Transition to gapless superconductivity in YBa2(Cu1−x Zn x )3O7

Point-contact spectra of YBa₂(Cu_1–x Zn _x )₃O₇/Ag are studied at various temperatures. The differential resistance dV/dI of the point contacts shows gap-related structures belowT _c which can be attributed to Andreev reflection. Evaluation of many spectra for each sample taken at 4.2 K yields a wide distribution of voltages /e at which these structures occur. The upper limit varies roughly as expected from the depression ofT _c by Zn-doping from /e=29 mV (x=0) to 9 mV (x=0.05), while the lower limit decreases much faster and disappears forx=0.05. Hence, the Zn doped samples exhibit a tendency to gapless superconductivity as suggested earlier on the basis of specific-heat measurements.     

Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in horizontal direction. We calculate correlations parallel to the layering in the horizontally layered model with periodv=2. If the model has a finite critical temperature,T _c>0, the order parameter in the frustrated case may become discontinuous forT0. Correlations atT=T _c decay algebraically with critical exponent =1/4 and exponentially forT>T _c. If the critical temperature vanishes,T _c=0, we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index =1/2, i.e.T=0 is thus a critical point.Work performed within the research program of the Sonder forschungsbereich 125 Aachen-Jülich-Köln     

Low temperature self-ion irradiation of pure and granular aluminium-films

Al-films, evaporated at room temperature under different oxygen partial pressures, were irradiated with self-ions (500 keV, Al⁺⁺) at low temperature (<7 K). The observed increase of the resistivity and of the superconducting transition temperatureT _c depends strongly on the oxygen contentc ₀ present in the layers. A qualitative different behaviour of the above quantities was found for different fluence ranges of the bombarding ions. For high fluences in all cases an oxygen stabilized disorder state was obtained with correspondingT _c-increases betweenT _c=0.2 K for the purest films (c ₀0.5 at %) andT _c =1.2 K for films with c ₀=40 at %. The annealing behaviour of the irradiated films is also dependent on the oxygen contentc ₀.     

High-resolution measurements of thermal expansion along the uniqueb-axis of squaric acid

The thermal expansion of squaric acid along the uniqueb-axis was measured between 323 K and 418 K with a resolution of 2·10^–7 in strain and 5·10^–4 K in temperature using a capacitance dilatometer. The anomaly associated with the antiferro-electric phase transition occuring atT _c=373.5 K was observed over the rangeT _c–50 K<T<T _c+7 K. The regular lattice expansion follows a generalized Grüneisen's law with a Debye-temperature _D =660 K and a uniaxial pressure-dependence of _D /p _b . The critical behaviour close toT _c was studied with a sweep rate of 36 mK/h. A hyteresis loop of width 23 mK was observed in the strain curve, indicating a 1st order transition. However, no discontinuity in dilatation was observed, and therefore the transition is close to a multicritical point. The anomalous increase in the expansion coefficient can be described with critical exponents ==0.56 in the interval 0.4 K<|T–T _c|<12 K. Closer toT _c the divergence is stronger. A generalized Pippard relation between the expansion coefficient and specific heat holds to within 1 K from the transition point. The inconsistencies apparent closer toT _c are interpreted as a consequence of a weak 1st order transition.     

On the high temperature staggered susceptibility of Heisenberg model antiferromagnetics

The critical ordering temperature, T _c′, for the antiferromagnetic Heisenberg model is investigated on the basis of the high temperature expansion for the staggered susceptibility. For the simple cubic and body-centred cubic lattices, it appears that

where q is the lattice coordination number, S the spin value and T _c the corre-sponding ferromagnetic Curie point. A possible counter argument asserting T _c′ ? T _c is discussed at some length.     

