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Crossed Andreev reflection in multiterminal structures in the diffusive regime is addressed within the quasiclassical Keldysh-Usadel formalism. The elastic cotunneling and crossed Andreev reflection of quasiparticles give nonlocal currents and voltages (depending on the actual biasing of the devices) by virtue of the induced proximity effect in the normal metal electrodes. The magnitude of the nonlocal processes is found to scale with the square of the barrier transparency and to decay exponentially with interface spacing. Nonlocal cotunneling and crossed Andreev conductances are found to contribute equally to the nonlocal current, which is of relevance to the use of normal metal-superconducting heterostructures as sources of entanglement.

We study theoretically the Josephson effect in junctions based on unconventional superconductors with diffusive barriers, using the quasiclassical Green's function formalism. Generalized boundary conditions at junction interfaces applicable to unconventional superconductors are derived by calculating a matrix current within the circuit transport theory. Applying these boundary conditions, we have calculated the Josephson current in structures with various pairing symmetries. A number of predictions are made: (a) nonmonotonic temperature dependence in d-wave superconductor/diffusive normal metal/d-wave superconductor (D/DN/D) junctions, (b) anomalous current-phase relation in $p $-wave superconductor/diffusive normal metal/$p$% -wave superconductor (P/DN/P) junctions, (c) second harmonics in D/DN/D and P/DN/P junctions, (d) a double peak structure of the critical current in D/DF/D junctions, (e) enhanced Josephson current by the exchange field in S/DF/P junctions. We have also investigated peculiarities of the Josephson coupling in D/DF/D, P/DF/P and S/DF/P junctions. An oscillatory behavior of the supercurrent and the second harmonics in the current-phase relation are studied as a function of the length of the diffusive ferromagnet., Comment: 15 pages, 14 figures, long version of Phys. Rev. B 73, 140504(R) (2006)(cond-mat/0605373)

Josephson effect in junctions between unconventional superconductors is studied theoretically within the model describing the effects of interface roughness. The particularly important issue of applicability of the frequently used Sigrist-Rice formula for Josephson current in d-wave superconductor / insulator / d-wave superconductor junctions is addressed. We show that although the SR formula is not applicable in the ballistic case, it works well for rough interfaces when the diffusive normal metal regions exist between the d-wave superconductor and the insulator. It is shown that the SR approach only takes into account the component of the d-wave pair potential symmetric with respect to an inversion around the plane perpendicular to the interface. Similar formula can be derived for general unconventional superconductors with arbitrary angular momentum l., Comment: 4 pages, 4 figures

Using the quasiclassical Green's function formalism, we study the influence of the odd-frequency spin-triplet superconductivity on the local density of states (LDOS) in a diffusive ferromagnet (DF) attached to a superconductor. Various possible symmetry classes in a superconductor are considered which are consistent with the Pauli's principle: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity (ETO) state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity (OSO) state. For each of these states, the pairing state in DF is studied. Particular attention is paid to the study of spin-singlet s-wave and spin-triplet p-wave superconductors as the examples of ESE and ETO superconductors. For spin-singlet case the magnitude of the OTE component of the pair amplitude is enhanced with the increase of the exchange field in DF. When the OTE component is dominant at low energy, the resulting LDOS in DF has a zero energy peak (ZEP). On the other hand, in DF / spin-triplet p-wave superconductor junctions LDOS has a ZEP in the absence of the exchange field, where only the OTE paring state exists. With the increase of the exchange field, the ESE component of the pair amplitude induced in DF is enhanced. Then, the resulting LDOS has a ZEP splitting. We demonstrate that the appearance of the dominant OTE component of the pair amplitude is the physical reason of the emergence of the ZEP of LDOS., Comment: 9 pages, 9 figures

We demonstrate that, quite generally, the spin-singlet even-parity (spin-triplet odd-parity) pair potential in a superconductor induces the odd-frequency pairing component with spin-singlet odd-parity (spin-triplet even-parity) near interfaces. The magnitude of the induced odd-frequency component is enhanced in the presence of the midgap Andreev resonant state due to the sign change of the anisotropic pair potential at the interface. The Josephson effect should therefore occur between odd- and even-frequency superconductors, contrary to the standard wisdom. A method to probe the odd-frequency superconductors is proposed.

