Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose and develop here a phenomenological Ginzburg-Landau-like theory of cuprate high-temperature superconductivity. The free energy of a cuprate superconductor is expressed as a functional F of the complex spin-singlet pair amplitude ψij≡ψm=Δmexp(iϕm), where i and j are nearest-neighbor sites of the square planar Cu lattice in which the superconductivity is believed to primarily reside, and m labels the site located at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form F[Δ,ϕ]=∑m[AΔm2+(B/2)Δm4]+C∑<mn>ΔmΔncos(ϕm−ϕn) for the functional, where m and n are nearest-neighbor sites on the bond-center lattice. This form is analogous to the original continuum Ginzburg-Landau free-energy functional; the coefficients A, B, and C are determined from comparison with experiments. A combination of analytic approximations, numerical minimization, and Monte Carlo simulations is used to work out a number of consequences of the proposed functional for specific choices of A, B, and C as functions of hole density x and temperature T. There can be a rapid crossover of <Δm> from small to large values as A changes sign from positive to negative on lowering T; this crossover temperature Tms(x) is identified with the observed pseudogap temperature T*(x). The thermodynamic superconducting phase-coherence transition occurs at a lower temperature Tc(x), and describes superconductivity with d-wave symmetry for positive C. The calculated Tc(x) curve has the observed parabolic shape. The results for the superfluid density ρs(x,T), the local gap magnitude <Δm>, the specific heat Cv(x,T) (with and without a magnetic field), as well as vortex properties, all obtained using the proposed functional, are compared successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the correlation function of the pair amplitude calculated from the functional, and compare the results successfully with the electronic spectrum measured through angle resolved photoemission spectroscopy (ARPES). For the specific heat, vortex structure, and electron spectral density, only some of the final results are reported here; the details are presented in subsequent papers