Temperature dependence of viscosity near the glass transition

Real glass transitions, where activated processes are included, are analysed near Whitney fold and cusp singularities. In particular the temperature dependence of the viscosity is studied. For sufficiently strongly coupled systems there is close to a fold singularity located atT=T _c , a crossover from an algebraic divergence (T–T _c )^– forT>T _c , to an Arrhenius dependence exp(E/k _B T) forT<T _c . If a parameter vector specifying the system also passes close to a cusp singularity, atT ₀<T _c , there may be a temperature region where the viscosity also shows Fogel-Fulcher like dependence. The results for the viscosity are intimately connected with the dynamics for the so-called -relaxation process, where relaxation occurs via a fractal time process in the delevant time region.     

Electronic phase separation in La-Cuprates

The mechanisms driving the phase separation in high-T _c La cuprates is studied by magnetic susceptibility and electrical resistivity measurements. The experiments are performed under different thermal treatment. Three temperature ranges can be resolved characteristic for different physical processes: At 150T170K a space limited diffusion of superparamagnetic clusters (single hole clusters) occurs leading to the formation of a small but rather tight percolative subphase which at highT _c values becomes superconducting. Above 180 K the cluster motion becomes unrestricted in space and a more extended subphase is built up, however, with lowerT _c values. Above 230 K oxygen diffusion starts leading to an unexpected destruction of the conducting/superconducting phase.     

Relationship between T c and electronegativity differences in compound superconductors

The electronegativity differences, N, between the anions and the cations in suggested resonating elements of some representative high-temperature superconductors with T _c - 10 K are evaluated adopting Pauling's scale. The relationship between N and T _c was found to separate all the examined high-T _csuperconductors onto two curves: One for the cuprate superconductors having two-dimensional layered structures was a straight line, T _c=29.8+4.1N; the other correlation curve representing the remaining compound superconductors including the doped 113 perovskite and the perovskite-related 214 structures was at lower T _c values but also suggested that increasing electronegativity differences was related to increasing T _c.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

Three-dimensional Gross-Neveu model at nonzero temperature and in the presence of an external electromagnetic field

The phase structure of the (2+1)-dimensional Gross-Neveu model is considered at a nonzero temperatureT and in the presence of an external electromagnetic field. The major results are as follows: 1. AtT=0,H0 (a magnetic field), the original symmetry of the model breaks for anyH values. 2. AtT=0,E0 (an electric field) anE _c is shown to exist, such that forEE _c the original symmetry is broken, but forE>E _c the vacuum of the model is symmetric. 3. AtT0,H0, and at a fixedT value such anH _c (T) is shown to exist that forH>H _c (T) the chiral invariance of the model is spontancously broken. For any fixedH value there exists such anT _c (H) that forT>T _c (H) the symmetry restores. The phase portrait of the model is drawn.     

Some numerical results on the block spin transformation for the 2D Ising model at the critical point

We study the block spin transformation for the 2D Ising model at the critical temperatureT _c . We consider the model with the constraint that the total spin in each block is zero. An old argument by Cassandro and Gallavotti strongly supports the Gibbsianness of the transformed measure, provided that such model has a critical temperatureT _c lower thanT _c . After describing a possible rigorous approach to the problem, we present numerical evidence that indeedT _c <T _c and study the Dobrushin-Shlosman uniqueness condition.     

Temperature-dependent electronic structure of gadolinium

We investigate the electronic structure of the ferromagnetic 4f-metal Gadolinium by use of a many-body evaluation of a generalized model of magnetism, the one-particle part of which is derived from an ASW-LSDA bandstructure calculation. A striking temperature-dependence of the conduction band states is traced back to a 4f-(5d, 6s) interband exchange. The conduction electron polarization (0.63 _B atT=0) decreases forTT _c very similar to the 4f-magnetization. A red shift of the lower -band edge of about 0.25 eV appears upon cooling fromT=T _c toT=0. — The quasiparticle band-structure exibits a remarkable non uniform magnetic behaviour at different positions in the Brillouin zone, and in particular for different subbands. Weakly correlated (s-like) dispersions show a Stoner-likeT-dependence of the exchange splitting. On the other hand, stronger correlated (d-like) dispersions split belowT _c into four branches, two for each spin direction. TheirT-dependence mainly concerns the spectral weights of the quasiparticle peaks and not so much the energetic positions. An exchange caused splitting remains even forT<T _c .     

