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arXiv1995

Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping

A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping $t^{\prime }=-0.35t$ as a model for high-temperature superconductors. Magnetic properties are analyzed using the Two-Particle Self-Consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite $% t^{\prime }$ and at $t^{\prime }=0$ but for two totally different physical reasons. When $t^{\prime }=0$, it is induced by antiferromagnetic correlations while at $t^{\prime }=-0.35t$ it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with $% T $-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the $d$-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.

cond-mat↗

arXiv1994

Symmetries and Mean-Field Phases of the Extended Hubbard Model

The two-dimensional extended Hubbard model that includes a nearest- neighbor Heisenberg interaction is studied using a mean-field theory where quasiparticles are defined by an U(8) group of canonical transformations. The theory is a generalization of the ordinary BCS theory, and Balian and Werthamer's theory of He-3 that permits both broken gauge, spin and sublattice symmetry. This allows us to investigate superconductivity, antiferromagnetic order, charge density waves and, by twisting the spin quantization axis, spiral antiferromagnetic order in the same theory. Our results for positive Hubbard U and Heisenberg exchange J suggest that antiferromagnetic ordering dominates close to half filling, while spiral states and d-wave superconductivity compete when doping is introduced. For moderate values of J, we find a phase diagram where a phase transition occurs from an antiferromagnet to a d-wave superconductor as doping is increased. A narrow region of (s+id)-wave superconductor is found for some values of J and U.

cond-mat↗

arXiv1994

Two-Dimensional t-J Model at Low Electron Density

The phase diagram of the two-dimensional t-J model is determined accurately at low electron density by a combination of analytic and numerical techniques. The ground state exhibits three phases in the limit of zero electron density: an unpaired state at small J/t, a gas of s-wave pairs for 2 < J/t < 3.4367, and a phase separated state at larger interaction strengths. Bound states of larger clusters are never realized, and the instabilities present at small densities are discussed.

cond-mat↗

arXiv1994

Phenomenological Models for the Gap Anisotropy of Bi-2212 as Measured by ARPES

Recently, high resolution angle-resolved photoemission spectroscopy has been used to determine the detailed momentum dependence of the superconducting gap in the high temperature superconductor Bi-2212. In this paper, we first describe tight binding fits to the normal state dispersion and superlattice modulation effects. We then discuss various theoretical models in light of the gap measurements. We find that the simplest model which fits the data is the anisotropic s-wave gap $\cos(k_x)\cos(k_y)$, which within a one-band BCS frame- work suggests the importance of next near neighbor Cu-Cu interactions. Various alternative interpretations of the observed gap are also discussed, along with the implications for microscopic theories of high temperature superconductors.

cond-mat↗

arXiv1995

Superconductivity from correlated hopping

We consider a chain described by a next-nearest-neighbor hopping combined with a nearest-neighbor spin flip. In two dimensions this three-body term arises from a mapping of the three-band Hubbard model for CuO$_2$ planes to a generalized $t-J$ model and for large O-O hopping favors resonance-valence-bond superconductivity of predominantly $d$-wave symmetry. Solving the ground state and low-energy excitations by analytical and numerical methods we find that the chain is a Luther-Emery liquid with correlation exponent $K_ρ = (2-n)^2/2$, where $n$ is the particle density.

supr-con↗

arXiv1995

Gapless Time-Reversal Symmetry Breaking Superconductivity

We consider a layered superconductor with a complex order parameter whose phase switches sign from one layer to the next. This system is shown to exhibit gapless superconductivity for sufficiently large interlayer pairing or interlayer hopping. In addition, this description is consistent with experiments finding signals of time-reversal symmetry breaking in high-temperature superconductors only at the surface and not in the sample bulk.

cond-mat↗

arXiv1995

Renormalization group approach to layered superconductors

A renormalization group theory for a system consisting of coupled superconducting layers as a model for typical high-temperature superconducters is developed. In a first step the electromagnetic interaction over infinitely many layers is taken into account, but the Josephson coupling is neglected. In this case the corrections to two-dimensional behavior due to the presence of the other layers are very small. Next, renormalization group equations for a layered system with very strong Josephson coupling are derived, taking into account only the smallest possible Josephson vortex loops. The applicability of these two limiting cases to typical high-temperature superconductors is discussed. Finally, it is argued that the original renormalization group approach by Kosterlitz is not applicable to a layered system with intermediate Josephson coupling.

