Landau theory of phase separation in cuprates

I discuss the problem of phase separation in cuprates from the point of view of the Landau theory of Fermi liquids. I calculate the rate of growth of unstable regions for the hydrodymanics and collisionless limit and, in presence of long range Coulomb interactions, the size of these regions. These are analytic results valid for any strength of the Landau parameters.Comment: RevteX, preprint ITP (1994

Quasi-1D dynamics and nematic phases in the 2D Emery model

We consider the Emery model of a Cu-O plane of the high temperature superconductors. We show that in a strong-coupling limit, with strong Coulomb repulsions between electrons on nearest-neighbor O sites, the electron-dynamics is strictly one dimensional, and consequently a number of asymptotically exact results can be obtained concerning the electronic structure. In particular, we show that a nematic phase, which spontaneously breaks the point- group symmetry of the square lattice, is stable at low enough temperatures and strong enough coupling.Comment: 8 pages, 5 eps figures; revised manuscript with more detailed discussions; two new figures and three edited figuresedited figures; 14 references; new appendix with a detailed proof of the one-dimensional dynamics of the system in the strong coupling limi

Andreev scattering in the asymmetric ladder with preformed bosonic pairs

We discuss the phase coherence which emanates from the ladder-like proximity effect between a ``weak superconductor'' with preformed bosonic pairs (here, a single-chain Luther-Emery liquid with superconducting correlations that decay approximately as $x^{-1}$) and a Fermi gas with unpaired fermions. Carefully studying tunneling mechanism(s), we show that the boson-mediated Cooper pairing between remaining unpaired electrons results in a quasi long-range superconductivity: Superconducting correlations decay very slowly as $x^{-\eta}$ with $\eta\approx 1/2$. This process is reminiscent of the coupling of fermions to preformed bosonic pairs introduced in the context of high-Tc cuprates.Comment: 5 pages, final version (To appear in PRB Rapid Communication

Physics in few dimensions

This article is a qualitative account of some aspects of physics in few dimensions, and its relationship to nonlinear field theories. After a survey of materials and some of the models that have been used to describe them, the various methods of solution are compared and contrasted. The roles of exact results, operator representations and the renormalization group transformation are described, and a uniform picture of the behavior of low-dimensional systems is presented

Proximity to a Nearly Superconducting Quantum Critical Liquid

The coupling between superconductors and a quantum critical liquid that is nearly superconducting provides natural interpretation for the Josephson effect over unexpectedly long junctions, and the remarkable stripe-spacing dependence of the critical temperature in LSCO and YBCO superconductors.Comment: four two-column pages, no figure

Superconductivity and Charge Density Wave in a Quasi-One-Dimensional Spin Gap System

We consider a model of spin-gapped chains weakly coupled by Josephson and Coulomb interactions. Combining such non-perturbative methods as bosonization and Bethe ansatz to treat the intra-chain interactions with the Random Phase Approximation for the inter-chain couplings and the first corrections to this, we investigate the phase diagram of this model. The phase diagram shows both charge density wave ordering and superconductivity. These phases are seperated by a line of critical points which exhibits an approximate an SU(2) symmetry. We consider the effects of a magnetic field on the system. We apply the theory to the material Sr_2 Ca_12 Cu_24 O_41 and suggest further experiments.Comment: 14 pages, 7 figure; submitted to PRB; Revised with new version: references added; section on the flux state remove

Avoided Critical Behavior in a Uniformly Frustrated System

We study the effects of weak long-ranged antiferromagnetic interactions of strength $Q$ on a spin model with predominant short-ranged ferromagnetic interactions. In three dimensions, this model exhibits an avoided critical point in the sense that the critical temperature $T_c(Q=0)$ is strictly greater than $\lim_{Q\to 0} T_c(Q)$. The behavior of this system at temperatures less than $T_c(Q=0)$ is controlled by the proximity to the avoided critical point. We also quantize the model in a novel way to study the interplay between charge-density wave and superconducting order.Comment: 32 page Latex file, figures available from authors by reques

Crossovers and Phase Coherence in Cuprate Superconductors

High temperature superconductivity is a property of doped antiferromagnetic insulators. The electronic structure is inhomogeneous on short length and time scales, and, as the temperature decreases, it evolves via two crossovers, before long range superconducting order is achieved. Except for overdoped materials, pairing and phase coherence occur at different temperatures, and phase fluctuations determine both T$_c$ and the temperature dependence of the superfluid density for a wide range of doping. A mechanism for obtaining a high pairing scale in a short coherence length material with a strong poorly-screened Coulomb interaction is described.Comment: 5 pages, Latex, Revte

Pairing and Phase Coherence in High Temperature Superconductors

Mobile holes in an antiferromagnetic insulator form a slowly fluctuating array of quasi one-dimensional metallic stripes, which induce a spin gap or pseudogap in the intervening Mott-insulating regions. The mobile holes on an individual stripe acquire a spin gap via pair hopping between the stripe and its environment; i.e. via a magnetic analog of the usual superconducting proximity effect. This process is the analog of pairing in conventional superconductors. At non-vanishing stripe densities, Josephson coupling between stripes produces a dimensional crossover to a state with long-range superconducting phase coherence. In contrast to conventional superconductors, the superconducting state is characterised by a high density of (spin) pairs, but the phase stiffness, which is determined by the density and mobility of holes on the stripes, is very low.Comment: 4 pages. Proceedings of MMS-High Temperature Superconductivity, V (1997) To be published in Physica

Application of the scattering rate sum-rule to the interplane optical conductivity of high temperature superconductors: pseudogap and bi-layer effects

We use a recently proposed model of the interplane conductivity of high temperature superconductors to investigate the `scattering rate sum-rule' introduced by Basov and co-workers. We present a new derivation of the sum-rule. The quantal and thermal fluctuations of the order parameter which have been argued to produce the observed pseudogap behavior are shown to increase the total integrated `scattering rate' but may either increase or decrease the `quasiparticle' contribution from frequencies greater than twice the superconducting gap.Comment: 4 pages, 5 figures, revise