On the two-parametric theory of superconductivity

The concept of spin fluctuations in the Hubbard model is used for deriving a closed system of equations for the superconducting order parameter Δ and spin susceptibility. The limiting cases of low temperatures and temperatures close to the superconducting transition temperature are considered. The temperature dependences of the parameter Δ and the Knight shift are obtained. The conditions under which the second-order phase transition turns to the first-order phase transition are established.     

Superconductivity in the pseudogap state in the hot-spot model: Ginzburg-Landau expansion

Peculiarities of the superconducting state (s and d pairing) are considered in the model of the pseudogap state induced by short-range order fluctuations of the dielectric (AFM (SDW) or CDW) type, which is based on the model of the Fermi surface with “hot spots.” A microscopic derivation of the Ginzburg-Landau expansion is given with allowance for all Feynman diagrams in perturbation theory in the electron interaction with short-range order fluctuations responsible for strong scattering in the vicinity of hot spots. The superconducting transition temperature is determined as a function of the effective pseudogap width and the correlation length of short-range order fluctuations. Similar dependences are derived for the main parameters of a superconductor in the vicinity of the superconducting transition temperature. It is shown, in particular, that the specific heat jump at the transition point is considerably suppressed upon a transition to the pseudogap region on the phase diagram.     

Disorder-induced inhomogeneities of the superconducting state close to the superconductor-insulator transition

Scanning tunneling spectroscopy at very low temperatures on homogeneously disordered superconducting titanium nitride thin films reveals strong spatial inhomogeneities of the superconducting gap Delta in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature Tc towards zero, enhancement of spatial fluctuations in Delta, and growth of the Delta/Tc ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition.     

Superconductivity on the localization threshold and magnetic-field-tuned superconductor-insulator transition in TiN films

Temperature-and magnetic-field-dependent measurements of the resistance of ultrathin superconducting TiN films are presented. The analysis of the temperature dependence of the zero-field resistance indicates an underlying insulating behavior, when the contribution of Aslamazov-Larkin fluctuations is taken into account. This demonstrates the possibility of the coexistence of the superconducting and insulating phases and of a direct transition from the one to the other. The scaling behavior of magnetic field data is in accordance with a superconductor-insulator transition (SIT) driven by quantum phase fluctuations in two-dimensional superconductor. The temperature dependence of the isomagnetic resistance data on the high-field side of the SIT has been analyzed, and the presence of an insulating phase is confirmed. A transition from the insulating to a metallic phase is found at high magnetic fields, where the zero-temperature asymptotic value of the resistance is equal to h/e².     

Superconductivity in the pseudogap state induced by short-order fluctuations

Peculiarities of the superconducting state (s and d pairing) are considered in a simple model of the pseudogap state caused by short-range fluctuations (e.g., of the antiferromagnetic type), which is based on the model of a Fermi surface with “hot” regions. A system of Gor’kov recurrence equations is constructed taking into account all diagrams in perturbation theory in the electron interaction with short-range fluctuations. The superconducting transition temperature is determined, and the temperature variation of the energy gap depending on the pseudogap width and the correlation length of short-range fluctuations is analyzed. In a similar approximation, a microscopic derivation of the Ginzburg-Landau expansion is carried out, and the behavior of the main physical parameters of the superconductor near the transition temperature is studied depending on the pseudogap width as well as the correlation length of the fluctuations. The obtained results are in qualitative agreement with a number of experiments with underdoped HTSC cuprates.     

Effect of vortex-antivortex fluctuations on the heat capacity of a type-II superconducting film

The small size vortex-antivortex pairs proliferation in a type-II superconducting film is considered below T(c). The corresponding contribution to the free energy is calculated. It is shown that these fluctuations give the main temperature dependent contribution to the heat capacity of the superconducting film in the sufficiently large interval of temperatures below the transition point.     

Spectral density and density of states in a superconductor in an exactly solvable model of a pseudogap state

A simple, exactly solvable model of a pseudogap state induced by fluctuations of dielectric short-range order is used to study the peculiarities of the electronic spectral density and density of states of a superconductor in the model of the Fermi surface with hot patches. The problem is considered for arbitrary values of the short-range order correlation length ξ_corr. It is shown that the absence of self-averaging of the superconducting order parameter over the random field of dielectric fluctuations causes the spectral density and density of states to change significantly. The superconducting character of these quantities persists in a wide temperature range above the temperature T _c of the superconducting transition, which is uniform over the whole sample.     

