Phenomenological model of the copper oxide superconductors

Abstract

We propose a phenomenological model for the copper oxide superconductors in which one complex s-wave order parameter (OP) is associated with each of the N conducting layers per unit cell, with N-1 equal spacings d and one different spacing d’; the c axis repeat distance s=d’+(N-1)d. The layers are coupled by Josephson-like tunneling, with parameters ζ1 and ζ2, respectively. The Gaussian fluctuation free energy is diagonalized, yielding N distinct Tc values. Just above the highest Tc, the fluctuations are usually dominated by the three-dimensional (3D) regime of a single cellular OP. In the 2D regime further above Tc, more of the OP’s contribute to the fluctuations, their relative contributions depending upon the ζ1 and ζ2 values. The temperature (T) and angular (θ) dependence of the resulting fluctuation magnetization M(θ,T) is calculated. In a weak magnetic field B [B<B0=φ0/(svFτφ), where φ0, vF, and τφ are the flux quantum, intralayer Fermi velocity, and phase coherence lifetime, respectively], the susceptibility χαβ is diagonal in the crystal representation, resulting in an ordinary (anisotropic mass) θ dependence at fixed T near Tc. At very high fields in very high-quality single crystals (ωcτφ≫1, where ωc is the pair cyclotron frequency), M is best evaluated in the field representation. The component MB(θ,T) exhibits anomalous oscillations in its θ dependence, arising from degenerate multiple minima in the pair potential, provided that the effective high-momentum cutoff qc* is sufficiently large. In this field regime, qc* is either on the order of πs/a, where a is the intralayer oxygen site repeat distance, or equal to π[1+(B/B0)sinθ]. The oscillations are similar to de Haas–van Alphen oscillations in the B dependence of the normal state M. They are broadened by local, clean-limit dynamic effects but should be observable for τφkBTc/ħ≳≳≳1 and N>=2, which we argue is the case in the best samples. In addition, the fluctuation specific heat (FSH) and Aslamazov-Larkin conductivity are calculated for B=0, including dynamic effects. For arbitrary N, the FSH above Tc is found to be proportional to χcc(T)/T. For fits of the theoretical FSH to experimental data, it is necessary to modify the mean-field expressions for T<Tc, such that the entropy of the superconducting transition remains zero. An example of such a modification is given. All fluctuation quantities exhibit dimensional crossover (DCR) from 3D behavior near Tc to 2D behavior further from Tc. For the fluctuation diamagnetism the DCR temperature T0(θ) depends strongly upon θ in the vicinity of π/2, where it diverges. Away from Tc dynamic effects are found to be important and can be so strong as to mimic DCR behavior, even for θ=π/2, for which DCR should not occur. The dynamic effects make quantitative corrections to the fluctuation quantities for T as close as 1 K to Tc. For N=2 detailed plots of the above fluctuation quantities for a range of the microscopic parameters are presented.

Source-reported materials — not catalogue approval

Similar papers