The Josephson effect in superconductor / diffusive ferromagnet / superconductor (SFS) junctions is studied using the recursive Green function method in the regime of large exchange energy in a ferromagnet. Motivated by recent experiment [R. S. Keizer, et. al., Nature 439, 825 (2006)] we also address the case of superconductor / diffusive half metal / superconductor junctions. The pairing function in spin-singlet and triplet channels, the Josephson current and their mesoscopic fluctuations are calculated. We show that the spin-flip scattering at the junction interfaces opens the Josephson channel of the odd-frequency spin-triplet Cooper pairs. As a consequence, the local density of states in half metals has a large peak at the Fermi energy. Therefore odd-frequency pairs can be detected experimentally by using the scanning tunneling spectroscopy., Comment: 5 pages, 4 figures embedded

We theoretically investigate the macroscopic quantum dynamics of a pi junction with a superconductor (S) and a multiferroic material or a ferromagnetic insulator (FI). By deriving the effective action from a microscopic Hamiltonian, a pi-junction qubit (a S-FI-S superconducting quantum interference device ring) is proposed. In this qubit, a quantum two-level system is spontaneously generated and the effect of the quasiparticle dissipation is found to be very weak. These features make it possible to realize a quiet qubit with high coherency. We also investigate macroscopic quantum tunneling (MQT) in current-biased S-FI-S pi junctions and show that the influence of the quasiparticle dissipation on MQT is negligibly small., Comment: 4 pages, 2 figures

We discuss the current status of the theory of the "high-temperature" superconductivity in intercalated graphites YbC6 and CaC6. We emphasize that while the general picture of conventional, phonon-driven superconductivity has already emerged and is generally accepted, there are still interesting problems with this picture, such as weak-coupling regime inferred from specific heat suggesting coupling exclusively with high-energy carbon phonons coming in direct contradiction with the isotope effect measurements suggesting coupling exclusively with the low-energy intercalant modes. At the same time, the first principle calculations, while explaining Tc, contradict both of the experiments above by predicting equal coupling with both groups of phonons., Comment: Contribution to the Proceedings of the M2S Conference in Dresden, 2006

We present a general theory of the proximity effect in junctions between diffusive normal metals (DN) and unconventional superconductors in the framework of the quasiclassical Green's function formalism. Various possible symmetry classes in a superconductor are considered which are consistent with the Pauli principle: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity (ETO) state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity (OSO) state. For each of the above four cases symmetry and spectral properties of the induced pair amplitude in the DN are determined. It is shown that the pair amplitude in a DN belongs respectively to an ESE, OTE, OTE and ESE pairing state., Comment: 5 pages with one figure

We study the Josephson effect in D/I/DN/I/D junctions, where I, DN and D denote an insulator, a diffusive normal metal and a d-wave superconductor, respectively.The Josephson current is calculated based on the quasiclassical Green's function theory with a general boundary condition for unconventional superconducting junctions. In contrast to s-wave junctions, the product of the Josephson current and the normal state resistance is enhanced by making the interface barriers stronger. The Josephson current has a nonmonotonic temperature dependence due to the competition between the proximity effect and the midgap Andreev resonant states., Comment: 5 pages, 4 figures

The complex decay length xi characterizing penetration of superconducting correlations into a ferromagnet due to the proximity effect is studied theoretically in the frame of the linearized Eilenberger equations. The real part xi_1 and imaginary part xi_2 of the decay length are calculated as functions of exchange energy and the rates of ordinary, spin flip and spin orbit electronic scattering in a ferromagnet. The lengths xi_1,2 determine the spatial scales of, respectively, decay and oscillation of a critical current in SFS Josephson junctions in the limit of large distance between superconducting electrodes. The developed theory provides the criteria of applicability of the expressions for xi_1 and xi_2 in the dirty and the clean limits which are commonly used in the analysis of SF hybrid structures., Comment: 5 pages, 3 figures

