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

Abstract

We propose a phenomenological Ginzburg-Landau-like theory of cuprate superconductivity. The free energy is expressed as a functional F of the spin-singlet pair amplitude psi_ij=psi_m=Delta_m exp(i phi_m); i and j are nearest-neighbor sites of the Cu lattice in which the superconductivity is believed to primarily reside and m labels the site 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[Delta,phi]=sum_m (A Delta_m^2+ B Delta_m^4/2)+C sum_<mn> Delta_m Delta_n cos(phi_m-phi_n), for the functional. The coefficients A, B and C are determined from comparison with experiments. We 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 <Delta_m> from small to large values as A changes sign on lowering T and the crossover temperatures is identified with the observed pseudogap temperature. The superconducting phase-coherence transition occurs at a different temperature T_c, and describes superconductivity with d-wave symmetry for C>0. We calculate T_c(x) which has the observed parabolic shape, being strongly influenced by the coupling between Delta_m and phi_m present in F. The superfluid density, the local gap magnitude, the specific heat (with and without a magnetic field) and vortex properties are obtained using F. We compare our results successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the pair correlation function calculated from F. Features such as temperature dependent Fermi arcs, antinodal pseudogap filling temperature, pseudogapped density of states in different momentum regions of the Fermi surface and `bending' of the energy gap versus momentum on the Fermi surface emerge from the theory.

19 pages, 16 figures (to appear in Phys. Rev. B)

References in corpus (13)

• Scanning tunneling spectroscopy of high-temperature superconductors
• Inelastic Light Scattering From Correlated Electrons
• Two Gaps Make a High Temperature Superconductor?
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• Laser ARPES, the sudden approximation, and quasiparticle-like peaks in Bi2Sr2CaCu2O8+delta
• Evolution of the electronic excitation spectrum with strongly diminishing hole-density in superconducting Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}
• Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films
• Specific-Heat Measurement of Residual Superconductivity in the Normal State of Underdoped Cuprate Superconductors
• 4D-XY quantum criticality in a doped Mott insulator
• Doping dependence of the vortex-core energy in bilayer films of cuprates
• Giant proximity effect in a phase-fluctuating superconductor
• Finite temperature superfluid density in very underdoped cuprates

Cited by in corpus (14)

• A Phenomenological Theory of the Anomalous Pseudogap Phase in Underdoped Cuprates
• Fractionalized pair density wave in the pseudo-gap phase of cuprate superconductors
• Effective SU(2) theory for the pseudogap state
• Magic gap ratio for optimally robust fermionic condensation and its implications for high-Tc superconductivity
• Pairing Fluctuations Determine Low Energy Electronic Spectra in Cuprate Superconductors
• Disordered XY model: effective medium theory and beyond
• Fluctuations and Higgs mechanism in Under-Doped Cuprates: a Review
• The correlation between the Nernst effect and fluctuation diamagnetism in strongly fluctuating superconductors
• Electronic spectral function in fractionalized Pair Density Wave scenario
• Incipient loop current order in the under-doped cuprate superconductors
• High Temperature Superconductivity in the Cuprates: Materials, Phenomena and a Mechanism
• Phase transitions and order in two-dimensional generalized nonlinear $\sigma$-models
• Reliability of the Ginzburg-Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions
• Ginzburg-Landau Like Theory for High Temperature Superconductivity in the Cuprates: Emergent d-wave Order