The “pair” Fermi contour and high-temperature superconductivity

Superconducting pairing of holes with a large (on the order of doubled Fermi) total pair momentum and small relative motion momenta is considered taking into account the quasi-two-dimensional electronic structure of high-T _c cuprates with clearly defined nesting of the Fermi contour situated in an extended neighborhood of the saddle point of the electronic dispersion law (the momentum space region with a hyperbolic metric) and the arising of a spatially inhomogeneous (stripe) structure as a result of the redistribution of current carriers (holes) that restores regions with antiferromagnetic ordering. The superconducting energy gap and condensation energy were determined, and their dependences on the doping level were qualitatively studied. The energy gap was shown to exist in some hole concentration region limited on both sides. The superconducting state with a positive condensation energy appears in a narrower range of doping within this region. The reason for the arising of the superconducting state at a repulsive screened Coulomb interaction between holes is largely the redistribution of hole pairs in the momentum space related to the special features of the hyperbolic metric, which is responsible for the formation of the “pair” Fermi contour, and the renormalization of the kinetic energy of holes when the chemical potential changes because of the condensation of pairs. Hole pairs of the type under consideration exist not only in the condensate but also in the form of quasi-stationary states with very weak decay at temperatures substantially exceeding the superconducting transition temperature. The pseudogap region of the phase diagram of high-T _c cuprates is related to such states. The pairing mechanism under consideration allows not only the principal characteristics of the phase diagram but also key experimental data on high-T _c cuprate materials to be qualitatively explained.     

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

Evidence for a three Tc behavior of the Kondo superconductor (La,Y)Ce

The dependence of the superconducting transition temperature T_c on Ce impurity concentration is reported for the (La_0.80Y_0.20)Ce system. Susceptibility and resistivity measurements on samples with about 0.85 at. % Ce show unique behavior which must be interpreted as a superposition of three transition curves: a first transition at 0.55 K from the normal to the superconducting state, a second one at 0.27 K back to the normal state, and finally a third one at about 0.05 K again to the superconducting state. The experimental evidence of this third transition (T_c3) is of special importance for the decision about the relevant physical mechanism of pair-breaking at low temperature (T ? T_K).     

Pressure dependence of the superconducting transition temperature of the stage-2 potassium mercurographitide intercalation compound

Measurements of the pressure (P) dependence of the superconducting transition temperature T_c of stage-two KHgC₈ are reported. T_c is found to decrease with applied pressure from a room pressure value of 1.85K at a rate dT_c/dP=-6.5 × 10^-5K/bar, similar to typical superconducting elements such as Sn. No superconductivity was detected for stage-one KHgC₄ or K_0.5Hg_0.5 amalgam to a limiting temperature T = 1.3K and a limiting pressure P = 22 kbar. These results are discussed in reference to the possible occurence of structural and charge density wave transitions in these materials and recent theoretical models of superconducting graphire intercalation compounds.     

The vortex-like excitations detected by Nernst signals in high-T c superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.     

Fractal superconductivity near localization threshold

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk “poor conductors” in which Fermi energy E_F is located in the region of localized states not so far from the Anderson mobility edge E_c. We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.We identify three distinct phases: ‘critical’ superconductive state formed at E_F = E_c, superconducting state with a strong pseudo-gap, realized due to pairing of weakly localized electrons and insulating state realized at E_F still deeper inside a localized band. The ‘critical’ superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gapped state is the presence of two independent energy scales: superconducting gap Δ, that is due to many-body correlations and a new “pseudo-gap” energy scale Δ_P which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T_c. Two gap nature of the pseudo-gapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudo-gapped superconducting state demonstrates anomalous behavior of the optical spectral weight. The insulating state is realized due to the presence of local pairing gap but without superconducting correlations; it is characterized by a hard insulating gap in the density of single electrons and by purely activated low-temperature resistivity ln R(T) ∼ 1/T.Based on these results we propose a new “pseudo-spin” scenario of superconductor-insulator transition and argue that it is realized in a particular class of disordered superconducting films. We conclude by the discussion of the experimental predictions of the theory and the theoretical issues that remain unsolved.     

