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A theoretical model for an electrical discharge in a cavitating liquid is developed and compared with experiments for the optimization of the water treatment device. The calculations based on solution of the Noltingk─Neppiras equation support the hypothesis that the electric field promotes the formation of vapor microchannels inside a liquid gap between the electrodes, where at a low gas pressure Paschen's conditions of rupture and abnormal glow discharge maintenance in those microchannels are fulfilled. Theoretical analysis of the cavitation processes and the discharge formation processes is in qualitative agreement with the experimental data obtained in this work in a water treatment device using a hydrodynamic emitter. The following graphic illustrates the experimental setup: (1) feeding tank, (2) hydrodynamic emitter, (3) zone of cavitation inside the plasma reactor, (4) high-frequency generator of electric impulses, and (5) outlet.

We present a quantitative study of the density of states (DOS) in SF bilayers (where S is a bulk superconductor and F is a ferromagnetic metal) in the diffusive limit. We solve the quasiclassical Usadel equations in the structure considering the presence of magnetic and spin-orbit scattering. For practical reasons, we propose the analytical solution for the density of states in SF bilayers in the case of a thin ferromagnet and low transparency of the SF interface. This solution is confirmed by numerical calculations using a self-consistent two-step iterative method. The behavior of DOS dependencies on magnetic and spin-orbit scattering times is discussed., (Copyright © 2022, Karabassov et al.)

Structural and electronic properties of ultrathin nanocrystals of chalcogenide Bi 2 (Te x Se 1- x ) 3 were studied. The nanocrystals were formed from the parent compound Bi 2 Te 2 Se on as-grown and thermally oxidized Si(100) substrates using Ar-assisted physical vapor deposition, resulting in well-faceted single crystals several quintuple layers thick and a few hundreds nanometers large. The chemical composition and structure of the nanocrystals were analyzed by energy-dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, electron backscattering, and X-ray diffraction. The electron transport through nanocrystals connected to superconducting Nb electrodes demonstrated Josephson behavior, with the predominance of the topological channels [Stolyarov et al. Commun. Mater. , 2020, 1, 38]. The present paper focuses on the effect of the growth conditions on the morphology, structural, and electronic properties of nanocrystals.

Made of a thin non-superconducting metal (N) sandwiched by two superconductors (S), SNS Josephson junctions enable novel quantum functionalities by mixing up the intrinsic electronic properties of N with the superconducting correlations induced from S by proximity. Electronic properties of these devices are governed by Andreev quasiparticles (Andreev, A. Sov. Phys. JETP 1965, 20, 1490) which are absent in conventional SIS junctions whose insulating barrier (I) between the two S electrodes owns no electronic states. Here we focus on the Josephson vortex (JV) motion inside Nb-Cu-Nb proximity junctions subject to electric currents and magnetic fields. The results of local (magnetic force microscopy) and global (transport) experiments provided simultaneously are compared with our numerical model, revealing the existence of several distinct dynamic regimes of the JV motion. One of them, identified as a fast hysteretic entry/escape below the critical value of Josephson current, is analyzed and suggested for low-dissipative logic and memory elements.

Unlike conventional planar Josephson junctions, nanowire-based devices have a bridge geometry with a peculiar coupling to environment that can favor non-equilibrium electronic phenomena. Here we measure the influence of the electron bath overheating on critical current of several bridge-like junctions built on a single Au-nanowire. Using the Usadel theory and applying the two-fluid description for the normal and superconducting components of the flowing currents, we reveal and explain the mutual influence of the neighbouring junctions on their characteristics through various processes of the electron gas overheating. Our results provide additional ways to control nanowire-based superconducting devices., (© 2021. The Author(s).)

