with long diffusive superconducting leads at low applied voltage eV 2Δ, and finite temperatures. Due to a small value of the Josephson frequency, the quasiparticle spectrum adiabatically follows the time evolution of the superconducting phase difference, which results in the formation of oscillating bound states in the vicinity of the tunnel junction (Andreev band). The quasiparticles trapped by the Andreev band generate higher even harmonics of the. Josephson ac current, and also, in the presence of inelastic scattering, a nonequilibrium dc current, which may considerably exceed the dc quasiparticle current given by the tunnel model. The distribution of traveling quasiparticles also deviates from the equilibrium due to the spectrum oscillations, which results in an additional contribution to the dc current, proportional to V.

Subgap current in superconducting tunnel junctions with diffusive electrodes

We calculate 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 imperfectness 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.

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 = tau(d)Delta of relative phase shifts between the electrons and retroreflected 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 gamma(-1), 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.

Resonant subgap current transport in Josephson field effect transistor

We study theoretically the current-voltage characteristics (IVCs) of the Josephson field effect transistor - a ballistic SNINS junction with superconducting (S) electrodes confining a planar normal-metal region (N), which is controlled by the gate-induced potential barrier (I). Using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflection (MAR) regime, we find a significant difference of the subgap current structure compared to the subharmonic gap structure in tunnel junctions and atomic-size point contacts. For long junctions, whose lengths significantly exceed the coherence length, the IVC exhibits current peaks at multiples (harmonics) of the distance ?m between the static Andreev levels eVn=n?m. Moreover, the averaged IVC follows the powerlike behavior rather than the exponential one and has a universal scaling with the junction transparency. This result is qualitatively understood using an analytical approach based on the concept of resonant MAR trajectories. In shorter junctions having lengths comparable to the coherence length, the IVC has an exponential form common for point contacts, however the current structures appear at the subharmonics of the interlevel distance eVn=?m/n rather than the gap subharmonics 2?/n.

Multiparticle tunnelling in diffusive superconducting junctions

We formulate a theoretical framework to describe multiparticle current transport in planar superconducting tunnel junctions with diffusive electrodes. The approach is based on the direct solving of quasiclassical Keldysh–Green function equations for nonequilibrium superconductors, and consists of a combination of circuit theory analysis and improved perturbation expansion. The theory predicts a much greater scaling parameter for the subharmonic gap structure of the tunnel current in diffusive junctions compared to the one in ballistic junctions and mesoscopic constrictions with the same barrier transparency.

Nonequilibrium and relaxation effects in tunnel superconducting junctions

The specific property of a planar tunnel junction with thin-film diffusive plates and long enough leads is an essential enhancement of its transmission coefficient compared to the bare transparency of the tunnel barrier [1,2]. In voltage-biased junctions, this creates favourable conditions for strong nonequilibrium of quasiparticles in the junction plates and leads, produced by multiparticle tunneling. We study theoretically the interplay between the nonequilibrium and relaxation processes in such junctions and found that nonequilibrium in the leads noticeably modifies the current-voltage characteristic at

Phase Dependent Current Statistics in a Short-Arm Andreev Interferometer

eV > 2\Delta

Enhanced current shot noise in superconducting junctions

, especially the excess current, whereas strong diffusive relaxation restores the result of the classical tunnel model. At