supr-con↗

arXiv1995

Antiferromagnetic Excitations and Van Hove Singularities in YBa$_2$Cu$_3$O$_{6+x}$

We show that in quasi-two-dimensional $d$-wave superconductors Van Hove singularities close to the Fermi surface lead to novel magnetic quasi-particle excitations. We calculate the temperature and doping dependence of dynamical magnetic susceptibility for YBCO and show that the proposed excitations are in agreement with inelastic neutron scattering experiments. In addition, the values of the gap parameter and in-plane antiferromagnetic coupling are much smaller than usually believed.

cond-mat↗

arXiv1995

Microwave Properties of Borocarbide Superconductors LnNi2B2C (Ln = Y, Er, Tm, Ho)

We report measurements of the microwave surface impedance of the borocarbide family of superconductors LnNi2B2C (Ln=Y, Er, Tm, Ho). The experiments enable direct measurements of the superfluid density, and are particularly sensitive to the influence of magnetic pairbreaking. In HoNi2B2C the antiferromagnetic transition is clearly observed at zero field, and leads to a drastic reduction of the superfluid density, which recovers at lower temperatures. In ErNi2B2C the antiferromagnetic transition is not seen in zero field data. Magnetic effects are responsible for anomalies in the low temperature surface impedance below approximately 4K in HoNi2B2C and TmNi2B2C. The temperature dependence of the microwave impedance disagrees with simple BCS calculations.

supr-con↗

arXiv1995

Umklapp scattering from spin fluctuations in Copper-Oxides

The $\mathbf k$-dependent electronic momentum relaxation rate due to Umklapp scattering from antiferromagnetic spin fluctuations is studied within a renormalized mean-field approach to an extended $t-J$ model appropriate to YBa$_2$Cu$_3$O$_{7-x}$ and other cuprates. Transport coefficients are calculated in a relaxation time approximation. We compare these results with those obtained with the phenomenological assumption that all scattering processes dissipate momentum. We show that the latter, which violates momentum conservation, leads to quite different magnitudes and temperature dependences of resistivities and Hall coefficients.

cond-mat↗

arXiv1995

Flux Creep and Flux Jumping

We consider the flux jump instability of the Bean's critical state arising in the flux creep regime in type-II superconductors. We find the flux jump field, $B_j$, that determines the superconducting state stability criterion. We calculate the dependence of $B_j$ on the external magnetic field ramp rate, $\dot B_e$. We demonstrate that under the conditions typical for most of the magnetization experiments the slope of the current-voltage curve in the flux creep regime determines the stability of the Bean's critical state, {\it i.e.}, the value of $B_j$. We show that a flux jump can be preceded by the magneto-thermal oscillations and find the frequency of these oscillations as a function of $\dot B_e$.

supr-con↗

arXiv1995

Electronic thermal conductivity and the Wiedemann-Franz law for unconventional superconductors

We use the quasiclassical theory of superconductivity to calculate the electronic contribution to the thermal conductivity. The theory is formulated for low temperatures when heat transport is limited by electron scattering from random defects and for superconductors with nodes in the order parameter. We show that certain eigenvalues of the thermal conductivity tensor are universal at low temperature, $k_B T\ll γ$, where $γ$ is the bandwidth of impurity bound states in the superconducting phase. The components of the electrical and thermal conductivity also obey a Wiedemann-Franz law with the Lorenz ratio, $L(T)=κ/σT$, given by the Sommerfeld value of $L_{\!S}=({π^2}/{3})(k_B/e)^2$ for $k_BT\llγ$. For intermediate temperatures the Lorenz ratio deviates significantly from $L_{\!S}$, and is strongly dependent on the scattering cross section, and qualitatively different for resonant vs.\ nonresonant scattering. We include comparisons with other theoretical calculations and the thermal conductivity data for the high $T_c$ cuprate and heavy fermion superconductors.