In Josephson junctions, a supercurrent across a nonsuperconducting weak link is carried by electron-hole bound states. Because of the helical spin texture of nondegenerate topological surface states, gapless bound states are established in junctions with topological weak link. These have a characteristic 4π-periodic current phase relation (CΦR) that leads to twice the conventional Shapiro step separation voltage in radio frequency-dependent measurements. In this context, we identify an attenuated first Shapiro step in (Bi 0.06 Sb 0.94 ) 2 Te 3 (BST) Josephson junctions with AlO x capping layer. We further investigate junctions on narrow, selectively deposited BST nanoribbons, where surface charges are confined to the perimeter of the nanoribbon. Within these junctions, previously identified signatures of gapless bound states are absent. Because of confinement, transverse momentum sub-bands are quantized and a topological gap opening is observed. Surface states within these quantized sub-bands are spin degenerate, which evokes bound states of conventional 2π-periodic CΦR within the BST nanoribbon weak link., (Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

The critical step for future quantum industry demands realization of efficient information exchange between different-platform hybrid systems that can harvest advantages of distinct platforms. The major restraining factor for the progress in certain hybrids is weak coupling strength between the elemental particles. In particular, this restriction impedes a promising field of hybrid magnonics. In this work, we propose an approach for realization of on-chip hybrid magnonic systems with unprecedentedly strong coupling parameters. The approach is based on multilayered microstructures containing superconducting, insulating, and ferromagnetic layers with modified photon phase velocities and magnon eigenfrequencies. The enhanced coupling strength is provided by the radically reduced photon mode volume. Study of the microscopic mechanism of the photon-to-magnon coupling evidences formation of the long-range superconducting coherence via thick strong ferromagnetic layers in superconductor/ferromagnet/superconductor trilayer in the presence of magnetization precession. This discovery offers new opportunities in microwave superconducting spintronics for quantum technologies., (Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

Topological insulators with broken time-reversal symmetry and the Fermi level within the magnetic gap at the Dirac cone provides exotic topological magneto-electronic phenomena. Here, we introduce an improved magnetically doped topological insulator, Fe-doped BiSbTe 2 Se (Fe-BSTS) bulk single crystal, with an ideal Fermi level. Scanning tunneling microscopy and spectroscopy (STM/STS) measurements revealed that the surface state possesses a Dirac cone with the Dirac point just below the Fermi level by 12 meV. The normalized d I /d V spectra suggest a gap opening with Δ mag ∼55 meV, resulting in the Fermi level within the opened gap. Ionic-liquid gated-transport measurements also support the Dirac point just below the Fermi level and the presence of the magnetic gap. The chemical potential of the surface state can be fully tuned by ionic-liquid gating, and thus the Fe-doped BSTS provides an ideal platform to investigate exotic quantum topological phenomena.

Inelastic interactions of quantum systems with the environment usually wash coherent effects out. In the case of Friedel oscillations, the presence of disorder leads to a fast decay of the oscillation amplitude. Here we show both experimentally and theoretically that in three-dimensional topological insulator Bi 2 Te 3 there is a nesting-induced splitting of coherent scattering vectors which follows a peculiar evolution in energy. The effect becomes experimentally observable when the lifetime of quasiparticles shortens due to disorder. The amplitude of the splitting allows an evaluation of the lifetime of the electrons. A similar phenomenon should be observed in any system with a well-defined scattering vector regardless of its topological properties.

In pnictide RbEuFe 4 As 4 , superconductivity sets in at 36 K and coexists, below 15-19 K, with the long-range magnetic ordering of Eu 4f spins. Here we report scanning tunneling experiments performed on cold-cleaved single crystals of the compound. The data revealed the coexistence of large Rb-terminated and small Eu-terminated terraces, both manifesting 1 × 2 and 2 × 2 reconstructions. On 2 × 2 surfaces, a hidden electronic order with a period ∼5 nm was discovered. A superconducting gap of ∼7 meV was seen to be strongly filled with quasiparticle states. The tunneling spectra compared with density functional theory calculations confirmed that flat electronic bands due to Eu 4f orbitals are situated ∼1.8 eV below the Fermi level and thus do not contribute directly to Cooper pair formation.

