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

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_ 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 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.Comment: 19 pages, 16 figures (to appear in Phys. Rev. B

Mott physics, sign structure, ground state wavefunction, and high-Tc superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-Tc superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature "strange metal phase" of the doped Mott insulator.Comment: 12 pages, 12 figure

Dirac's method for constraints - an application to quantum wires,the 0.7 conductance anomaly

We investigate the Hubbard model in the limit $U=\infty$, which is equivalent to the statistical condition of exclusion of double occupancy. We solve this problem using Dirac's method for constraints. The constraints are solved within the Bosonization method. We find that the constraints modify the anomalous commutator. We apply this theory to quantum wires at finite temperatures where the Hubbard interaction is $U=\infty$. We find that the anomalous commutator induced by the constraints gives rise to the 0.7 anomalous conductance.Comment: To be published in J.Phys:Condens.Matter, April 201

Ground state and finite temperature behavior of 1/4-filled band zigzag ladders

We consider the simplest example of lattice frustration in the 1/4-filled band, a one-dimensional chain with next-nearest neighbor interactions. For this zigzag ladder with electron-electron as well as electron-phonon interactions we present numerical results for ground state as well as thermodynamic properties. In this system the ground state bond distortion pattern is independent of electron-electron interaction strength. The spin gap in the ground state of the zigzag ladder increases with the degree of frustration. Unlike in one-dimension, where the spin-gap and charge ordering transitions can be distinct, we show that in the ladder they occur simultaneously. We discuss spin gap and charge ordering transitions in 1/4-filled materials with one, two, or three dimensional crystal structures. We show empirically that regardless of dimensionality the occurrence of simultaneous or distinct charge and magnetic transitions can be correlated with the ground state bond distortion pattern.Comment: 12 pages, 8 eps figure

The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins

We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N=40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J2^{c1} and J2 > J2^{c2} separated by a gapful quantum paramagnetic phase. We estimate J2^{c1} \approx 0.35J1 and J2^{c2} \approx 0.66J1.Comment: 16 pages, 2 tables, 11 figure