High pressure study of BaPb0.7Bi0.3O3 films

The resistance R, the superconducting transition temperature T_c and the energy gap Δ(T) have been measured on the BaPb_0.7Bi_0.3O₃ films up to 14 kbar. We have found that up to 14 kbar: (1) pressure suppresses T_c and Δ(T) while enhances R, (2) the value of 2Δ(0)/kT_c is 3.8±0.1, independent of pressure, and (3) the Δ(T)/Δ(0) varies with T/T_c in a BCS fashion but only for T/T_c<0.75 and independent of pressure. The results show that BaPb_1?xBi_xO₃ is a weak-coupling superconductor, but fail to provide information about the cause for the high T_c of the compound.     

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.     

Tunneling in single-layer Bi2Sr2CuO6+δ single crystals in high magnetic field

In tunneling experiments with high-quality single crystals of a single-layer cuprate superconductor Bi₂Sr₂CuO_6+δ using the break junction and point-contact techniques at T<T _c, the coexistence of the superconducting-state gap and the normal-state gap was observed. The values of the superconducting energy gap 2Δ_p?p are in the range from 13.4 to 15 meV (Δ_p?p=6.7–7.5 meV). The values of 2Δ_p?p are similar for two samples with T _c=4 K and for two samples with T _c=9–10 K and are independent of the carrier concentration. The normal-state gap, with the magnitude approximately equal to 50 meV, persists at T<T _c and in the magnetic field H?H _c2 up to 28 T. After the transition of the sample to the normal state, the intensity of the tunneling conductance rapidly decreases with increasing magnetic field strength and temperature. The observed large broadening of the tunneling spectra and large zero-bias conductances can be caused by a strong angular dependence of the superconducting gap. The tunneling results are in full agreement with the data of the angle-resolved photoemission spectroscopy measurements.     

High-resolution photoemission study of FeSr2YCu2O7+δ

We have performed high-resolution photoemission spectroscopy (PES) on FeSr₂YCu₂O_7+δ, of which superconductivity of T_c=49 K was recently reported. We clearly observed opening of a d-wave-like superconducting gap and estimated the maximum gap value (Δ_max) to be 10 meV at 15 K. This gap value gives 2Δ_max/k_BT_c∼5, suggesting a strong-coupling nature of superconductivity in FeSr₂YCu₂O_7+δ. Comparative PES study with superconducting and insulating samples shows that the valence band is rigidly shifted as a function of doping without evolution of additional states within the insulating gap.     

Übergangstemperatur zur Supraleitung,Energielücke und Widerstandsverlauf amorpher und kristallisierter Thallium-Tellur-Schichten

Thin Tl/Te-films are condensed onto a cooled substrate at 4 K. An amorphous phase is obtained. The maximum superconducting transition temperature of the amorphous Tl/Te-films is 4.2 K. Measurements of the energy gap by superconducting tunneling yield a ratio 2Δ/k T _c =4.6 for amorphous Tl/Te-films and 2Δ/k T _c =3.8 for disordered, pure Tl-films.     

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.     

B NMR relaxation in superconductors: YRuB2 and LuRuB2

To investigate the electronic states in YRuB₂ and LuRuB₂, we have carried out ¹¹B NMR measurements. In the normal state, the spin-lattice relaxation rates 1/T₁'s in these compounds are proportional to the temperature T. 1/T₁'s show a small coherence peak just below the superconducting transition temperature T_c and decrease exponentially well below T_c. YRuB₂ and LuRuB₂ are found to be BCS superconductors with the energy gap 2Δ(0)=3.52 k_BT_c.     

Superconductivity in the t-J model in the large-N limit

Using a 1/N expansion for X-operators the leading contributions to the linearized equation for the superconducting gap of the t-J model are derived and the gap equation solved numerically on a square lattice. We find a strong instability towards superconductivity only in the d-wave (T ₃) channel with T _c/│t│ ～ 0:01 where T _c is the transition temperature and t the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term with the band width, and a retarded term due to charge and spin fluctuations with ～ J, as energy scale.     

Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition

A theory of high-temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap, which can be as big as Δ₁～0.1ε _F , with ε _F being the Fermi level. We show that the critical temperature 2T _c ?Δ₁. If the pseudogap exists above T _c , then 2T*?Δ₁ and T* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at T _c is calculated. The transition from conventional superconductors to high-T _c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered     

Normal phase and superconducting instability in the attractive Hubbard model: a DMFT(NRG) study

We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T _c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.     

Superconducting behavior of amorphous Zr70Cu30

Measurement of the Meissner penetration depth, λ(T) were made in amorphous Zr₇₀Cu₃₀ samples. The results indicate that this amorphous alloy behaves as a BCS superconductor with 2Δ(0)?kT_c = 3.8, where Δ(0) is the superconducting energy gap at T=0 and T_c the critical temperature. It is also concluded that the low energy excitation, TLS, characteristics of amorphous material does not contribute to T_c.     

Thermal expansion of a YBa2Cu3O7 superconducting ceramic

The thermal expansion of the High T_c superconducting ceramic YBa₂Cu₃O_7-δ has been measured from 50 K up to room temperature by means of a capacitance dilatometer. No detectable anomalous change in lenght is observed at the critical temperature T_c, within the resolution of our experimental set up: Δl/l = 5 10⁻⁸. This indicates a weak dependence of T_c on pressure, contrarily to the one measured on (LaBa)CuO lower T_c superconducting ceramics. The Debye temperature is also estimated.     

