Confinement and Bose Condensation in Gauge Theory of High-Tc Superconductors

Abstract

The issue of confinement and bose condensation is studied for gauge models of high-Tc superconductors. First the Abelian-Higgs model in (2+1)D, i.e., XY-model coupled to lattice gauge field $a_μ$ with coupling $g$, is studied taking into account both the instantons and vortices. This model corresponds to integer filling of the bosons, and can be mapped to a dual superconductor. Our main resut is that the instantons introduce a term which couples linearly to the dual superconductor order parameter, and tend to pin its phase. As a result the vortex condensation always occurs due to the instantons, and the Meissner effect for the gauge field $a_μ$ is absent, although $a_μ$ is massive. This state is essentially the same as the confining phase of the pure gauge model. Away from integer filling, a ``magnetic field'' $μ$ (the chemical potential of the bosons) is applied to this dual superconductor. Then the Higgs phase revives in the case of weak $g$ and large $x$, where vortices do not condense in spite of the instantons. In the opposite case, i.e., strong $g$ and small $x$, phase separation occurs, forming either microscopic patches or macroscopic stripe domains of the Mott insulating state.