Effect of thermal phase fluctuations on the superfluid density of two-dimensional superconducting films

High precision measurements of the complex sheet conductivity of superconducting a-Mo77Ge23 thin films have been made from 0.4 K through T(c). A sharp drop in the inverse sheet inductance, L-1(T), is observed at a temperature, T(c), which lies below the mean-field transition temperature T(c0). Just below T(c), the suppression of L-1(T) below its mean-field value indicates that longitudinal phase fluctuations have nearly their full classical amplitude, but they disappear rapidly as T decreases. We argue that there is a quantum crossover at about 0.94T(c0), below which classical phase fluctuations are suppressed.     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

The onset of superconductivity in the time dependent Ginzburg-Landau theory

The fluctuations of the local order parameter above the superconducting transition temperature give rise to singularities in the electrical conductivity and the diamagnetic susceptibility. Using the time dependent Ginzburg-Landau equation the fluctuation of the current density is calculated. By means of the fluctuation-dissipation theorem and a dispersion relation the electromagnetic response function is then determined for small frequencies and wave-numbers. The dynamical conductivity for bulk material, thin films, and thin wires shows an increasing peak at zero frequency the width of which decreases as the transition temperature is approached. This structure should be observable in microwave experiments.     

Tetracritical point and staggered vortex currents in superconducting state

A phase diagram reflecting the main features of the typical phase diagram of cuprate superconductors has been studied within the framework of the Ginzburg-Landau phenomenology in the vicinity of a tetracritical point, which appears as a result of the competition of the superconducting and insulating pairing channels. The superconducting pairing under repulsive interaction corresponds to a two-component order parameter, whose relative phase is related to the orbital antiferromagnetic insulating ordering. Under weak doping, the insulating order coexists with the superconductivity at temperatures below the superconducting phase transition temperature and is manifested as a weak pseudogap above this temperature. A part of the pseudogap region adjacent to the superconducting state corresponds to developed fluctuations of the order parameter in the form of quasi-stationary states of noncoherent superconducting pairs and can be interpreted as a strong pseudogap. As the doping level is increased, the system exhibits a phase transition from the region of coexistence of the superconductivity and the orbital antiferromagnetism to the usual superconducting state. In this state, a region of developed fluctuations of the order parameter in the form of quasi-stationary states of uncorrelated orbital circular currents exists near the phase transition line.     

Resonance enhancement of electron-phonon interaction

A superconducting state near the phase transition curve from paramagnetic phase to superconducting phase for perovskites La_{2 ? x} Sr _x CuO₄ and YBa₂Cu₃O₆ is considered. Expressions for effective parameters of electron-spin-phonon interaction are obtained. It is shown that the critical temperature of the phase transition from paramagnetic phase to superconducting phase T _c is determined by the enhancement of electron-phonon interaction by spin fluctuations of exchange type.     

Fluctuations in superconductors belowT c

Thermal fluctuations of the order parameter in the superconducting state are investigated, particularly near the transition temperature, using the time dependent Ginzburg-Landau theory. These fluctuations give rise to a contribution of the dynamical conductivity, which strongly increases as the temperature is raised towardsT _c , in contrast to the temperature dependence of the electromagnetic response due to the static order parameter. At the transition temperature this contribution joins continuously to the extra response (conductivity, susceptibility) which has been calculated and observed in the temperature region aboveT _c , where it represents the onset of superconductivity in the normal state. Particularly the dynamical conductivity due to fluctuations is calculated and discussed for bulk material, thin films and thin wires belowT _c . The temperature and frequency dependence should be observable in microwave experiments.     

Observation of lateral long range order in superconducting FeTe thin films

<正>We find that the superconductivity in the thin films of the formerly believed non-superconducting parent compound FeTe is accompanied by an emergence of second order with a correlation length of 742 nm and 258 nm at 10 K and 300 K,respectively.The structural phase transition found in iron pnictide superconductors,in non-superconducting FeTe bulk samples,and in FeSe superconducting thin films is not observed in the superconducting FeTe thin films.The interplay between superconductivity and long range order may suggest the crucial role of competition between electronic localization and itinerancy which leads to strong quantum fluctuations in the FeTe system.     

