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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). The calculations were performed using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflections (MAR) regime. We find significant difference of the subgap current structure in these junctions compared to the subharmonic gap structure in tunnel junctions and atomic-size point contacts. For long junctions, whose length significantly exceeds the coherence length, the IVC exhibits current peaks at multiples (harmonics) of the difference $\delta_m$ between the static Andreev levels, $eV_n = n\delta_m$. Moreover, the averaged IVC follows the power rather than exponential behavior, 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 whose length is 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 Andreev interlevel distance, $eV_n = \delta_m/n$ rather than the gap subharmonics $2\Delta/n$., Comment: 10 pages, 11 figures, submitted to Phys. Rev. B

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 figures

Andreev bound states in superconducting quantum point contacts (QPC) can be accessed for manipulation and measurement by embedding the QPC in a superconducting loop. We discuss the characteristics of such a device suitable for qubit operation, methods of manipulations with the Andreev levels, and qubit coupling.

We report the results of an investigation of the effect of the superconducting bound states on coherent multiple Andreev reflections in quantum SNS junctions. A rich resonant structure of the current, associated with the bound states and consisting of peaks, onsets and oscillations, is found by numerical calculations. Positions of the current structures are not given by subharmonics of the energy gap but rather determined by the junction geometry. We present analytical classification of the resonant current structures and calculate their positions and amplitudes. We show that the resonant current structures in three-terminal SNS interferometers can be controlled by external magnetic flux.

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 $eV > 2\Delta$, especially the excess current, whereas strong diffusive relaxation restores the result of the classical tunnel model. At $eV \leq 2\Delta$, the diffusive relaxation decreases the peaks of the multiparticle currents. The inelastic relaxation in the junction plates essentially suppresses the $n$-particle currents ($n>2$) by the factor $n$ for odd and $n/2$ for even $n$. The results may be important for the problem of decoherence in Josephson-junction based superconducting qubits., Comment: 8 pages, 5 figures, references added, accepted by Superconductor Science and Technology

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 is 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 OTBK 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, and the maximum slopes of the differential resistance correspond to the gap subharmonics. The influence of inelastic scattering on the subgap anomalies of the differential resistance is analyzed., 14 pages, 9 figures, title and text revised, to appear in PRB

Single atom junctions between superconducting niobium leads are produced using the Mechanically Controllable Break Junction technique. The current-voltage characteristics of these junctions are analysed using an exact formulation for a superconducting quantum point contact. For tunnelling between two single atoms with a sufficiently large vacuum barrier, it is found that a single channel dominates the current, and that the current-voltage characteristic is described by the theory, without adjustable parameters. For a contact of a single Nb atom it is shown that five conductance channels contribute to the conductance, in agreement with the number expected based on the number of valence orbitals for this d-metal. For each of the channels the transmission probability is obtained from the fits and the limits of accuracy for these numbers are discussed., 11 pages; submitted to Phys. Rev. B

We study the dc conductance and current fluctuations in mesoscopic diffusive SNS junctions at subgap applied voltages $\mathrm{eV}l2\ensuremath{\Delta}$. We find that in spite of the multiple Andreev reflections, the current-voltage characteristic of a long SNINS structure obeys Ohm's law. At the same time, non-equilibrium heating of subgap electrons produces giant shot noise with pronounced subharmonic gap structure which corresponds to stepwise growth of the effective transferred charge. At $\mathrm{eV}\ensuremath{\rightarrow}0$, the shot noise approaches the magnitude of the Johnson-Nyquist noise with the effective temperature ${T}^{\ensuremath{\star}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\Delta}/3$. We analyze the role of inelastic scattering and present a criterion of strong nonequilibrium.

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. Phys

We calculate the current-voltage characteristics (IVC) of a biased superconducting junction with a tunnel resonance. Within a simple one-dimensional model we discuss how the IVCs depend on the position and width of the resonance. We consider both subgap region and excess current. The results provide a possible explanation of the anomaly in the onset of c-axis current in recent experiments on intrinsic Josephson effect in BSCCO.

Multiple Andreev scattering in single-mode superconducting junctions with arbitrary normal electron transparency 01 is studied in the limit of low applied voltage eV\ensuremath{\ll}\ensuremath{\Delta}. A quasiclassical approach is developed for investigation of the dense lattice of inelastic sidebands associated with multiple Andreev scattering, which gives a global description of inelastic-scattering amplitudes and spectral distribution of the current. The crossover from the contact to the tunnel regime is investigated for the dc current and ac Josephson current as function of junction transparency and applied voltage. A mesoscopic interference effect in junctions with intermediate transparency is discussed. This effect shows up in oscillating features of the current of thermal excitations.