Repulsive effect of low frequency phonons on superconductivity

The Eliashberg integral equations are investigated to determine the effect of low frequency phonons on the superconducting transition temperature T_c. It is found that phonons of frequency less than T_c are repulsive (diminish T_c) while phonons of higher frequency have a diminished attraction unless the frequency is substantially above T_c. Various implications are discussed concerning observed values of T_c and predicted mechanisms for raising T_c.     

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.     

Effect of impurity scattering on superconductivity in K2Cr3As3

Impurity scattering in a superconductor may serve as an important probe for the nature of superconducting pairing state. Here we report the impurity effect on superconducting transition temperature T c in the newly discovered Cr-based superconductor K₂Cr₃As₃.The resistivity measurements show that the crystals prepared using high-purity Cr metal（99.99%） have an electron mean free path much larger than the superconducting coherence length. For the crystals prepared using impure Cr that contains various nonmagnetic impurities, however, the T c decreases significantly, in accordance with the generalized Abrikosov-Gor’kov pair-breaking theory. This finding supports a non-s-wave superconductivity in K₂Cr₃As₃.     

Superconductivity in a simple model of the pseudogap state

An analysis is made of characteristics of the superconducting state (s-and d-pairing) using a simple, exactly solvable model of the pseudogap state produced by fluctuations of the short-range order (such as antiferromagnetic) based on a Fermi surface model with “hot” sections. It is shown that the superconducting gap averaged over these fluctuations is nonzero at temperatures higher than the mean-field superconducting transition temperature T _c over the entire sample. At temperatures T > T _c superconductivity evidently exists in isolated sections (“ drops”). Studies are made of the spectral density and the density of states in which superconducting characteristics exist in the range T > T _c however, in this sense the temperature T = T _c itself is no different in any way. These anomalies show qualitative agreement with various experiments using underdoped high-temperature superconducting cuprates.     

Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

“Magnetodipole” self-organization of charge carriers in high-T c superconductors and the kinetics of phase transition

A phenomenological model describing “magnetodipole” self-organization of charge carriers (the formation of so-called stripe-structures and the energy gap in the spectrum of states) was suggested to interpret the data of nonstationary nonlinear spectroscopy of high-T _c superconductors. It was shown that, after rapidly heating a superconducting sample, the kinetics of the succeeding phase transition depended on initial temperature T. At small “overheatings” T*<T<T _m x≈(1.4?1.5)T* (T _c and T*≈T _c are the temperatures of the transition to the superconducting state and the formation of stripe-structures) and the optimal level of doping, the decay of stripe-structures (and of the gap in the spectrum of states) occurred at a low rate (in times above to 10^?9 s) in spite of the virtually instantaneous disappearance of superconductivity.     

Effect of pressure on transition temperature of Rb3C60 fullerides

Electronic structure parameters play a significant role in fullerides leading to a superconducting state. Relevant electronic parameter as renormalized Coulomb repulsive parameter μ* and the attractive electron-phonon coupling strength λ are obtained within the dielectric function formalism for random phase approximation. As a first step, the superconducting transition temperature is deduced within the framework of McMillan approximation and strong coupling results using the widely spread phonon spectrum. In view of the importance of Coulomb screening for doped fullerides, the influence of pressure and volume on T _c are estimated to be within the range of experimental values. The isotope and dopant effects are also discussed. It is noticed that the high-T _c , the huge pressure effect, negative pressure derivative of T _c and positive volume derivative of T _c in alkali intercalated fullerides are dictated by the properties of Coulomb and on-ball-C₆₀ high energy intramolecular modes.     