We examine the influence of superconductivity on the magneto-transport properties of a ferromagnetic Ni nanowire connected to Nb electrodes. We show experimentally and confirm theoretically that the Nb/Ni interface plays an essential role in the electron transport through the device. Just below the superconducting transition, a strong inverse proximity effect from the nanowire suppresses superconducting correlations at Nb/Ni interfaces, resulting in a conventional anisotropic magneto-resistive response. At lower temperatures however, the Nb electrodes operate as superconducting shunts. As the result, the magneto-resistance exhibits a strongly growing hysteretic behavior accompanied by a series of saw-like jumps. The latter are associated with the penetration/escape of individual Abrikosov vortices that influence non-equilibrium processes at the Nb/Ni interface. These effects should be taken into account when designing superconducting quantum nano-hybrids involving ferromagnetic nanowires.

Josephson vortices play an essential role in superconducting quantum electronics devices. Often seen as purely conceptual topological objects, 2π-phase singularities, their observation and manipulation are challenging. Here we show that in Superconductor-Normal metal-Superconductor lateral junctions Josephson vortices have a peculiar magnetic fingerprint that we reveal in Magnetic Force Microscopy (MFM) experiments. Based on this discovery, we demonstrate the possibility of the Josephson vortex generation and manipulation by the magnetic tip of a MFM, thus paving a way for the remote inspection and control of individual nano-components of superconducting quantum circuits.

The interplay of Dirac physics and induced superconductivity at the interface of a 3D topological insulator (TI) with an s-wave superconductor (S) provides a new platform for topologically protected quantum computation based on elusive Majorana modes. To employ such S-TI hybrid devices in future topological quantum computation architectures, a process is required that allows for device fabrication under ultrahigh vacuum conditions. Here, we report on the selective area growth of (Bi,Sb) 2 Te 3 TI thin films and stencil lithography of superconductive Nb for a full in situ fabrication of S-TI hybrid devices via molecular-beam epitaxy. A dielectric capping layer was deposited as a final step to protect the delicate surfaces of the S-TI hybrids at ambient conditions. Transport experiments in as-prepared Josephson junctions show highly transparent S-TI interfaces and a missing first Shapiro step, which indicates the presence of Majorana bound states. To move from single junctions towards complex circuitry for future topological quantum computation architectures, we monolithically integrated two aligned hardmasks to the substrate prior to growth. The presented process provides new possibilities to deliberately combine delicate quantum materials in situ at the nanoscale.

In this work, a class of metamaterials is proposed on the basis of ferromagnet/superconductor hybridization for applications in magnonics. These metamaterials comprise of a ferromagnetic magnon medium that is coupled inductively to a superconducting periodic microstructure. Spectroscopy of magnetization dynamics in such hybrid evidences formation of areas in the medium with alternating dispersions for spin wave propagation, which is the basic requirement for the development of metamaterials known as magnonic crystals. The spectrum allows for derivation of the impact of the superconducting structure on the dispersion: it takes place due to a diamagnetic response of superconductors on the external and stray magnetic fields. In addition, the spectrum displays a dependence on the superconducting critical state of the structure: the Meissner and the mixed states of a type II superconductor are distinguished. This dependence hints toward nonlinear response of hybrid metamaterials on the magnetic field. Investigation of the spin wave dispersion in hybrid metamaterials shows formation of allowed and forbidden bands for spin wave propagation. The band structures are governed by the geometry of spin wave propagation: in the backward volume geometry the band structure is conventional, while in the surface geometry the band structure is nonreciprocal and is formed by indirect band gaps., Competing Interests: The authors declare no conflict of interest.

Although signatures of superconductivity in Dirac semimetals have been reported, for instance by applying pressure or using point contacts, our understanding of the topological aspects of Dirac semimetal superconductivity is still developing. Here, we utilize nanoscale phase-sensitive junction technology to induce superconductivity in the Dirac semimetal Bi 1-x Sb x . Our radiofrequency irradiation experiments then reveal a significant contribution of 4π-periodic Andreev bound states to the supercurrent in Nb-Bi 0.97 Sb 0.03 -Nb Josephson junctions. The conditions for a substantial 4π contribution to the supercurrent are favourable because of the Dirac cone's very broad transmission resonances and a measurement frequency faster than the quasiparticle poisoning rate. In addition, we show that a magnetic field applied in the plane of the junction allows tuning of the Josephson junctions from 0 to π regimes. Our results open the technologically appealing avenue of employing the topological bulk properties of Dirac semimetals for topological superconductivity research and topological quantum computer development.

