This review provides a theoretical basis for understanding the current-phase relation (C⌽R) for the stationary (dc) Josephson effect in various types of superconducting junctions. The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the C⌽R from the standard sinusoidal form. A new experimental tool for measuring the C⌽R is described and its practical applications are discussed. The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy. A number of examples illustrate the importance of the C⌽R measurements for both fundamental physics and applications.

We report measurements of the temperature dependence of the critical current in Josephson junctions consisting of conventional superconducting banks of Nb and a weakly ferromagnetic interlayer of a Cu x Ni 1−x alloy, with x around 0.5. With decreasing temperature I c generally increases, but for specific thicknesses of the ferromagnetic interlayer, a maximum is found followed by a strong decrease down to zero, after which I c rises again. Such a sharp cusp can only be explained by assuming that the junction changes from a 0-phase state at high temperatures to a π-phase state at low temperatures.

In this paper we calculate the electron-phonon coupling of the newly-discovered superconductor LaO1−xFxFeAs from first-principles, using Density Functional Perturbation Theory. For pure LaOFeAs, the calculated electron-phonon coupling constant λ = 0.21 and logarithmic-averaged frequency ω ln = 206K, give a maximum Tc of 0.8 K, using the standard Migdal-Eliashberg theory. For the F −doped compounds, we predict even smaller coupling constants, due to the strong suppression of the electronic Density of States at the Fermi level. To reproduce the experimental Tc = 26K, a 5-6 times larger coupling constant would be needed. Our results indicate that electron-phonon coupling is not sufficient to explain superconductivity in the newly-discovered LaO1−xFxFeAs superconductor, probably due to the importance of strong correlation effects.PACS numbers: 74.25.Jb, 74.25.Kc, 74.70.Dd The very recent report of superconductivity with the remarkablehas stimulated an intense experimental and theoretical activity, aimed at identifying the possible superconducting mechanism. This compound belongs to a family of quaternary oxypnictides of the form LnOMPn, where Ln=La and Pr, M=Mn, Fe, Co and Ni; Pn=P and As, synthesized in 1995.[2] Superconductivity was first reported in LaOFeP, with a relatively low T c of ∼ 7 K [3], and later in F-doped LaOFeAs, with a maximum T c of 26 K at x=0.12 (apparently pure LaOFeAs shows no superconductivity).The first bulk measurements on a sample with x = 0.1 have shown that F-doped LaOFeAs has a relatively small in-plane coherence length (ξ ab = 81Å) and a T-dependent Hall coefficient [4], the electronic specific heat displays a vanishingly small jump at T c , and its behavior under magnetic field [5] as well as point-contact spectroscopy [6] suggest the presence of nodes in the superconducting gap. All these observation suggest a strong analogy with the high-T c cuprates.A recent LSDA calculation predicts that pure LaOFeAs is on the verge of a ferromagnetic instability, due to a very high Density of States (DOS) of Fe d electrons at the Fermi level.[8] A DMFT calculation in the paramagnetic phase, including strong-correlation effects beyond LDA, shows that for U = 4 eV, a large amount of spectral weight is shifted away from the Fermi level, and the undoped system has a bad metallic behaviour. [9] Both papers rule out standard e − ph theory as a possible explanation for superconductivity, without estimating the magnitude of the e − ph coupling constant.In this Letter, we calculate from first-principles the electron-phonon properties of LaOFeAs, using Density Functional Perturbation Theory [10,11]. Similar calculations, in conjunction with Migdal-Eliashberg theory, reproduced the superconducting properties of many standard e − ph superconductors [11], including MgB 2 [12] with considerable accuracy. On the other hand, they fail dramatically in the the High-T c cuprates, [13,14] where the Local Density Approximation is not sufficient to describe the strong local electronic correlations, and their intera...

The heat capacity anomaly at the transition to superconductivity of the layered superconductor MgB 2 is compared to first-principles calculations with the Coulomb repulsion, µ * , as the only parameter which is fixed to give the measured T c . We solve the Eliashberg equations for both an isotropic one-band and a two-band model with different superconducting gaps on the π-band and σ-band Fermi surfaces. The agreement with experiments is considerably better for the two-band model than for the one-band model.

