c-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO₂ layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT _c. Our model calculation demonstrates that a pronounced enhancement ofT _c in thed-wave channel is possible. The largest enhancement ofT _c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.     

Effects of phonons and antiferromagnetic spin fluctuations on the pairing and density of states in high-T c superconductors

We solve the Eliashberg equations for a two-dimensional, tight-binding band and anisotropic interaction due to exchange of phonons and antiferromagnetic spin fluctuations. For small band fillings, a mixture of simple and extendeds-wave pairing is stable, while for band fillings closer to half-filling thed-wave pairing state becomes stable. The density of statesN() becomes highly asymmetric in for smaller band fillings, which is an effect of particle-hole asymmetry. For thed-wave stateN() is linear in for small and exhibits a logarithmic singularity at the gap amplitude. For the mixeds-wave stateN() shows the BCS singularity at the gap edge. Antiferromagnetic spin fluctuations give rise to a pseudogap inN() for the normal state.     

Odd frequency pairing in superconductors

The properties of a superconductor having an energy gap function _k( _n ) which is an odd function of frequency _n, or time, are investigated. One finds (a) the allowed pair orbital angular momenta for spin zero and spin one are interchanged, permittingS= 0, l=1 and S=1, l=0 condensates; (b) there exists an equal-time order parameter corresponding to condensation of a spin wave coupled to two fermions, in contrast to the conventional timereversed fermion pair condensate; an explicit energy gap equation is derived for this composite operator condensate; (c) the coherence factors are shown to be reversed from those of conventional pairing, for>2, removing the peak in thea+C conductivity() and generating a peak in the>2 acoustic attenuation as a function of temperature; (d) the Josephson current vanishes between an even and odd frequency superconductor, and vanishes to leading order in the tunneling rates t ₁₂ ² .The authors wish to acknowledge the support of the National Science Foundation, grant No. DMR92-13295 (J.R.S.) and No. DMR 92-205027 (D.J.S.). They would like to thank Leo Lilly and William Putikka for helpful discussions.     

Phase separation and charge density waves: Possible sources of non-Fermi liquid behavior and pairing in high-temperature superconductors

In the absence of a sufficiently singular interaction between the particles, the Fermi-liquid state is stable above one dimension. To reconcile this finding with the observed anomalies in the cuprates one is therefore led to the search for mechanisms giving singular interactions. A recent proposal indicates the cuprates as being close to a charge instability, which would drive the system toward phase separation (in the absence of long-range Coulomb forces between the carriers) or toward the formation of incommensurate charge-density waves in the more physical case of charged carriers. Close to these instabilities strong singular and attractive scattering arises between the quasiparticles at the Fermi surface. This scattering would easily account for both the anomalous behavior of the normal metallic phase and for the strong pairing mechanism leading to high-temperature superconductivity. The strong momentum dependence of the singular attraction would also give rise to the (likely) observed unusuald-wave symmetry of the superconducting order parameter in these systems.     

In-plane impurities in high-temperature superconductors

We review important results on the influence of substitutional elements in the CuO₂-planes of the high-T_c-superconductors and compare them with recent measurements on Bi₂Sr₂Ca₁Cu₂O₈₊ single crystals with doping of Fe, Ni and Zn. The results on the single crystals reveal a remarkably strong influence of the in-plane impurities on the superconducting parameters. The impurities introduce a very effective elastic and inelastic scattering and cause a definitive change of the coherence length and the penetration depth.     

Temperature-dependent resistivity from phonons in cuprate superconductors

The temperature dependence of the resistivity of the cuprate superconductors arising from phonon scattering is considered within standard Bloch-Gruneisen theory allowing for several different shapes of transport spectral functions _tr ² F(). In contrast to often made comments that linear resistivity is not characteristic of electron-phonon scattering, it is shown rather that it is more difficult to get muchnonlinearity from this theory except below 50–100 K, and in this low-T regime better solutions to the Boltzmann equation might be required. The reasons for the linear behavior are clarified, and the variations to be expected from possible coupling functions are explored. Possible origins of the nonlinear resistivity seen in YBa₂Cu₄O₈ and recently in YBa₂Cu₃O₇ are suggested, and effects not included specifically in these calculations are discussed. It is also pointed out that phonon contributions to the energy () dependence of quasiparticles, which is a closely related consequence of electron-phonon coupling, will differ significantly from the simple ² Fermi liquid behavior that is commonly assumed.     