We study momentum and energy dependencies of the quasiparticle interference (QPI) response function in multiband superconductors in the framework of the strong-coupling Eliashberg approach. Within an effective two-band model we study the s ± and s ++ symmetry cases, corresponding to opposite or equal signs of the order parameters in the bands. We demonstrate that the momentum dependence of the QPI function is strikingly different for s ± and s ++ symmetries of the order parameter at energies close to the small gap. At the same time, the QPI response becomes indistinguishable for both symmetries at higher energies around the large gap. This result may guide future experiments on probing pairing symmetry in iron pnictides as well as in other unconventional superconductors.

The interplay between superconductivity and magnetism is one of the oldest enigmas in physics. Usually, the strong exchange field of ferromagnet suppresses singlet superconductivity via the paramagnetic effect. In EuFe 2 (As 0.79 P 0.21 ) 2 , a material that becomes not only superconducting at 24.2 K but also ferromagnetic below 19 K, the coexistence of the two antagonistic phenomena becomes possible because of the unusually weak exchange field produced by the Eu subsystem. We demonstrate experimentally and theoretically that when the ferromagnetism adds to superconductivity, the Meissner state becomes spontaneously inhomogeneous, characterized by a nanometer-scale striped domain structure. At yet lower temperature and without any externally applied magnetic field, the system locally generates quantum vortex-antivortex pairs and undergoes a phase transition into a domain vortex-antivortex state characterized by much larger domains and peculiar Turing-like patterns. We develop a quantitative theory of this phenomenon and put forth a new way to realize superconducting superlattices and control the vortex motion in ferromagnetic superconductors by tuning magnetic domains-unprecedented opportunity to consider for advanced superconducting hybrids.

Vortices in quantum condensates exist owing to a macroscopic phase coherence. Here we show, both experimentally and theoretically, that a quantum vortex with a well-defined core can exist in a rather thick normal metal, proximized with a superconductor. Using scanning tunneling spectroscopy we reveal a proximity vortex lattice at the surface of 50 nm-thick Cu-layer deposited on Nb. We demonstrate that these vortices have regular round cores in the centers of which the proximity minigap vanishes. The cores are found to be significantly larger than the Abrikosov vortex cores in Nb, which is related to the effective coherence length in the proximity region. We develop a theoretical approach that provides a fully self-consistent picture of the evolution of the vortex with the distance from Cu/Nb interface, the interface impedance, applied magnetic field, and temperature. Our work opens a way for the accurate tuning of the superconducting properties of quantum hybrids.

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients ensure the possibility of the odd-frequency pairing: (1) the topological surface states, (2) the induced pair potential, and (3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac point in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary, the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.

We investigate transport and shot noise in lateral normal-metal-3D topological-insulator-superconductor contacts, where the 3D topological insulator (TI) is based on Bi. In the normal state, the devices are in the elastic diffusive transport regime, as demonstrated by a nearly universal value of the shot noise Fano factor F_{N}≈1/3 in magnetic field and in a reference normal-metal contact. In the absence of magnetic field, we identify the Andreev reflection (AR) regime, which gives rise to the effective charge doubling in shot noise measurements. Surprisingly, the Fano factor F_{AR}≈0.22±0.02 is considerably reduced in the AR regime compared to F_{N}, in contrast to previous AR experiments in normal metals and semiconductors. We suggest that this effect is related to a finite thermal conduction of the proximized, superconducting TI owing to a residual density of states at low energies.

An array of superconducting islands placed on a normal metal film offers a tunable realization of nanopatterned superconductivity. This system enables investigation of the nature of competing vortex states and phase transitions between them. A square array creates the eggcrate potential in which magnetic field-induced vortices are frozen into a vortex insulator. We observed a vortex insulator-vortex metal transition driven by the applied electric current and determined critical exponents that coincided with those for thermodynamic liquid-gas transition. Our findings offer a comprehensive description of dynamic critical behavior and establish a deep connection between equilibrium and nonequilibrium phase transitions., (Copyright © 2015, American Association for the Advancement of Science.)

