Holographic order parameter for charge fractionalization

Nonlocal order parameters for deconfinement, such as the entanglement entropy and Wilson loops, depend on spatial surfaces \Sigma. These observables are given holographically by the area of a certain bulk spatial surface \Gamma, ending on \Sigma. At finite charge density it is natural to consider the electric flux through the bulk surface \Gamma, in addition to its area. We show that this flux provides a refined order parameter that can distinguish `fractionalized' phases, with charged horizons, from what we term `cohesive' phases, with charged matter in the bulk. Fractionalization leads to a volume law for the flux through the surface, the flux for deconfined but cohesive phases is between a boundary and a volume law, while finite density confined phases have vanishing flux through the surface. We suggest two possible field theoretical interpretations for this order parameter. The first is as information extracted from the large N reduced density matrix associated to \Sigma. The second is as surface operators dual to polarized bulk `D-branes', carrying an electric dipole moment.Comment: 1+22 pages. 4 figure

Fluctuating order parameter in doped cuprate superconductors

We discuss static fluctuations of the d-wave superconducting order parameter $\Delta$ in CuO$_2$ planes, due to quasiparticle scattering by charged dopants. The analysis of two-particle anomalous Green functions at $T = 0$ permits to estimate the mean-square fluctuation $\delta^2 = - ^2$, averaged in random dopant configurations, to the lowest order in doping level $c$. Since $\Delta$ is found to saturate with growing doping level while $\delta$ remains to grow, this can explain the collapse of $T_c$ at overdoping. Also we consider the spatial correlations $$ for order parameter in different points of the plane.Comment: RevTex4, 3 pages, to be published in Proceedings of New3SC-4 International Conference, San Diego, California, January 15-21, 200

Dual Order Parameter for the Nodal Liquid

The guiding conception of vortex-condensation-driven Mott insulating behavior is central to the theory of the nodal liquid. We amplify our earlier description of this idea and show how vortex condensation in 2D electronic systems is a natural extension of 1D Mott insulating and 2D bosonic Mott insulating behavior. For vortices in an underlying superconducting pair field, there is an important distinction between the condensation of flux hc/2e and flux hc/e vortices. The former case leads to spin-charge confinement, exemplified by the band insulator and the charge-density-wave. In the latter case, spin and charge are liberated leading directly to a 2D Mott insulator exhibiting *spin-charge separation*. Possible upshots include not only the nodal liquid, but also a novel undoped antiferromagnetic insulating phase with gapped excitations exhibiting spin-charge separation.Comment: 16 pages, 2 figure

Complex order parameter symmetry and thermal conductivity

Thermal behaviour of superconductors with complex order parameter symmetry is studied within a weak coupling theory. It is shown numerically, that the thermal nature of the different components of complex order parametrs are qualitatively different. Within the complex order parameter scenario, the recent experimental observations by Krishna {\it et al.}, [Science {\bf 277}, 83 (1997)] on magnetothermal conductivity and by J. Ma {\it et al.}, [Science {\bf 267}, 862 (1995)] on temperature dependent gap anisotropy for high temperature superconductors can have natural explanation.Comment: 6 pages, 3 figures and macros attached, Europhysics Letters (1998) in pres