Metallic stripes in high-temperature superconductors

A phenomenological approach is applied to explore signatures of disordered charge stripes and antiphase spin domains in single-particle properties of the high-temperature superconductors. Stripe phases are shown to explain many experimentally observed unusual features measured in angle-resolved photoemission and optical spectroscopy. It is argued that disordered and fluctuating stripe phases are a common feature of high-temperature superconductors, supported by the additional evidence from neutron scattering and NMR.     

Magnetic resonance in high-temperature superconductors

Since the discovery of high-temperature superconductors a new microwave absorption has been found. The microwaves are absorbed in the flux-quantized eigenstates so that the absorption is proportional to the Josephson current and hence it varies as the gap of the superconductor. This absorption is found in the electron-paramagnetic resonance configuration. The flux-quantized fields are found in small domains of the size of 10⁻⁶ cm. A giant moment is found to occur. The necessary theory as well as experiments in YBa₂Cu₃O_7−δ type compounds are described. The Cu²⁺ electron-paramagnetic resonance gives an anisotropic exchange narrowed line with anisotropicg-values withg-shift proportional to susceptibility. The symmetry of theg-value also reflects the symmetry of the superconducting gap.     

Thermodynamics of D-wave pairing in cuprate superconductors

The mechanism of d-pairing with account of antiferromagnetic spin fluctuations was considered. The thermodynamics of d-wave pairing in cuprate supercoductors was calculated. For the calculation the method of functional integrals was used. It has been shown that the temperature dependence of specific heat corresponds to d-pairing. The value of the jump of specific heat /T_c for the compounds YBa₂ Cu₃ O_6.63 was given.     

Cryocoolers for the new high-temperature superconductors

Compact, reliable, low-cost cryocoolers operated simply by closing a switch are an essential requirement for the coming age of superconductivity and cold electronic systems. The advent of high-temperature superconductors has substantially eased the task of those seeking to fill the above need. This article reviews some recent developments in cryocooler systems and examines some prospects for the future.     

Structural commonalities of high-temperature superconductors

It is shown that all of the presently known high-temperature superconductors belong to one structural type with a basic cell of approximate 4/mmm,D _4h symmetry in tetragonal compounds andmmm,D _2h symmetry in orthorhombic compounds. In the Ba(Pb1–xBi _x )O₃ and YBa₂Cu₃O_7– compounds the basic cell is the unit cell and in the (La_1–x Sr _x )₂CuO₄, BiSrCaCuO and TIBaCaCuO compounds it is half the unit cell. The features of more than one copper oxide layer per basic cell, oxygen-free cation layers (e.g., Ca, Y) between CuO₂ layers, and slightly puckered CuO₂ planes seem to favor higher transition temperatures. The feasibility of several proposed or potentially superconducting structures are analyzed by this scheme.     

Thermal properties of high-temperature superconductors

The specific heat and thermal conductivity measurements of YBa₂Cu₃O_7– high-T _c superconductors were performed by an a.c. calorimetry method. Investigations of the specific heat of YBa₂Cu₃O_7– ceramics in magnetic fields show that an increase in the magnetic field reduces the jump in the specific heat, broadens the transition region, and shifts the transition temperature downward by about 0.5 K, Temperature dependence of the specific heat of a YBa₂Cu₃O_7– high-T _c superconducting ceramic reveals that fluctuation affect the specific heat near the superconducting transition, Critical exponents = = 0.5, the critical amplitudesC ⁺ =C ^– = 0.5 J · mol^–1 K^–1, the space dimensionalityd = 3, and the number of components in the order parametern = 3 is calculated, The specific heat and the along-c-axis thermal conductivity of YBa₂Cu,₃O_7– single crystal were simultaneously measured.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder. Colorado, U.S.A.     