To guide experimental work on the search for Majorana zero-energy modes, we calculate the superconducting pairing symmetry of a three-dimensional topological insulator in combination with an s-wave superconductor. We show how the pairing symmetry changes across different topological regimes. We demonstrate that a dominant p-wave pairing relation is not sufficient to realise a Majorana zero-energy mode useful for quantum computation. Our main result is the relation between odd-frequency pairing and Majorana zero energy modes by using Green functions techniques in three-dimensional topological insulators in the so-called Majorana regime. We discuss thereafter how the pairing relations in the different regimes can be observed in the tunneling conductance of an s-wave proximised three-dimensional topological insulator. We discuss the necessity to incorporate a ferromagnetic insulator to localise the zero-energy bound state to the interface as a Majorana mode.

We discuss fluctuations near the second-order phase transition where the free energy has an additional non-Hermitian term. The spectrum of the fluctuations changes when the odd-parity potential amplitude exceeds the critical value corresponding to the PT-symmetry breakdown in the topological structure of the Hilbert space of the effective non-Hermitian Hamiltonian. We calculate the fluctuation contribution to the differential resistance of a superconducting weak link and find the manifestation of the PT-symmetry breaking in its temperature evolution. We successfully validate our theory by carrying out measurements of far from equilibrium transport in mesoscale-patterned superconducting wires.

We discuss the dynamic response of odd-frequency Cooper pairs to an electromagnetic field. By using the quasiclassical Green function method, we calculate the impedance (Z=R-iX) of a normal-metal thin film which covers a superconductor. In contrast with the standard relation (i.e., R≪X), the impedance in spin-triplet proximity structures shows anomalous behavior (i.e., R>X) in the low frequency limit. This unusual relation is a result of the penetration of odd-frequency pairs into the normal metal and reflects the negative Cooper pair density., (© 2011 American Physical Society)

The specific heat of high-purity Ba(0.68)K(0.32)Fe2As2 single crystals with the highest reported superconducting Tc=38.5 K was studied. The electronic specific heat Cp below Tc shows two gap features, with Δ1≈11 meV and Δ2≈3.5 meV obtained from an α-model analysis. The reduced gap value, 2Δ(max)/kBTc≈6.6, the magnitude of the specific-heat jump, ΔCp(Tc)/Tc, and its slope below Tc exhibit a strong-coupling character. We also show that an Eliashberg model with two hole and two electron bands gives the correct values of Tc, the superconducting gaps, and the free-energy difference.

We predict anomalous atomic-scale 0-pi transitions in a Josephson junction with a ferromagnetic-insulator (FI) barrier. The ground state of such junction alternates between 0 and pi states when thickness of FI is increasing by a single atomic layer. We find that the mechanism of the 0-pi transition can be attributed to thickness-dependent phase shifts between the wave numbers of electrons and holes in FI. Based on these results, we show that a stable pi state can be realized in junctions based on high-T{c} superconductors with a La2BaCuO5 barrier.

A theory of Andreev conductance is formulated for junctions involving normal metals (N) and multiband superconductors (S) and applied to the case of superconductors with nodeless extended s(+/-)-wave order parameter symmetry, as possibly realized in the recently discovered ferropnictides. We find qualitative differences from tunneling into s-wave or d-wave superconductors that may help to identify such a state. First, interband interference leads to a suppression of Andreev reflection in the case of a highly transparent N/S interface and to a current deficit in the tunneling regime. Second, surface bound states may appear, both at zero and at nonzero energies.

We review the theory of odd-frequency pairing in superconducting heterostructures, where an odd-frequency pairing component is induced near interfaces. A general description of the superconducting proximity effect in a normal metal or a ferromagnet attached to an unconventional superconductor (S) is given within quasiclassical kinetic theory for various types of symmetry state in S. 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. As an example, we consider a junction between a diffusive normal metal (DN) and a p-wave superconductor (even-frequency spin-triplet odd-parity symmetry), where the pairing amplitude in DN belongs to an odd-frequency spin-triplet even-parity symmetry class. We also discuss the manifestation of odd-frequency pairing in conventional superconductor/normal (S/N) proximity systems and its relation to the classical McMillan-Rowell oscillations.