Dependence ofT c on doping in oxygen-hole induced Jahn-Teller mediated superconductors

A bipolaronic model of high-T _c superconductivity, that is based upon the idea that a doped oxygenhole reduces the separation between the and levels of the neighbouring Cu-ion and hence causes a Jahn-Teller mixing between the two levels, is suggested. Within the BCS scheme, the bipolaron Hamiltonian is investigated for the superconducting order parameter and the critical temperatureT _c as a function of hole-doping. Under suitable approximation for the bipolaronic kinetic energy, the hole-doping dependence ofT _c shows a universal behaviour. For temperatures close toT _c and forT _c 1, obeys the BCS type of relation with pre-factor of (1–T/T _c )² related to the range of superconducting-phase against the doping axis.     

Pressure effect onT c and resistivity: Localization in YBa2Cu3O x oxides

We have studied the effect of hydrostatic pressures up to 20 Kbar on the temperature dependence of the resistivity (T) and the effect of quasihydrostatic pressure up to 200 Kbar on the lattice parameters of YBa₂Cu₃O _x for different oxygen concentrations (x=6.95–6.2). Pressure produces a decrease of resistivity in normal state, an increase ofT _c , and a suppression of semiconducting-like resistivity (T) at lowx. The dependence of dT _c (x)/dP onx is nonmonotonic; the record values of dT _c /dP=(1.0±0.1) K/Kbar are observed forx=6.7 and 6.8. The derivative dln/dP atT=293 K differs by the factor 1.8 between superconducting and nonsuperconducting compounds. The compressibility and its pressure derivative alonga, b andc-directions in YBa₂Cu₃O _x have been determined. The most remarkable variation is alongc-direction. A nonmonotonic dependence of dk _c (x)/dP onx has been observed.The results are discussed in the context of localized effects in disordered oxygen-deficient YBa₂Cu₃O _x .     

Point-contact measurements of CeB6 and CeCu6 in high magnetic fields

Epitaxial YBa₂Cu₄O₇-thin films with thec-axis oriented perpendicular to the film plane were prepared bydc-sputtering from a single stoichiometric target on (100) SrTiO₃-substrates. Typical values of the inductively measured superconducting transitions were about 90 K with a width less than 0.5 K. Critical current densities were measured on 5 to 10 m wide strips as function of magnetic field and temperature. The temperature dependences ofj _c follow a universal functionj _c(B,T)=j _c ^* (T=0,B)·(1–T/T _c (B)) with =1.5±0.1. ForB=0 andT=77 K we obtainedj _c =4·10⁶ A/cm². The field dependence of the resistive transitions was measured with the magnetic field parallel to thec-axis. The slope of the upper critical fieldB _c2 (T) was determined for different criteria. The carrier concentration evaluated from Hall-effect measurements was found to decrease linearly from one per unit cell at 240 K with decreasing temperature extrapolating nearly through zero forT=0. Highly resolved angular dependent measurements of the critical current density withB perpendicular to the current but tilted from thec-axis show a very strong and sharp enhancement ofj _c for the magnetic field parallel to the (CuO₂)-layers (Bc). Additionally to this phenomenon, which is caused by an intrinsic pinning mechanism due to the layered structure of high-T _c -superconductors the influence of the anisotropy of the upper critical field onj _c (B, T, ) is evident nearT _c .     

Thermal expansion,sound velocities,specific heat and pressure derivative ofT c in YBa2Cu3O7

We report measurements, between helium and room temperature, of the thermal expansion (T), sound velocitiesv _L (T) andv _T (v) and specific heatC(T) of YBa₂Cu₃O₇ samples, all cut from the same sintered pellet. A linear term in (T) is resolved at low temperatures. It is compared with a corresponding term in the low temperature specific heat and, using the bulk modulus from our sound propagation measurements, a Grüneisen parameter of usual size (1.2±0.4) is derived-in conformity with the possible existence of non-superconducting carriers well belowT _c . Longtime drift effects in the length of the sample between 30 K and 60 K point to the vicinity of a structural instability. The Debye temperature derived fromC(T) amounts to about 450 K atT=T _c =91 K and forT0 approaches 350 K, in agreement with the value deduced fromv _L (T) andv _T (T). The superconducting transition is indicated by anomalies with idealized discontinuities and C. A thermodynamic relation between and C yields the relative pressure derivative ofT _c ,t _p =T _c ^–1 (T _c /p) _p0=+(0.7±0.2)·10^–7 kbar^–1.     