Synthesis of heavy fermion CeCoIn5 thin film via pulsed laser deposition

CeCoIn₅ (Co115) thin films have been grown on Al₂O₃ (000l) substrates through the pulsed laser deposition (PLD). The films are grown mainly along the c-axis, with CeIn₃ and In-related alloys. The rock-salt type grains are nucleated, where Co115 grains mixed with excess indium are evenly distributed over the substrate. The electrical resistivity of the films shows a Kondo coherence peak near 47 K and the zero-resistance superconducting state at 1.8 K, which is the first observation in the PLD grown thin films of Co115. The Rietveld refinement of the thin films shows that the c/a ratio (tetragonality) is suppressed to 1.6312 from 1.6374 of single crystals, which is consistent with the linear relationship between the superconducting transition temperature and tetragonality. The good agreement indicates that the PLD could provide an alternative route to tune the 2D character of the critical spin fluctuations to understand the superconducting pairing mechanism of Co115.     

Strong pairing fluctuations and lattice anomalies in the pseudogap phase of the cuprates

Abstract

The pseudogap state in underdoped cuprates shows many very anomalous features. Among them are an extended temperature region of pairing fluctuations above the superconducting transition temperature and an unusual giant phonon anomaly in the same temperature and hole density range. A recent theoretical proposal that ascribes these anomalies to the presence of strong phase fluctuations related to a Leggett mode, is summarised.     

Coexistence of ferromagnetism and superconductivity close to a quantum phase transition: the Heisenberg- to Ising-type crossover

A microscopic mean-field theory of the phase coexistence between ferromagnetism and superconductivity in the weakly ferromagnetic itinerant electron system is constructed, while incorporating a realistic mechanism for superconducting pairing due to the exchange of critical spin fluctuations. The self-consistent solution of the resulting equations determines the superconducting transition temperature which is shown to depend strongly on the exchange splitting. The effect of phase crossover from isotropic (Heisenberg-like) to uniaxial (Ising-like) spin fluctuations near the quantum phase transition is analyzed and the generic phase diagram is obtained. This scenario is then applied to the case of itinerant ferromagnet ZrZn2, which sheds light on the proposed phase diagram of this compound. A possible explanation of superconductivity in UGe2 is also discussed.     

High field superconductivity in thin films

Thin films provide an ideal means for studying the role of spin paramagnetism in the theory of superconductivity. A review is given of the theoretical and experimental work available until now with respect to this problem. It includes a study of the excitation spectrum of thin films in a parallel magnetic field and the experimental evidence of Zeeman splitting of superconducting quasiparticles. The role of spin-orbit interaction is discussed in detail. The application of spin selective tunnelling is shown. Furthermore, it includes a study of the order of phase transition between the normal state and the paramagnetically limited superconducting state. A detailed discussion is given of the generalized Ginzburg-Landau equation including numerical evaluations. The applicability of Tinkham's formula is discussed, which is relevant for the determination of critical fields of arbitrary orientations to the film. Finally, account is given of the work which deals with the influence of spin paramagnetism on superconducting fluctuations. Recent experimental and theoretical work is described and discussed.     

Superconducting fluctuations in a magnetic field

The rounding of the transition curve is measured for superconducting bismuth films in a perpendicular magnetic field. The contribution of the fluctuating superconducting wave function to the conductivity aboveT _c in an applied magnetic field is calculated with a simple model. The allowed states of the fluctuations are cylinders in momentum space. During their life time the fluctuating superconducting electrons can be accelerated by an electrical field and contribute to the conductivity. Experiment and theory are in fair agreement. We obtain some information about the Pauli spin paramagnetism of the electrons.     

Superconducting proximity effect in the presence of strong spin scattering

We report measurements of the four terminal temperature dependent resistance of narrow Au wires implanted with 100 ppm Fe impurities in proximity to superconducting Al films. The wires show an initial decrease in resistance as the temperature is lowered through the superconducting transition of the Al films, but then show an increase in resistance as the temperature is lowered further. In contrast to the case of pure Au wires in contact with a superconducting film, the resistance at the lowest temperatures rises above the normal state resistance. Analysis of the data shows that, in addition to contributions from magnetic scattering and electron-electron interactions, the temperature dependent resistivity shows a substantial contribution from the superconducting proximity effect, which exists even in the presence of strong spin scattering.