Point-contact study of the heavy-fermion superconductor CeCoIn5

We have investigated the differential conductance spectra of the point contacts between the heavy-fermion superconductor CeCoIn₅ and Pt. Many of them show a double-maximum structure that indicates the superconducting energy gap Δ. The Δ values derived using Blonder-Tinkham-Klapwijk model, however, varies from 0.47 to 0.77 meV, and yet they are within the scatter of the reported values. The evolution of Δ below T_c is slow as compared with that of BCS gap probably reflecting the unconventional superconductivity in CeCoIn₅.     

Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ_corr. It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T _c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T>T _c, superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ_corr; in particular, the range of existence for drops becomes narrower and vanishes as ξ_corr → 0, but for finite values of ξ_corr, complete self-averaging does not take place.     

Some parameters of superconductors with an extreme singularity in the density of state: (s+d) model

We study some parameters of superconductors with δ-function type singularities in the electronic density of states (DOS), exhibiting (s+d)-wave symmetry of the order parameter. Starting with a pure s-wave pairing potential V_s, the critical temperature T_c at first slightly increases with increasing the d-wave interaction potential V_d, being determined by this interaction only for stronger V_d values. The ratio R=2|Δ(0)|/k_BT_c of the mean value of the zero temperature energy gap |Δ(0)| to T_c increases with increasing V_d, reaching a maximum which depends on the mixing interaction term. The maximum values of R are comparable with very high values obtained in some gap measurements. The jump in the specific heat at critical temperature is by a factor 2.4 higher for the extreme singularity of pure s-wave symmetry, as compared with the BCS theory with constant DOS. Such higher values of the jump are in agreement with the experimentally observed values, as well as with the calculations determined by extended saddle points in the electronic bands. By switching the d-wave channel, the value of the jump decreases. The results show the usefulness of calculations with δ-type singularities as a limiting case of very strong singularities in the DOS.     

Temperature dependence of the gap in the density of states near the Fermi level in a hole doped manganite

In this paper, we report a model-based quantitative analysis of temperature dependent scanning tunneling spectroscopy (STS) data taken on epitaxial thin films of the hole doped manganite La_0.7Ca_0.3MnO₃. The film, grown on lattice matched NdGaO₃ substrate, has a ferromagnetic transition temperature T_c=268 K. The analysis allows us to evaluate how the tunneling curve evolves across the transition temperature. We find that there is a gap Δ in the density of states (DOS), which peaks at T≈T_c. The gap closes in the ferromagnetic state following the evolution of the magnetization. The gap closing is gradual and not sudden at T=T_c. Above T_c the gap reduces from the peak value and reaches a limiting value of ≈75 meV for T/T_c≥1.1 which is close to the value of 60 meV seen from transport experiments.     

Superconducting coherent quasiparticle weight in high-Tc superconductor from angle-resolved photoemission

We study the doping and temperature dependence of the single-particle coherent weight, z_A, for high-T_c superconductors Bi₂Sr₂CaCu₂O_8+x using angle-resolved photoemission. We find that at low temperatures the coherent weight z_A at (π,0) is proportional to the carrier concentration x and that the temperature-dependence of z_A is similar to that of the c-axis superfluid density. We show that, for a wide range of carrier concentration, the superconducting transition temperature scales with the product of the low-temperature coherent weight and the maximum superconducting gap.     

Exotic superconducting state embedded in the hidden order state of URu2Si2

The heavy-fermion compound URu₂Si₂ has mystified researchers since the superconducting state (T_c = 1.45 K) is embedded within the enigmatic ‘‘hidden order” phase (T_h = 17.5 K). Here, we report charge and thermal transport measurements on ultraclean single crystals of URu₂Si₂ with very large residual-resistivity-ratio down to 30 m K (∼T_c/50), which reveal a number of unprecedented superconducting properties. The results provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology. We propose a gap function with chiral d-wave form Δ(k) = Δ₀k_z(k_x + ik_y). We also demonstrate that a distinct flux line lattice melting transition with outstanding characters occurs well below the upper critical fields even at sub-Kelvin temperature. The intriguing superconducting state of URu₂Si₂ adds a unique and exciting example to the list of unconventional superconductors.     

Analytical assessment of some characteristic ratios for <Emphasis Type="Italic">s</Emphasis>-wave superconductors

We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high-temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ? T_c are discussed using the method of successive approximations. The equation for the ratio R₁, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R₂, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low-T_c superconductors. The prospect of application of the presented model in studies of high-T_c superconductors and other superconducting systems of the new generation is also discussed.     

d-Wave superconductivity via buckling-like phonon mode

We follow the classic strong-coupling theory of superconductivity through electron-phonon interaction with a buckling-like phonon mode. We find a nonzero d-wave order parameter in the sense of the Eliashberg theory. We derive a zero temperature gap Δ(0,π) at the gap edge versus the electron-phonon coupling strength g² relation. We find that large enough value for Δ(0,π) as compared to those of high-T_c superconductors cannot be realized in the electron-buckling-like-phonon coupling on the CuO₂ planes.