We report on experimental studies of superconducting coupling through a thin Ni76Al24 film. A new patterning process has been developed, which allows in combination with the wedge shaped deposition technique the in situ deposition of 20 single Nb/Al/Al2O3/Ni3Al/Nb multilayers, each with its own well defined Ni3Al thickness. Every single multilayer consists of 10 different sized Josephson junctions, showing a high reproducibility and scaling with its junction area. Up to six damped oscillations of the critical current density against F-layer thickness were observed, revealing three single 0-pi transitions in the ground state of Josephson junctions. Contrary to former experimental studies, the exponential decay length is one magnitude larger than the oscillation period defining decay length. The theoretical predictions based on linearized Eilenberger equations result in excellent agreement of theory and experimental results., Comment: 4 pages, 5 figures

We developed the self-consistent method for the calculation of the density of states $N(\epsilon)$ in the SF bilayers. It based on the quasi-classical Usadel equations and takes into account the suppression of superconductivity in the S layer due to the proximity effect with the F metal, as well as existing mechanisms of the spin dependent electron scattering. We demonstrate that the increase of the spin orbit or spin flip electron scattering rates results in completely different transformations of $N(\epsilon)$ at the free F layer interface. The developed formalism has been applied for the interpretation of the available experimental data., Comment: 5 pages, 8 figures

We investigate Superconductor/Ferromagnet (S/F) hybrid structures in the dirty limit, described by the Usadel equations. More precisely, the oscillations of the critical temperature and critical current with the thickness of the ferromagnetic layers are studied. We show that spin-flip and spin-orbit scattering lead to the decrease of the decay length and the increase of the oscillations period. The critical current decay is more sensitive to these pair-breaking mechanisms than that of the critical temperature. These two scattering mechanisms should be taken into account to get a better agreement between experimental results and theoretical description. We also study the influence of the interface transparency on the properties of S/F structures., Comment: 28 pages, 9 figures accepted for publication in Phys. Rev. B; reference added

We report on an \textit{ab}-anisotropy of $J_{c \parallel b}/J_{c \parallel a}% \cong 1.8$ and $I_{c}R_{n \parallel b}/I_{c}R_{n \parallel a}\cong 1.2$ in ramp-edge junctions between untwinned YBa$_{2}$Cu$_{3}$O$_{7}$ and $s$% -wave Nb. For these junctions, the angle $\theta $ with the YBa$_{2}$Cu$_{3}$O$_{7}$ crystal b-axis is varied as a single parameter. The $R_{n}$A($\theta$)-dependence presents 2-fold symmetry. The minima in $I_{c}R_{n}$ at $\theta \cong 50^{\circ}$ suggest a real s-wave subdominant component and negligible $d_{xy}$-wave or imaginary s-wave admixtures. The $I_{c}R_{n}$($\theta$)-dependence is well-fitted by 83% $d_{x^{2}-y^{2}}$-, 15% isotropic $s$- and 2% anisotropic s-wave order parameter symmetry, consistent with $\Delta_{b}/\Delta_{a} \cong 1.5$., Comment: 4 pages, 3 figures, to be published in Physical Review Letters

Resonant proximity effect in the normal metal / insulator / diffusive ferromagnet / insulator / $s$- and d-wave superconductor (N/I/DF/I/S) junctions is studied for various regimes by solving the Usadel equation with the generalized boundary conditions. It is shown that the resonant proximity effect originating from the exchange field in DF layer strongly modifies the tunneling conductance and density of states., Comment: 14 pages, 11 figures, sequel to Phys. Rev. B 72, 052512 (2005)(cond-mat/0510657)

The conditions for the formation of zero-energy peak in the density of states (DOS) in the normal metal / insulator / diffusive ferromagnet / insulator / s-wave superconductor (N/I/DF/I/S) junctions are studied by solving the Usadel equations. The DOS of the DF is calculated in various regimes for different magnitudes of the resistance, Thouless energy and the exchange field of the DF, as well as for various resistances of the insulating barriers. The conditions for the DOS peak are formulated for the cases of weak proximity effect (large resistance of the DF/S interface) and strong proximity effect (small resistance of the DF/S interface)., Comment: 4 pages, 4 figures