A theoretical model for quasiparticle and Josephson tunneling in multiband superconductors is developed and applied to MgB2-based junctions. The gap functions in different bands in MgB2 are obtained from an extended Eliashberg formalism, using the results of band structure calculations. The temperature and angle dependencies of MgB2 tunneling spectra and the Josephson critical current are calculated. The conditions for observing one or two gaps are given. We argue that the model may help to settle the current debate concerning two-band superconductivity in MgB2. PACS numbers: 74.50.+r, 74.70.Ad, 74.80.Fp, 85.25.Cp Soon after the discovery of superconductivity in MgB 2 , 1 first principle calculations were performed to determine the electronic structure of this material. It was found that the Fermi surface consists of two three-dimensional sheets, from the π bonding and antibonding bands, and two nearly cylindrical sheets from the two-dimensional σ bands.2,3,4,5 The multiband picture has given rise to the concept that two superconducting energy gaps can coexist 6,7 in MgB 2 . Two-band superconductivity is a phenomenon that has been observed in Nb doped SrTiO 3 .8 Recent experimental STM and point-contact spectroscopy, 9,10,11 high-resolution photoemission spectroscopy, 12 Raman spectroscopy, 13 specific heat measurements 14 and muon-spin-relaxation studies of the magnetic penetration depth 15 support the concept of a double gap in MgB 2 (see Ref.16 for a review of experiments). However, there is an ambiguity in the interpretation of point-contact data concerning the existence of two gaps. 9,10,11 Moreover, some tunneling measurements 17 show only one gap with a magnitude smaller than the BCS value of ∆ = 1.76 k B T c .In order to resolve this discrepancy, we address the question, how multiband superconductivity will manifest itself in tunneling. We present the theoretical model for quasiparticle and Josephson tunneling in MgB 2 -based junctions. Using the results of band-structure calculations, we apply an extended Eliashberg formalism to obtain the gap functions in different bands, taking strong coupling effects into account. Tunneling from a normal metal (N) into MgB 2 is considered in an extended Blonder-Tinkham-Klapwijk (BTK) model. 18 The temperature dependencies and absolute values of the I c R N product (I c is the critical current and R N is the normal state resistance) are calculated in MgB 2 -based SIS tunnel junctions, where S denotes a superconductor and I an insulator. Tunneling in the direction of the a-b plane, in the c-axis direction and under arbitrary angle is considered. Furthermore, the Josephson supercurrent between a single-gap superconductor and MgB 2 is calculated.According to the labeling of Liu et al., 6 the four Fermi surface sheets in MgB 2 are grouped into quasi-two-dimensional σ bands and three-dimensional π bands. Hence, normal and superconducting properties of MgB 2 can be described by an effective two-band model. Within this model, Liu et al.6 estimated the coupling constants a...

We present a general theory of the proximity effect in junctions between diffusive normal metals (DN) and superconductors. Various possible symmetry classes in a superconductor are considered: even-frequency spinsinglet 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. It is shown that the pair amplitude in a DN belongs respectively to an ESE, OTE, OTE and ESE pairing state since only the even-parity s-wave pairing is possible due to the impurity scattering. PACS numbers: 74.45.+c, 74.50.+r, 74.20.Rp It is well established that superconductivity is realized due to the formation of Cooper pairs consisting of two electrons. In accordance with the Pauli principle, it is customary to distinguish spin-singlet even-parity and spin-triplet odd-parity pairing states in superconductors, where odd (even) refer to the orbital part of the pair wave function. For example, s -wave and d-wave pairing states belong to the former case while p-wave state belongs to the latter one [1]. In both cases, the pair amplitude is an even function of energy. However, the so-called odd-frequency pairing states when the pair amplitude is an odd function of energy can also exist. Then, the spin-singlet odd-parity and the spin-triplet even-parity pairing states are possible.The possibility of realizing the odd-frequency pairing state was first proposed by Berezinskii in the context of 3 He, where the odd-frequency spin-triplet hypothetical pairing was discussed [2]. The possibility of the odd-frequency superconductivity was then discussed in the context of various mechanisms of superconductivity involving strong correlations [3,4]. There are several experimental evidences [5] which are consistent with the realization of the odd-frequency bulk superconducting state in Ce compounds [4,5]. In more accessible systems (ferromagnet/superconductor heterostructures with inhomogeneous magnetization) the odd-frequency pairing state was first proposed in Ref. 6 and then various aspects of this state were intensively studied [7]. At the same time, the very important issue of the manifestation of the oddfrequency pairing in proximity systems without magnetic ordering received no attention yet. This question is addressed in the present Letter.Coherent charge transport in structures involving diffusive normal metals (DN) and superconductors (S) was extensively studied during the past decade both experimentally and theoretically. However, almost all previous work was restricted to junctions based on conventional s-wave superconductors [8]. Recently, new theoretical approach to study charge transport in junctions based on p-wave and d-wave superconductors was developed and applied to the even-frequency pairing state [9,10]. It is known that in the anisotropic paring state, due to the sign change of the pair potential on the Fermi surface, a so-called midgap Andreev resonant state (MARS) is formed at the interface [11,12]. As w...

