Superconducting transitions from the pseudogap state: d-wave symmetry, lattice, and low-dimensional effects

We investigate the behavior of the superconducting transition temperature within a previously developed BCS-Bose Einstein crossover picture. This picture, based on a decoupling scheme of Kadanoff and Martin, further extended by Patton, can be used to derive a simple form for the superconducting transition temperature in the presence of a pseudogap. We extend previous work which addressed the case of s-wave pairing in jellium, to explore the solutions for T_c as a function of variable coupling in more physically relevant situations. We thereby ascertain the effects of reduced dimensionality, periodic lattices and a d-wave pairing interaction. Implications for the cuprate superconductors are discussed.Comment: REVTeX, 11 pages, 6 EPS figures included, Replace with published versio

Superconductivity and Density Wave in the Quasi-One-Dimensional Systems: Renormalization Group Study

The anisotropic superconductivity and the density wave have been investigated by applying the Kadanoff-Wilson renormalization group technique to the quasi-one-dimensional system with finite-range interactions. It is found that a temperature (T) dependence of response functions is proportional to exp(1/T) in a wide region of temperature even within the one-loop approximation. Transition temperatures are calculated to obtain the phase diagram of the quasi-one-dimensional system, which is compared with that of the pure-one-dimensional system. Next-nearest neighbor interactions (V_2) induce large charge fluctuations, which suppress the d_{x^2 -y^2}-wave singlet superconducting (dSS) state and enhance the f-wave triplet superconducting (fTS) state. From this effect, the transition temperature of fTS becomes comparable to that of dSS for large V_2, so that field-induced f-wave triplet pairing could be possible. These features are discussed to comprehend the experiments on the (TMTSF)_2PF_6 salt.Comment: 8 pages, 4 figures, submitted to J. Phys. Soc. Jp

Ginzburg-Landau theory of superconductors with short coherence length

We consider Fermions in two dimensions with an attractive interaction in the singlet d-wave channel of arbitrary strength. By means of a Hubbard-Stratonovich transformation a statistical Ginzburg-Landau theory is derived, which describes the smooth crossover from a weak-coupling BCS superconductor to a condensate of composite Bosons. Adjusting the interaction strength to the observed slope of H_c2 at T_c in the optimally doped high-T_c compounds YBCO and BSCCO, we determine the associated values of the Ginzburg-Landau correlation length xi and the London penetration depth lambda. The resulting dimensionless ratio k_F xi(0) approx 5-8 and the Ginzburg-Landau parameter kappa=lambda xi approx 90-100 agree well with the experimentally observed values. These parameters indicate that the optimally doped materials are still on the weak coupling side of the crossover to a Bose regime.Comment: 12 pages, RevTeX, 6 postscript figures, resubmitted with minor changes in section III, to appear in Physical Review

Pseudogap and Superconducting Fluctuation in High-Tc Cuprates: Theory beyond 1-loop Approximation

The pseudogap phenomena induced by the SC fluctuation are investigated in details. We perform a calculation beyond the 1-loop approximation. The SC fluctuation is microscopically derived on the basis of the repulsive Hubbard model. The vertex corrections are collected in the infinite order with use of the quasi-static approximation. The single-particle excitations, NMR 1/T_{1}T, spin susceptibility and superconducting transition temperature are discussed. The important role of the vertex correction is pointed out for the single particle spectral function. On the other hand, the validity of the 1-loop order theory is confirmed for other quantities. We shed light on the essential nature of SC fluctuation leading to the pseudogap from the comparison with spin and charge fluctuations

Nonperturbative XY-model approach to strong coupling superconductivity in two and three dimensions

For an electron gas with delta-function attraction we investigate the crossover from weak- to strong-coupling supercoductivity in two and three dimensions. We derive analytic expressions for the stiffness of phase fluctuations and set up effective XY-models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature T_c as a monotonous function of the coupling strength and carrier density both in two and three dimensions, and give analytic formulas for the merging of the temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.Comment: Few typos corrected. Emails that were sent to the address [email protected] in June and July 1999 were lost in a computer crash, so if your comments were not answered please send them once mor