The Meissner effect in diffusive normal metal / insulator / d-wave superconductor junctions is studied theoretically in the framework of the Usadel equation under the generalized boundary condition. The effect of midgap Andreev resonant states (MARS) formed at the interface of d-wave superconductor is taken into account. It is shown that the formation of MARS suppresses the susceptibility of the diffusive normal metal., Comment: 5 pages, 4 figures, Proceedings of the ISSP International Symposium (ISSP-9) on Quantum Condensed System

Anomalous features of the proximity effect specific to diffusive normal metal / triplet superconductor (DN/TS) junctions are studied within the quasiclassical Green's function formalism. The pair amplitude $f_{N}$ as a function of energy $\epsilon$ in DN, satisfies an anomalous relation, $% f_{N}(\epsilon)=-f^{*}_{N}(-\epsilon)$, contrary to that in singlet superconductor junctions case where $f_{N}(\epsilon)=f^{*}_{N}(-% \epsilon)$. Such an unusual $\epsilon$ dependence is responsible for a zero energy peak in the local density of states and is a source of an anomalous penetration of the applied magnetic field into DN. % Our results are relevant to Sr$_{2}$RuO$_{4}$, which is considered to have a $p_{x}+ip_{y}$-wave symmetry., Comment: 5 pages

We reconsider the long-standing problem of the effect of spin fluctuations on the critical temperature and isotope effect in a phonon-mediated superconductor. Although the general physics of the interplay between phonons and paramagnons had been rather well understood, the existing approximate formulas fail to describe the correct behavior of $% T_{c}$ for general phonon and paramagnon spectra. Using a controllable approximation, we derive an analytical formula for $T_{c}$ which agrees well with exact numerical solutions of the Eliashberg equations for a broad range of parameters. Based on both numerical and analytical results, we predict a strong enhancement of the isotope effect when the frequencies of spin fluctuation and phonons are of the same order. This effect may have important consequences for near-magnetic superconductors such as MgCNi$_{3}$, Comment: 5 pages, 2 figures

Thermal and charge transport in the diffusive normal metal(DN) / insulator / $s$-, $d$- and p-wave superconductor junctions are studied for various situations, where we have used the Usadel equation with Nazarov's generalized boundary condition. Thermal and electrical conductance of the junction and the Lorentz ratio are calculated by varying the magnitudes of the resistance, the Thouless energy and the magnetic scattering rate in DN, the transparency of the insulating barrier, and the angle between the normal to the interface and the crystal axis of d-wave superconductors or the angle between the normal to the interface and the lobe direction of the p-wave pair potential. New general expression is derived for the calculation of the thermal conductance. It is demonstrated that the proximity effect doesn't influence the thermal conductance while the mid gap Andreev resonant states suppress it. We have also discussed a possibility of distinguishing pairing symmetries based on the dependencies of the electrical and thermal conductance on temperatures., Comment: 21 pages, 20 figures, stylistic changes in v2

The $J(\phi)$ relation in SFIFS, SNINS and SIS tunnel junctions is studied. The method for analytical solution of linearized Usadel equations has been developed and applied to these structures. It is shown that the Josephson current across the structure has the sum of $\sin \phi $ and $\sin 2\phi $ components. Two different physical mechanisms are responsible for the sign of $\sin 2\phi $. The first one is the depairing by current which contributes positively to the $\sin 2\phi $ term, while the second one is the finite transparency of SF or SN interfaces which provides the negative contribution. In SFIFS junctions, where the first harmonic vanishes at 0 - $\pi$ transition, the calculated second harmonic fully determines the $J(\phi)$ curve., Comment: 6 pages, 2 figures

Samuely et al. (cond-mat/0503153) make the strong claim that our letter is 'contradicting several established experimental results'. As we will show below this is not justified and the claims from are based on a misinterpretation of our results., Comment: 1 page

Thermodynamic properties of the multiband superconductor MgB$_{2}$ have often been described using a simple sum of the standard BCS expressions corresponding to $\sigma$- and $\pi$-bands. Although, it is \textit{a priori} not clear if this approach is working always adequately, in particular in cases of strong interband scattering. Here we compare the often used approach of a sum of two independent bands using BCS-like $\alpha$-model expressions for the specific heat, entropy and free energy to the solution of the full Eliashberg equations. The superconducting energy gaps, the free energy, the entropy and the heat capacity for varying interband scattering rates are calculated within the framework of two-band Eliashberg theory. We obtain good agreement between the phenomenological two-band $\alpha$-model with the Eliashberg results, which delivers for the first time the theoretical verification to use the $\alpha$-model as a useful tool for a reliable analysis of heat capacity data. For the thermodynamic potential and the entropy we demonstrate that only the sum over the contributions of the two bands has physical meaning., Comment: 27 pages, 10 figures, 1 table, submitted to Phys. Rev. B