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. B

We formulate a theoretical framework to describe multiparticle current transport in planar superconducting tunnel junctions with diffusive electrodes. The approach is based on direct solving of quasiclassical Keldysh-Green function equations for nonequilibrium superconductors, and consists of a combination of a circuit theory analysis and improved perturbation expansion. The theory predicts 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., Comment: 18 pages, 6 figures, to be published in Supercond. Sci. Techn

We calculate analytically the full counting statistics for a short normally conducting diffusive wire connecting a normal reservoir and a short superconductornormal metal-superconductor junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference φ across the junction and approaches the normal-state value at φ = π. At T = 0 and at applied voltage much smaller than the proximity gap ∆φ, the current noise PI doubles and the third current cumulant C3 is 4 times larger compared to the normal state; at eV ≫∆φ they acquire large excess components. At the gap edge, eV = ∆φ, the differential shot noise dPI/dV exhibits sharp peak, while the differential Fano factor dPI/dI turns to zero along with the differential resistance, which reflects the transmission resonance associated with the singularity of the density of states. At nonzero temperature, C3 shows a non-monotonous voltage dependence with a dip near eV = ∆φ; the zero-bias slope of C3(V ) is much larger (up to 5 times) than at the zero temperature. During last few years the statistics of quantum and thermal fluctuations of the electric current in mesoscopic systems has been attracted a rapidly growing attention. It was recognized that measuring the fluctuation properties of mesoscopic conductors provide unique and important information about correlations and statistics of charge carriers, the information that is not accessible through conventional conductance measurements. An adequate and powerful

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., 4 pages, 4 figures, to be published in Phys. Rev. B

We present detailed theory for Andreev level qubit, the system consisting of a highly transmissive quantum point contact embedded in a superconducting loop. The two-level Hamiltonian for Andreev levels interacting with quantum phase fluctuations is derived by using the path integral method. We also derive kinetic equation describing qubit decoherence due to interaction of the Andreev levels with acoustic phonons. The collision terms are non-linear due to fermionic nature of the Andreev states, leading to slow non-exponential relaxation and dephasing of the qubit at temperature smaller than the qubit level spacing., 22 pages, 7 figures

We calculate analytically the current statistics for a short diffusive wire between the normal reservoir and a short superconductor-normal metal-superconductor (SNS) junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference $\phi$ across the junction, approaching the normal-state value at $\phi=\pi$. At T=0 and at the applied voltage much smaller than the proximity gap $\Delta_\phi$, the current noise $P_I$ doubles and the third current cumulant $C_3$ is 4 times larger with respect to their values in the normal state; at $eV \gg \Delta_\phi$ they acquire large excess components. At the gap edge, $eV = \Delta_\phi$, the effective transferred charge defined through $dP_I/dI$ and $dP_I/dV$ approaches $0e$ and $3e$, respectively, which makes doubtful the interpretation of these quantities as physical elementary transferred charge. At $T \neq 0$, $C_3$ shows a non-monotonous voltage dependence with a dip near $eV = \Delta_\phi$., Comment: 13 pages, to be published in Proc. NATO ARW "Quantum Transport in Metallic and Hybrid Nanostructures", StPetersburg, 2003

We present theory for a current shot noise in mesoscopic diffusive superconductor-normal metal-superconductor (SNS) junctions. The current shot noise is tremendously enhanced at small applied voltage, V < Δ/e, due to the mechanism of multiple Andreev reflection (MAR), which creates long correlated trains of transmitted electrons. The central result for the MAR regime is a universal value for the noise power in the limit of small voltage and at zero physical temperature, which corresponds to the effective noise temperature of the order of superconducting energy gap Δ. At very small voltage, MAR is destroyed by inelastic relaxation, consequently, the level of noise reduces and approaches at V = 0 the thermal noise value. We investigate the suppression of MAR by inelastic scattering processes and analyze the crossover from the MAR regime to a hot electron regime.

During last decade considerable progress has been made in the investigation and understanding the mechanisms of current transport in mesoscopic superconducting junctions. The term mesoscopic here refers to the junctions where bulk superconducting electrodes in equilibrium (reservoirs) are connected by small nonsuperconducting region with the size smaller than any inelastic mean free path. Such junctions include metallic atomic-size contacts, tunnel junctions, diffusive (metallic) and ballistic (2D electron gas) SNS junctions. A common feature of all these structures concerns the fact that the quasiparticles injected in the junction at zero temperature cannot escape into the reservoir unless the applied voltage is larger than the superconducting energy gap in the reservoir, eV > 2Δ. In 1963, Schrieffer and Wilkins suggested that the necessary energy for the quasiparticle transmission at subgap voltage, eV < 2Δ can be provided by transferring Cooper pairs between the reservoirs [1].