cond-mat↗

arXiv1995

Vortex structure and resistive transitions in high-Tc superconductors

The nature of the resistive transition for a current applied parallel to the magnetic field in high-Tc materials is investigated by numerical simulation on the three dimensional Josephson junction array model. It is shown by using finite size scaling that for samples with disorder the critical temperature Tp for the c axis resistivity corresponds to a percolation phase transition of vortex lines perpendicularly to the applied field. The value of Tp is higher than the critical temperature for j perpendicular to H, but decreases with the thickness of the sample and with anisotropy. We predict that critical behavior around Tp should reflect in experimentally accessible quantities, as the I-V curves.

supr-con↗

arXiv1995

Vortex structure in $d$-wave superconductors

Vortex structure of pure $d_{x^2-y^2}$-wave superconductors is microscopically analyzed in the framework of the quasi-classical Eilenberger equations. Selfconsistent solution for the $d$-wave pair potential is obtained for the first time in the case of an isolated vortex. The vortex core structure, i.e., the pair potential, the supercurrent and the magnetic field, is found to be fourfold symmetric even in the case that the mixing of $s$-wave component is absent. The detailed temperature dependences of these quantities are calculated. The fourfold symmetry becomes clear when temperature is decreased. The local density of states is calculated for the selfconsistently obtained pair potential. From the results, we discuss the flow trajectory of the quasiparticles around a vortex, which is characteristic in the $d_{x^2-y^2}$-wave superconductors. The experimental relevance of our results to high temperature superconductors is also given.

supr-con↗

arXiv1995

$s$- and $d_{xy}$-wave components induced around a vortex in $d_{x^2-y^2}$-wave superconductors

Vortex structure of $d_{x^2-y^2}$-wave superconductors is microscopically analyzed in the framework of the quasi-classical Eilenberger equations. If the pairing interaction contains an $s$-wave ($d_{xy}$-wave) component in addition to a $d_{x^2-y^2}$-wave component, the $s$-wave ($d_{xy}$-wave) component of the order parameter is necessarily induced around a vortex in $d_{x^2-y^2}$-wave superconductors. The spatial distribution of the induced $s$-wave and $d_{xy}$-wave components is calculated. The $s$-wave component has opposite winding number around vortex near the $d_{x^2-y^2}$-vortex core and its amplitude has the shape of a four-lobe clover. The amplitude of $d_{xy}$-component has the shape of an octofoil. These are consistent with results based on the GL theory.

supr-con↗

arXiv1995

Electromagnetic Absorption in an Anisotropic Layered Superconductor

We calculate the infrared conductivity tensor of a layered superconductor considering two different order parameter symmetries: strongly anisotropic $s$-wave with line nodes, and pure ($d_{x^2-y^2}$) $d$-wave. The calculations are performed within the quasiclassical theory of superconductivity and include the effects of non-magnetic scattering processes. We discuss to what extent measurements of the optical absorption can be relied upon to distinguish between these two order parameter symmetries.

cond-mat↗

arXiv1995

Vortex reflection at boundaries of Josephson-junction arrays

We study the propagation properties of a single vortex in square Josephson-junction arrays (JJA) with free boundaries and subject to an applied dc current. We model the dynamics of the JJA by the resistively and capacitively shunted junction (RCSJ) equations. For zero Stewart-McCumber parameter $β_c$ we find that the vortex always escapes from the array when it gets to the boundary. For $β_c\geq 2.5$ and for low currents we find that the vortex escapes, while for larger currents the vortex is reflected as an antivortex at one edge and the antivortex as a vortex at the other, leading to a stationary oscillatory state and to a non-zero time-averaged voltage. The escape and the reflection of a vortex at the array edges are qualitatively explained in terms of a coarse-grained model of a vortex interacting logarithmically with its image. We also discuss the case when the free boundaries are at $45$ degrees with respect to the direction of the vortex motion. Finally, we discuss the effect of self-induced magnetic fields by taking into account the full-range inductance matrix of the array, and find qualitatively equivalent results.

cond-mat↗

arXiv1995

Screening current effects in Josephson junction arrays

The purpose of this work is to compare the dynamics of arrays of Josephson junctions in presence of magnetic field in two different frameworks: the so called XY frustrated model with no self inductance and an approach that takes into account the screening currents (considering self inductances only). We show that while for a range of parameters the simpler model is sufficiently accurate, in a region of the parameter space solutions arise that are not contained in the XY model equations.

supr-con↗