Microscopic Model of Cuprate Superconductivity

We present a model for cuprate superconductivity based on the identification of an experimentally detected "local superconductor" as a charge 2 fermion pairing in a circular, stationary density wave. This wave acts like a highly correlated local "boson" satisfying a modified Cooper problem with additional correlation stabilization relative to the separate right- and left-handed density waves composing it. This local "boson" could be formed in a two-bound roton-like manner; it has Fermion statistics. Delocalized superconductive pairing (superconductivity) is achieved by a Feshbach resonance of two unpaired holes (electrons) resonating with a virtual energy level of the bound pair state of the local "boson" as described by the Boson-Fermion-Gossamer (BFG) model. The spin-charge order interaction offers an explanation for the overall shape of the superconducting dome as well a microscopic basis for the cuprate superconducting transition temperatures. An explanation of the correlation of superconducting transition temperature with experimental inelastic neutron and electron Raman scattering is proposed, based on the energy of the virtual bound pair. These and other modifications discussed suggest a microscopic explanation for the entire cuprate superconductivity dome shape.Comment: 27 pages, 7 figures, presented at the 50th Sanibel Symposiu

Kinetic Mixing and the Supersymmetric Gauge Hierarchy

The most general Lagrangian for a model with two U(1) gauge symmetries contains a renormalizable operator which mixes their gauge kinetic terms. Such kinetic mixing can be generated at arbitrarily high scales but will not be suppressed by large masses. In models whose supersymmetry (SUSY)-breaking hidden sectors contain U(1) gauge factors, we show that such terms will generically arise and communicate SUSY-breaking to the visible sector through mixing with hypercharge. In the context of the usual supergravity- or gauge-mediated communication scenarios with D-terms of order the fundamental scale of SUSY-breaking, this effect can destabilize the gauge hierarchy. Even in models for which kinetic mixing is suppressed or the D-terms are arranged to be small, this effect is a potentially large correction to the soft scalar masses and therefore introduces a new measurable low-energy parameter. We calculate the size of kinetic mixing both in field theory and in string theory, and argue that appreciable kinetic mixing is a generic feature of string models. We conclude that the possibility of kinetic mixing effects cannot be ignored in model-building and in phenomenological studies of the low-energy SUSY spectra.Comment: 16 pages, LaTeX, 1 figure. Revised to match published versio

Proposed lower bound for the shear viscosity to entropy density ratio in some dense liquids

Starting from relativistic quantum field theories, Kovtun et al. (2005) have quite recently proposed a lower bound eta/s >= hbar /(4 pi kB), where eta is the shear viscosity and s the volume density of entropy for dense liquids. If their proposal can eventually be proved, then this would provide key theoretical underpinning to earlier semiempirical proposals on the relation between a transport coefficient eta and a thermodynamic quantity s. Here, we examine largely experimental data on some dense liquids, the insulators nitrogen, water, and ammonia, plus the alkali metals, where the shear viscosity eta(T) for the four heaviest alkalis is known to scale onto an `almost universal' curve, following the work of Tankeshwar and March a decade ago. So far, all known results for both insulating and metallic dense liquids correctly exceed the lower bound prediction of Kovtun et al.Comment: to appear in Phys. Lett.

Superconducting transition temperatures of the elements related to elastic constants

For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian in which nuclear and electron motions are to be treated from the outset on the same footing, has parameters, for the elements, which can be classified as (i) atomic mass M, (ii) atomic number Z, characterizing the external potential in which electrons move, and (iii) bcc lattice spacing, or equivalently one can utilize atomic volume, Omega. Since the thermodynamic quantities can be determined from H, we conclude that Tc, the superconducting transition temperature, when it is non-zero, may be formally expressed as Tc = Tc^(M) (Z, Omega). One piece of evidence in support is that, in an atomic number vs atomic volume graph, the superconducting elements lie in a well defined region. Two other relevant points are that (a) Tc is related by BCS theory, though not simply, to the Debye temperature, which in turn is calculable from the elastic constants C_{11}, C_{12}, and C_{44}, the atomic weight and the atomic volume, and (b) Tc for five bcc transition metals is linear in the Cauchy deviation C* = (C_{12} - C_{44})/(C_{12} + C_{44}). Finally, via elastic constants, mass density and atomic volume, a correlation between C* and the Debye temperature is established for the five bcc transition elements.Comment: EPJB, accepte

Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

We give here the derivation of a Gross-Pitaevskii--type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91 (2003) 030401]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided.Comment: Phys. Rev. A (accepted

Scaling of the superconducting transition temperature in underdoped high-Tc cuprates with a pseudogap energy: Does this support the anyon model of their superfluidity?

In earlier work, we have been concerned with the scaling properties of some classes of superconductors, specifically with heavy Fermion materials and with five bcc transition metals of BCS character. Both of these classes of superconductors were three-dimensional but here we are concerned solely with quasi-two-dimensional high-Tc cuprates in the underdoped region of their phase diagram. A characteristic feature of this part of the phase diagram is the existence of a pseudogap (pg). We therefore build our approach around the assumption that kB Tc / E_pg is the basic dimensionless ratio on which to focus, where the energy E_pg introduced above is a measure of the pseudogap. Since anyon fractional statistics apply to two-dimensional assemblies, we expect the fractional statistics parameter allowing `interpolation' between Fermi-Dirac and Bose-Einstein statistical distribution functions as limiting cases to play a significant role in determining kB Tc / E_pg and experimental data are analyzed with this in mind.Comment: Phys. Chem. Liquids, to be publishe