Critical current density of a YBa2Cu3O7 film: Comparison between experiment and collective pinning theory

With the vibrating reed technique we have measured the critical current densityJ _c of a Y 123 200 nm thin film as a function of magnetic field perpendicular to the CuO₂ planes (O T<B8 T) and temperature (20KT60 K). At fieldsB<0.1 TJ _c is magnetic field independent and decreases at higher fields. A comparison with theory indicates that a crossover from a single pinning to a small bundle collective pinning regime may explain the observed behaviour. According to our estimate the main pinning centers are weak point pins due to oxygen vacancies. From the temperature dependence ofJ _c atB0 we obtain a temperature dependence of the thermodynamical critical fieldB _c (1–T/T _c )² forT20 K which agrees with the anomalous temperature dependence ofB _c2 observed recently in highly anisotropic high temperature superconductors.     

On the Bose-Einstein condensation of free relativistic bosons with or without mass

The Bose-Einstein condensation of free relativistic particles [=(M ² c ⁴ +c ² p ² ) ^1/2 –Mc ² ] is studied rigorously. For massless bosons (=cp), the condensation transition of third (second) order occurs in2 (3) dimensions (D). The molar heat capacity follows the T ² (T ³ ) law below the condensation temperature T_c [k ^B T_c=(2 ² c ² n/1.645) ^1/2 [( ^{2 3} c ³ n/1.202) ^1/3 ], reaches4.38 (10.8) R at T=T_c, and approaches the high-temperature-limit value2 (3) R with no jump (a jump equal to6.75R) in2 (3)D. For finite-mass (M) bosons, the phase transition occurs only in3D with the condensation temperature T_c always smaller than that of the corresponding nonrelativistic bosons [=(2M) ^–1 p ² ]. If the mass M is reduced to zero, the condensation temperature T_c grows monotonically and reaches eventually that of massless relativistic bosons. This mass-dependence of T_c is therefore distinct from the case of nonrelativistic bosons, where T_c grows to infinity as M 0. A brief discussion is given for a possible connection with the normal-to-super transition of the independently moving Cooper pairs (bosons).     

The dynamical correlation function for isotropic ferromagnets forT≧T c

The dynamic correlation function for an isotropic ferromagnet forTT _c is calculated in first order in =6–d. Applying an exponentiation procedure then leads to results which are relevant for the analysis of neutron scattering experiments in the vicinity of the critical point.Supported by the Fonds zur Förderung der wissenschaftlichen Forschung     

Nonequilibrium thermodynamics of lasing and bistable optical systems

A simple model of nonlinear optical systems exhibiting instability—such as in laser action and in bistable absorption—is presented that provides a prototype of nonequilibrium thermodynamics on a statistical basis. The adiabatic reduction of the atomic degrees of freedom in a revised Langevin treatment establishes a fully consistent framework in which the active electromagnetic field mode is in contact with two thermal reservoirs (the cavity and the atoms) as well as being acted upon by an external field. The results are summarized by the first and second laws,dE=W+Q _c +Q _A anddS Q_c/¯T_c+Q_A/¯T_A, with the statistical mechanical representations of the entities therein exhibiting the nature of the mode; i.e., (a) a heat-engine structure operating between two reservoirs of temperatures¯T _c > 0 and¯T _A < 0 for the laser, and (b) a nonlinear response against external work balanced by a single reservoir (¯ T _c = ¯T _A ) for the absorptive bistability.Originally presented at the Taniguchi Symposium, October 1979.⁴⁴