Transport of high-temperature superconductors in the normal state

The impurity mechanism proposed earlier is used to interpret the transport properties of high-temperature superconductors in the normal state. Temperature and impurity concentration dependences of the resistance and the Seebeck and Hall coefficients are discussed. An explanation for the sharp drop in the Seebeck and Hall coefficients with impurity concentration and reducing them to zero in La_2–x Sr _x CuO₄ at the maximumx at which superconductivity exists is put foward.     

Spin glass state in high-temperature superconductors

The glass state of high-temperature superconductors in the models of Josephson weak links is studied. Reversibility phenomena in weak magnetic fields are outlined.     

Constraints on the pairing state of the cuprate superconductors

The pairing state of the cuprate superconductors is a key issue in understanding experiments and in clarifying possible mechanisms. A wide range of experiments now show that the gap function is predominantly in character. Here we discuss the relevant experiments, especially focusing on those which provide constraints on possible mixed pairing states, such as s+d and s+id.     

Cooperative polaronic and electronic effects in high-temperature superconductors

An anharmonic electron phonon interaction model is used to study lattice and electronic effects of high-temperature superconductors (HTSC). Due to higher-order electron densitymultiphonon interactions the effective electron-phonon coupling experiences a strongq-dependence which leads to incommensurations, stripes, and tweeds in the dynamical ionic displacement pattern. Simultaneously these terms induce strong interband interactions which enhance the intraband electron-hole pair formation and contribute substantially to the high superconducting transition temperaturesT _c . The resulting superconducting gap structure is highly anisotropic. and using its energy-dependent structure the experimentally observed electromagnetic response is calculated and well reproduced.     

Radio frequency sputtering and the deposition of high-temperature superconductors

This paper reviews the background to glow-discharge sputter deposition of thin films and the deposition of YBCO superconducting thin films in particular. The background to sputtering is briefly reviewed with reference to the recent literature on analytical and numerical techniques for investigating radiofrequency (r.f.) plasmas, magnetron sputtering and hysteretic behaviour in reactive sputtering. Low-energy, ion-assisted deposition techniques are briefly reviewed, and the effect of ion-beam interactions on film nucleation and growth is also discussed. The background to the sputter deposition of high-temperature superconductors (HTS) is given along with the choice of sputtering system for HTS deposition. Resputtering effects, off-axis andin-situ/ex-situ processing are also discussed. The sputter deposition of YBa₂Cu₃O _x is considered in detail along with theP-T-x oxidation conditions and the tetragonal/orthorhombic line. Typical experimental arrangements and results for YBCO sputtered onto SrTiO₃ and MgO are given. The problem of producing high-critical-current-density polycrystalline films by sputtering is also discussed.     

Dynamical stripe correlations in Cuprate superconductors

Based on the recent observation of the stripe instability in Cuprate superconductors, we present the hypothesis that the normal state finds its origin in a particular kind of stripe-quantum fluid. The charged domain walls are interpreted as strings on a lattice and the quantum fluctuation of an individual string is driven by a proliferation of kinks. The kink dynamics gives rise to meandering fluctuations of the string as a whole. We identify a special string vacuum characterized by a proliferation of charged kinks. This state carries a Luttinger-liquid like electronic excitation spectrum.     

Activated flux creep in layered high-temperature superconductors

We study thermally activated flux creep in layered superconductors in the case when the magnetic field is parallel to the layers and vortices move across the layers. We assume that the sample is without imperfections, so that the pinning is due to an interaction between vortices and the layered microstructure of the superconductors. The height of the energy barrier that vortices overcome during each activation process is calculated in the case when the vortex lattice period is commensurate with the interlayer spacing. This energy barrier depends on the transport current: it grows at small currents and goes to zero linearly whenjj _c wherej _c is the depinning current.