New superconductor with a layered crystal structure: Nickel oxybismuthide LaO<Subscript>1−δ</Subscript>NiBi

The results of synthesizing a new layered phase—nickel oxybismuthide LaO_1?δNiBi in a series of superconducting oxypnictides—and its properties in the superconducting and normal states are reported. Although the temperature of the transition of this phase to the superconducting state, T _c ～ 4 K, is much lower than the value T _c = 55 K reached at present in oxyarsenide SmO_1?δFeAs, the similarity of the crystal structures and ρ(T) dependencies indicates that the mechanism responsible for the appearance of the semiconducting state is the same in lanthane oxybismuthide and samarium oxyarsenide.     

Correlation between structural and superconducting properties of nano-granular disordered Nb thin films

We report on low temperature transport measurements on nano-granular Nb thin films deposited on Si (1 0 0) substrates using DC magnetron sputtering. The superconducting transition temperature (T_c) is found to decrease monotonically with the increase of the lattice parameter (a) irrespective of its thickness and grain size. The superconducting transition temperature is found to depend only on the lattice parameter whereas the normal state resistivity depends both on lattice parameter and the details of the sample morphology. We have modeled this T_c variation with lattice expansion in terms of Debye temperature reduction using Morse potential as the interatomic potential in Nb.     

Another approach to mechanism of ferromagnetic superconductor UGe2

We study the ferromagnetic superconductor of UGe₂ applying our previous model [Phys. Rev. B 61 (2000), 4289] for the high transition temperature superconductivity (HTSC). The Coulomb interaction for triplet electron pairs is reduced by a difference of the exchange interaction. In the case of UGe₂ including other heavy fermion superconductors, coexistence of triplet superconductivity and ferromagnetism is possible in the case of our scheme. We also investigate the pressure-dependence of Curie temperature, T_c and superconducting temperature, T_sc.     

Superconducting plate in a transverse magnetic field: New state

A model is proposed for describing Cooper pairs near the transition (in temperature and magnetic field) point when their spacing is larger than their size. The essence of the model is as follows: the Ginzburg-Landau functional is written in operator form in terms of field operators of the Bose type so that the average value of the density operator gives the concentration of Cooper pairs, and the same Ginzburg-Landau expression is obtained for the Bose condensate. The model is applied to a superconducting plate with a thickness smaller than the size of a pair in a transverse magnetic field near its upper critical value H _c2. A new state is discovered that is energetically more advantageous in a certain interval in the vicinity of the transition point as compared to the Abrikosov vortex state. The wavefunction of the system in this state is of the type of the Laughlin function used in the fractional quantum Hall effect (naturally, as applied to Cooper pairs as Bose particles in our case) and corresponds to a homogeneous incompressible fluid. The energy of this state is proportional to the first power of quantity (1 ? H/H _c2) in contrast to the energy of the vortex state containing the square of this quantity. The interval of the existence of the new state is the larger, the dirtier the sample.     

The resistance jump in the pure type-I superconductors tin,indium and lead

It is shown that for tin, indium and lead samples of sufficiently high purity, sufficiently large diameter (2–3mm), and sufficiently close to the critical temperature (ΔT<0.15K), there exists a common value close to $\text{2}\text{3}$(0.64?R(i_c)/R_n ? 0.69) of the resistance jump at the transition from the superconducting to the intermediate state.     

Superconductivity in polymeric sulfur nitride (SN)x at high pressure

Investigations of the pressure dependence of the superconducting transition temperature T_c up to 17 kbar, and of the normal conductivity up to 50 kbar are reported. It is observed that below 8 kbar, the value of T_c increases linearly with the pressure. In addition, there is a significant drop of T_c at about 9 kbar which may be due to a phase transition.     

Domain-like magnetic structure in superconductors of ErRh4B4 and HoMo6S8 type

The problem of the coexistence of superconductivity and magnetic order is studied by taking into account the indirect exchange interaction, magnetic dipolar interaction and magnetic anisotropy. It is shown that the domain-like magnetic structure should be realized in the superconducting phases of ErRh₄B₄ and HoMo₆S₈ at the temperatures T_m = 1.4 and 0.7 K respectively. The transition from superconducting domain-like phase (DS) to the normal ferromagnetic (FN) state is described.