The results of calculations of the spatially-resolved density of states (DoS) in an S(F/N) bilayer are presented (S is a superconductor, F is a metallic ferromagnet, N is a normal metal) within quasiclassical theory in the dirty limit. Analytical solutions are obtained in the case of thin F, N layers which demonstrate the peculiar features of DoS in this system. The dependencies of the minigap and the DoS peak positions on the exchange energy and parameters of the layers are studied numerically, Comment: 5 pages, 5 figures

We argue, based on band structure calculations and Eliashberg theory, that the observed decrease of $T_c$ of Al and C doped MgB$_2$ samples can be understood mainly in terms of a band filling effect due to the electron doping by Al and C. A simple scaling of the electron-phonon coupling constant $\lambda$ by the variation of the density of states as function of electron doping is sufficient to capture the experimentally observed behavior. Further, we also explain the long standing open question of the experimental observation of a nearly constant $\pi$ gap as function of doping by a compensation of the effect of band filling and interband scattering. Both effects together generate a nearly constant $\pi$ gap and shift the merging point of both gaps to higher doping concentrations, resolving the discrepancy between experiment and theoretical predictions based on interband scattering only., Comment: accepted by PRL

A generalized model for the critical temperature Tc of superconducting bilayers is presented, which is valid with no restrictions to film thicknesses, Tc of the layers and interface resistivity. The model is verified experimentally on a series of Nb-Al and Ta-Al bilayers with Nb, Ta layer thicknesses of 100 nm and Al layer thicknesses ranging from 5 nm to 200 nm. Excellent agreement between theory and experiment was found for the energy gap and the Tc of bilayers. The results are important for designing practical superconducting devices., Comment: 3 pages, 2 figures

We describe a model for photon absorption by superconducting tunnel junctions in which the full energy dependence of all the quasiparticle dynamic processes is included. The model supersedes the well-known Rothwarf-Taylor approach, which becomes inadequate for a description of the small gap structures that are currently being developed for improved detector resolution and responsivity. In these junctions relaxation of excited quasiparticles is intrinsically slow so that the energy distribution remains very broad throughout the whole detection process. By solving the energy-dependent kinetic equations describing the distributions, we are able to model the temporal and spectral evolution of the distribution of quasiparticles initially generated in the photo-absorption process. Good agreement is obtained between the theory and experiment., Comment: 25 pages, 15 figures

This paper presents a general model for calculating the density of states and the Cooper pair potential in proximity coupled superconducting bi- and tri-layer films. The typical example of superconducting tunnel junctions is used to show that the model is working., Comment: 25 pages, 6 figures

Charge transport in the diffusive normal metal (DN) / insulator / $s$- and $% d $-wave superconductor junctions is studied in the presence of magnetic impurities in DN in the framework of the quasiclassical Usadel equations with the generalized boundary conditions. The cases of $s$- and d-wave superconducting electrodes are considered. The junction conductance is calculated as a function of a bias voltage for various parameters of the DN metal: resistivity, Thouless energy, the magnetic impurity scattering rate and the transparency of the insulating barrier between DN and a superconductor. It is shown that the proximity effect is suppressed by magnetic impurity scattering in DN for any value of the barrier transparency. In low-transparent s-wave junctions this leads to the suppression of the normalized zero-bias conductance. In contrast to that, in high transparent junctions zero-bias conductance is enhanced by magnetic impurity scattering. The physical origin of this effect is discussed. For the d-wave junctions, the dependence on the misorientation angle $\alpha$ between the interface normal and the crystal axis of a superconductor is studied. The zero-bias conductance peak is suppressed by the magnetic impurity scattering only for low transparent junctions with $\alpha \sim 0$. In other cases the conductance of the d-wave junctions does not depend on the magnetic impurity scattering due to strong suppression of the proximity effect by the midgap Andreev resonant states., Comment: 11 pages, 13 figures;d-wave case added