The local density of states is studied theoretically in terms of the odd-frequency (odd-omega) Cooper pairing induced around a vortex core. We find that a zero energy peak in the density of states at the vortex center is robust against nonmagnetic impurities in a chiral p-wave superconductor owing to an odd-omega s-wave pair amplitude. We suggest how to discriminate a spin-triplet pairing symmetry and spatial chiral-domain structure by scanning tunneling spectroscopy via odd-omega pair amplitudes inside vortex cores.

In this Letter, we calculate the electron-phonon coupling of the newly discovered superconductor LaFeAsO1-xFx using linear response. For pure LaFeAsO, the calculated electron-phonon coupling constant lambda=0.21 and logarithmic-averaged frequency omegaln=206 K 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. To reproduce the experimental Tc, 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 whole family of Fe-As-based superconductors, probably due to the importance of strong-correlation effects.

We propose a novel experiment to identify the symmetry of superconductivity on the basis of theoretical results for differential conductance of a normal metal connected to a superconductor. The proximity effect from the superconductor modifies the conductance of the remote current depending remarkably on the pairing symmetry: spin singlet or spin triplet. The clear-cut difference in the conductance is explained by symmetry of Cooper pairs in a normal metal with respect to frequency. In the spin-triplet case, the anomalous transport is realized due to an odd-frequency symmetry of Cooper pairs.

We demonstrate that, contrary to standard wisdom, the lowest-order Josephson coupling is possible between odd- and even-frequency superconductors. The origin of this effect is the induced odd- (even-)frequency pairing component at the interface of bulk even- (odd-)frequency superconductors. The resulting current-phase relation is found to be proportional to cosphi, where phi is the macroscopic phase difference between the two superconductors.

Motivated by a recent experiment [Keizer et al., Nature (London) 439, 825 (2006)], we study the Josephson effect in superconductor/diffusive half metal/superconductor junctions using the recursive Green function method. 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 a half metal has a large peak at the Fermi energy. Therefore the odd-frequency pairs can be detected experimentally by using the scanning tunneling spectroscopy.

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 spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity 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.

We report on an ab anisotropy of Jc parallel b/Jc parallel a approximately/= 1.8 IcRn parallelb/IcRn parallel a approximately/= 1.2 and in ramp-edge junctions between untwinned YBa2Cu3O7 and s-wave Nb. For these junctions, the angle theta with the YBa2Cu3O7 crystal b axis is varied as a single parameter. The RnA(theta) dependence presents twofold symmetry. The minima in IcRn at theta approximately/= 50 degrees suggest a real s-wave subdominant component and negligible d(xy)-wave or imaginary s-wave admixtures. The IcRn(theta) dependence is well fitted by 83% dx2-y2-, 15% isotropic s-, and 2% anisotropic s-wave order parameter symmetry, consistent with deltab/deltaa approximately/= 1.5.

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 has been rather well understood, the existing approximate formulas fail to describe the correct behavior of Tc for general phonon and paramagnon spectra. Using a controllable approximation, we derive an analytical formula for Tc 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 MgCNi3.

We argue, based on band structure calculations and the Eliashberg theory, that the observed decrease of T(c) of Al and C doped MgB2 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 a 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 a 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.

It is well established that the superconductivity in the recently discovered superconducting compound MgB2 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 a region of applicability, because gradient expansion in the c direction breaks down. In the case of a dirty pi band, we derive the simplest equations, which describe properties of such superconductors near Tc, and explore some consequences of these equations.

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 scanning tunneling microscopy experiments on vortex structure imaging in MgB2.

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.

We report measurements of the temperature dependence of the critical current, I(c), in Josephson junctions consisting of conventional superconducting banks of Nb and a weakly ferromagnetic interlayer of a CuxNi1-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 be explained only by assuming that the junction changes from a 0-phase state at high temperatures to a pi phase state at low temperatures.