We generalize Abrikosov-Gor'kov solution of the problem of weakly coupled superconductor with impurities on the case of a multiband superconductor with arbitrary interband order parameter anisotropy, including interband sign reversal of the order parameter. The solution is given in terms of the effective (renormalized) coupling matrix and describes not only T c suppression but also renormalization of the superconducting gap basically at all temperatures. In many limiting cases we find analytical solutions for the critical temperature suppression. We illustrate our results by numerical calculations for two-band model systems.

A large number of experimental facts and theoretical arguments favor a two-gap model for superconductivity in MgB2. However, this model predicts strong suppression of the critical temperature by interband impurity scattering and, presumably, a strong correlation between the critical temperature and the residual resistivity. No such correlation has been observed. We argue that this fact can be understood if the band disparity of the electronic structure is taken into account, not only in the superconducting state, but also in normal transport.Most researchers ascribe the superconductivity in MgB 2 [1] to the electron-phonon mechanism, enhanced by interband anisotropy of the order parameter [2,3]. Interband anisotropy, as expressed by the two-gap model [2,4], offers a simple explanation of many anomalous experimental findings, most importantly of tunneling and thermodynamic measurements [5]. But there is a strong argument against it: As illustrated in Fig. 1, existing bulk samples of MgB 2 have essentially the same critical temperature although their residual resistivities, ρ 0 , vary greatly, between 0.4 and 40 µΩ cm. Such a behavior is expected for s-wave pairing (Anderson's theorem), but not when two gaps are present. In that case one expects T c to fall with increasing ρ 0 . Indeed, impurity interband scattering (magnetic and nonmagnetic) with rate γ inter suppresses two-band superconductivity as: ∆T c ∝ γ inter /(πT c ) [6], and it is tempting to assume that γ intra ∼ γ inter ∝ ρ 0 . For a sample with ρ 0 ∼ 40 µΩ cm it seems unlikely that γ inter can be smaller than πT c . In fact, the body of experimental evidence (Fig. 1) can be reconciled with the two-gap model only if γ inter ≪ γ intra . Until this paradox is resolved, the twogap model for superconductivity in MgB 2 cannot be accepted, despite much compelling evidence. Two further problems are: (a) The high-temperature slope of the resistivity is clearly correlated with the residual resistivity (violation of Matthiessen's rule) [5], and (b) the plasma frequency estimated from the measured infrared reflectivity is 5 times smaller than the calculated one [7,8,9].In this letter we shall show that the paradox can be resolved to support the two-gap model. It turns out that due to the particular electronic structure of MgB 2 , the impurity scattering between the σ-and π-bands is exceptionally small. Thus, the large variation of the residual resistivities reflects primarily a large variation of the scattering rate inside the σ-and the π-bands, while the interband σπ-scattering plays no role in normal transport. In the superconducting state, the two different gaps in the σ-and the π-bands are preserved even in dirty samples due to the extreme weakness of the σπ-interband