We consider the effect of the finite size in the ab-plane on the surface density of states (DoS) in clean d-wave superconductors. In the bulk, the DoS is gapless along the nodal directions, while the presence of a surface leads to formation of another type of the low-energy states, the midgap states with zero energy. We demonstrate that finiteness of the superconductor in one of dimensions provides the energy gap for all directions of quasiparticle motion except for \theta=45 degrees (\theta is the angle between the trajectory and the surface normal); then the angle-averaged DoS behaves linearly at small energies. This result is valid unless the crystal is 0- or 45-oriented (\alpha \ne 0 or 45 degrees, where \alpha is the angle between the a-axis and the surface normal). In the special case of \alpha=0, the spectrum is gapped for all trajectories \theta; the angle-averaged DoS is also gapped. In the special case of \alpha=45, the spectrum is gapless for all trajectories \theta; the angle-averaged DoS is then large at low energies. In all the cases, the angle-resolved DoS consists of energy bands that are formed similarly to the Kronig-Penney model. The analytical results are confirmed by a self-consistent numerical calculation., Comment: 9 pages (including 5 EPS figures), REVTeX 4

A theory of the proximity effect in normal metal - multiband superconductor hybrid structures is formulated within the quasiclassical Green's function formalism. It is shown that the existence of multiple superconducting bands manifests itself as the occurence of additional peaks in the density of states in the structure. The interplay between the proximity effect and the interband coupling influences the magnitudes of the gaps in a superconductor in a non-trivial way. The developed theory is applied to the calculation of supercurrent in multiband Superconductor - Normal metal - Superconductor Josephson junctions with low-transparent interfaces, and the results are compared with the predictions for multiband tunnel junctions.

It is well established that the superconductivity in the recently discovered superconducting compound MgB$_{2}$ resides in the quasi-two-dimensional band ($\sigma$-band) and three-dimensional band ($\pi$-band). We demonstrate that, due to such band structure, the anisotropic Ginzburg-Landau theory practically does not have region of applicability, because gradient expansion in the $c$ direction breaks down. In the case of dirty $\pi$-band we derive the simplest equations which describe properties of such superconductors near $T_{c}$ and explore some consequences of these equations., Comment: 4 pages, 2 fugures, Subm. Phys. Rev. Lett

We analyze the transport properties of contacts between unconventional superconductor and normal diffusive metal in the framework of the extended circuit theory. We obtain a general boundary condition for the Keldysh-Nambu Green's functions at the interface that is valid for arbitrary transparencies of the interface. This allows us to investigate the voltage-dependent conductance (conductance spectrum) of a diffusive normal metal (DN)/ unconventional singlet superconductor junction in both ballistic and diffusive cases. For d-wave superconductor, we calculate conductance spectra numerically for different orientations of the junctions, resistances, Thouless energies in DN, and transparencies of the interface. We demonstrate that conductance spectra exhibit a variety of features including a $V$-shaped gap-like structure, zero bias conductance peak (ZBCP) and zero bias conductance dip (ZBCD). We show that two distinct mechanisms: (i) coherent Andreev reflection (CAR) in DN and (ii) formation of midgap Andreev bound state (MABS) at the interface of d-wave superconductors, are responsible for ZBCP, their relative importance being dependent on the angle $\alpha$ between the interface normal and the crystal axis of d-wave superconductors. For $\alpha=0$, the ZBCP is due to CAR in the junctions of low transparency with small Thouless energies, this is similar to the case of diffusive normal metal / insulator /s-wave superconductor junctions. With increase of $\alpha$ from zero to $\pi/4$, the MABS contribution to ZBCP becomes more prominent and the effect of CAR is gradually suppressed. Such complex spectral features shall be observable in conductance spectra of realistic high-$T_c$ junctions at very low temperature.