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., 4 pages, 1 figure

A theory of coherent multiple Andreev reflections (MAR) is developed for superconductor-normal metal-superconductor (SNS) interferometers. We consider a Y-shape normal electron beam splitter connecting two superconducting reservoirs, where the two connection points to the same superconductor can have different phase. The current is calculated in the quantum transport regime as a function of applied voltage and phase difference, $I(V,\phi)$. MAR in interferometers incorporates two features: interference in the arms of the splitter, and interplay with Andreev resonances. The latter feature yields enhancement of the subgap current and current peaks with phase-dependent positions and magnitudes. The interference effect leads to suppression of the subgap current and complete disappearance of the current peaks at $\phi=\pi$. The excess current at large voltage decreases and changes sign with increasing phase difference.

Spectral density of current fluctuations at zero frequency is calculated for a long diffusive SNS junction with low-resistive interfaces. At low temperature, $T\ensuremath{\ll}\ensuremath{\Delta},$ the subgap shot noise approaches linear voltage dependence, $S=(2/3R)(eV+2\ensuremath{\Delta}),$ 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 $q=e(1+2\ensuremath{\Delta}/eV)$ transferred by incoherent multiple Andreev reflections (MAR). At higher temperatures, anomalies of the current noise develop at the gap subharmonics, $eV=2\ensuremath{\Delta}/n.$ The crossover to the hot electron regime from the MAR regime is analyzed in the limit of small applied voltages.

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 figures

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., 47 pages, 9 figures, [preprint,eqsecnum,aps]{revtex}

We develop a theory of subharmonic gap structure (SGS) in superconducting one-mode tunnel junction. The subgap current is attributed to inelastic multichannel quasiparticle tunneling assisted by the time-dependent phase difference at the contact. Opening of inelastic scattering channels is manifested in onsets and peaks of tunnel current forming SGS. An explicit analytical expansion is found for the tunnel current in powers of small contact transparency.

We study the manifestations of superconducting current-induced bound states in the ac Josephson effect in tunnel contacts. Due to the normal elelctron backscattering by the contact, the bound states have a two-level structure, which allows direct interlevel transitions driven by an electromagnetic field introduced in the dielectric layer. We find substantial nonequilibrium suppression of the Josephson current, and nonlinear current oscillations induced by a resonant applied electromagnetic field.

The research of V. P. Galaiko, Fiz. Nizk. Temp. 19, 123 (1993) [Low Temp. Phys. 19, 87 (1993)] on electronic orbital effects in samples of a high-Tc superconductor (Y–Ba–Cu–O) in the normal state is continued for the case of dc galvanomagnetic effects. The conductivity tensor, resistivity, and Hall coefficient are calculated. The results agree qualitatively with experiment.

The problem of nonlinear absorption of a stochastic acoustic signal in superconductors is reduced to an investigation of the states of the one-dimensional Dirac equation in a coordinate system moving with constant velocity and with a random potential. In the present paper a study is made of the properties of the problem of scattering by a random potential that determine the rate of dissipation of the acoustic energy and also of the localized properties of solutions in the case of an infinitely extended signal. If the projection of the Fermi velocity of an electron onto the direction of propagation of the signal is less than the velocity of sound, then all states in the field of an infinitely extended signal are localized (there is a purely point spectrum), and the mean coefficient of transmission of an electron through the region occupied by the sound is exponentially small for a sufficiently long signal. In the opposite case all states are delocalized (the spectrum is absolutely continuous), and on scattering reflection is replaced by partial transformation, for which the mean coefficient of disbalance is exponentially small for a sufficiently long signal.

The problem of nonlinear absorption of a finite length stochastic signal by quasiparticles of an ordered medium is reduced to the scattering problem of a static random potential, which is traditional for the theory of disordered systems. The case of interaction of a sound signal with electrons of a superconductor is considered. The peculiar localization properties of an electron in a coordinate system moving with the wave are studied. It is shown that the role of nonlinear absorption of a stochastic signal is essentially higher than that of a periodic length and is partially independent of the signal amplitude.

The problem of inelastic electron interaction in a perfectly pure superconductor with a longitudinal sound impulse is considered. It is shown that the problem reduces to the equivalent one of elastic scattering by the static potential, and the sound absorption is expressed in terms of the reflection coefficient of this scattering. The classical and quantum properties of the scattering are studied and the phase region in which new excitations are created is indicated. A formula is derived that expresses the density matrix of the excitations created in terms of the exact scattering matrix of an impulse. The quasiclassical creation of excitations by a smooth-shaped impulse is investigated with regard to both overbarrier and underbarrier processes.

General methods of the electrodynamics of media with spatial and frequency dispersion are used to develop a formalism for the dielectric functions of the response of a superconducting metal to electromagnetic perturbations. The transformation of electromagnetic waves into long-wave oscillations of the longitudinal field in a superconductor is investigated. The temperature and frequency dependences of the collective mode contribution to the superconductor surface impedance are found. Resonant excitation of a collective mode in superconducting samples of finite size is predicted, which may result in selective transparency of superconducting films.