In strong-coupling superconductors with a short electron mean free path the self-energy effects in the superconducting order parameter play a major role in the phonon manifestation of the point-contact spectra at the above-gap energies. We derive asymptotic expressions of the phonon structure in MgB$%_{2}$ in the case $eV\gg\Delta $ for tunnel, ballistic, and diffusive point-contacts and show that these expressions not only qualitatively, but also semi-quantitatively correspond to the measurements of the phonon structure in the point-contact spectra for the $\pi$-band of MgB$_{2}$ c-axis oriented thin films., Comment: 4 pages, 4 figures

We study nonequilibrium charge transport in a double-barrier Josephson junction, including nonstationary phenomena, using the time-dependent quasiclassical Keldysh Green's function formalism. We supplement the kinetic equations by appropriate time-dependent boundary conditions and solve the time-dependent problem in a number of regimes. From the solutions, current-voltage characteristics are derived. It is understood why the quasiparticle current can show excess current as well as deficit current and how the subgap conductance behaves as function of junction parameters. A time-dependent nonequilibrium contribution to the distribution function is found to cause a non-zero averaged supercurrent even in the presence of an applied voltage. Energy relaxation due to inelastic scattering in the interlayer has a prominent role in determining the transport properties of double-barrier junctions. Actual inelastic scattering parameters are derived from experiments. It is shown as an application of the microscopic model, how the nature of the intrinsic shunt in double-barrier junctions can be explained in terms of energy relaxation and the opening of Andreev channels., Comment: Accepted for Phys. Rev. B

We report on the fabrication of highly transparent superconductor/normal metal/two-dimensional electron gas junctions formed by a superconducting NbN electrode, a thin (10nm) Au interlayer, and a two-dimensional electron gas in a InGaAs/InP heterostructure. High junction transparency has been achieved by exploiting of a newly developed process of Au/NbN evaporation and rapid annealing at 400C. This allowed us to observe for the first time a decrease in the differential resistance with pronounced double-dip structure within the superconducting energy gap in superconductor-2DEG proximity systems. The effect of a magnetic field perpendicular to the plane of the 2DEG on the differential resistance of the interface was studied. It has been found that the reduced subgap resistance remains in high magnetic fields. Zero-field data are analyzed within the previously established quasiclassical model for the proximity effect., Comment: 15 pages, 5 figures

We calculate the tunneling density of states (DOS) of MgB2 for different tunneling directions, by directly solving the real-axis, two-band Eliashberg equations (EE). Then we show that the numeric inversion of the standard single-band EE, if applied to the DOS of the two-band superconductor MgB2, may lead to wrong estimates of the strength of certain phonon branches (e.g. the E_2g) in the extracted electron-phonon spectral function alpha^(2)F(omega). The fine structures produced by the two-band interaction turn out to be clearly observable only for tunneling along the ab planes in high-quality single crystals. The results are compared to recent experimental data., Comment: 2 pages, 2 figures, proceedings of M2S-HTSC-VII conference, Rio de Janeiro (May 2003)

We study the Josephson junction between two d-wave superconductors, which is discussed as an implementation of a qubit. We propose an approach that allows to calculate the decoherence time due to an intrinsic dissipative process: quantum tunneling between the two minima of the double-well potential excites nodal quasiparticles which lead to incoherent damping of quantum oscillations. The decoherence is weakest in the mirror junction, where the contribution of nodal quasiparticles corresponds to the superohmic dissipation and becomes small at small tunnel splitting of the energy level in the double-well potential. For available experimental data, we estimate the quality factor., Comment: 5 pages, 3 EPS figures; the style file jetpl.cls is included. Version 2: minor corrections

We study the critical temperature T_c of FSF trilayers (F is a ferromagnet, S is a singlet superconductor), where the triplet superconducting component is generated at noncollinear magnetizations of the F layers. An exact numerical method is employed to calculate T_c as a function of the trilayer parameters, in particular, mutual orientation of magnetizations. Analytically, we consider limiting cases. Our results determine conditions which are necessary for existence of recently investigated odd triplet superconductivity in SF multilayers., Comment: 5 pages, 4 EPS figures; the style file jetpl.cls is included. Version 2: minor corrections, added reference. Version 3: minor corrections

We investigate the upper critical field in a dirty two-band superconductor within quasiclassical Usadel equations. The regime of very high anisotropy in the quasi-2D band, relevant for MgB$_{2}$, is considered. We show that strong disparities in pairing interactions and diffusion constant anisotropies for two bands influence the in-plane $H_{c2}$ in a different way at high and low temperatures. This causes temperature-dependent $H_{c2}$ anisotropy, in accordance with recent experimental data in MgB$_{2}$. The three-dimensional band most strongly influences the in-plane $H_{c2}$ near $T_{c}$, in the Ginzburg-Landau (GL) region. However, due to a very large difference between the c-axis coherence lengths in the two bands, the GL theory is applicable only in an extremely narrow temperature range near $T_c$. The angular dependence of $H_{c2}$ deviates from a simple effective-mass law even near $T_c$., Comment: 12 pages, 5 figures, submitted to Phys.Rev.B

In the present work we calculate the tunneling density of states (DOS) of MgB% $_{2}$ for different tunneling directions by directly solving the two-band Eliashberg equations (EE) in the real-axis formulation. This procedure reveals the fine structures of the DOS due to the optical phonons. Then we show that the numeric inversion of the standard \emph{single-band} EE (the only available method), when applied to the \emph{two-band} DOS of MgB$_{2}$, may lead to wrong estimates of the strength of certain phonon branches (e.g. the $E_{2g}$) in the extracted electron-phonon spectral function $\alpha^{2}F(\omega)$. The fine structures produced by the two-band interaction at energies between 20 and 100 meV turn out to be clearly observable only for tunneling along the $ab$ planes, when the extracted $\alpha ^{2}F(\omega)$ contains the combination $\alpha ^{2}F_{\sigma \sigma}(\omega)$\textbf{+}$\alpha ^{2}F_{\sigma \pi }(\omega)$, together with a minor $\alpha ^{2}F_{\pi \pi}(\omega )$\textbf{+}$\alpha ^{2}F_{\pi \sigma} (\omega)$ component. Only in this case it is possible to extract information on the $\sigma$-band contribution to the spectral functions. For any other tunneling direction, the $\pi$-band contribution (which does not determine the superconducting properties of MgB$_{2}$) is dominant and almost coincides with the whole $\alpha^2F(\omega)$ for tunneling along the c axis. Our results are compared with recent experimental tunneling and point-contact data., Comment: 5 pages, 3 figures. Submitted to Phys. Rev. B (Brief Reports)

Choi et al. [Phys. Rev. B 66, 020513 (2002)] recently presented first principles calculations of the electron-phonon coupling and superconductivity in MgB2, emphasizing the importance of anisotropy and anharmonicity. We point out that (1) variation of the superconducting gap inside the sigma- or the pi-bands can hardly be observed in real samples, and (2) taking the anisotropy of the Coulomb repulsion into account influences the size of the small gap, Delta_pi., Comment: 3 pages, 2 color figures

Tunneling conductance in diffusive normal metal / insulator / s-wave superconductor (DN/I/S) junctions is calculated for various situations by changing the magnitudes of the resistance and Thouless energy in DN and the transparency of the insulating barrier. The generalized boundary condition introduced by Yu. Nazarov [Superlattices and Microstructures 25 1221 (1999)] is applied, where the ballistic theory by Blonder Tinkham and Klapwijk (BTK) and the diffusive theory by Volkov Zaitsev and Klapwijk based on the boundary condition of Kupriyanov and Lukichev (KL) are naturally reproduced. It is shown that the proximity effect can enhance (reduce) the tunneling conductance for junctions with a low (high) transparency. A wide variety of dependencies of tunneling conductance on voltage bias is demonstrated including a $U$-shaped gap like structure, a zero bias conductance peak (ZBCP) and a zero bias conductance dip (ZBCD).

We investigate the vortex state in a two-band superconductor with strong intraband and weak interband electronic scattering rates. Coupled Usadel equations are solved numerically and the distributions of the pair potentials and local densities of states are calculated for two bands at different values of magnetic fields. The existence of two distinct length scales corresponding to different bands is demonstrated. The results provide qualitative interpretation of recent STM experiments on vortex structure imaging in MgB_2., Comment: 4 pages, 5 figures

We present an application of the generalised proximity effect theory., Comment: 15 pages, 11 figures, presented at workshop on low temperature superconducting electronics at the University of Twente, The Netherlands