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

TL;DR

This paper investigates confinement and Bose condensation in gauge models of high-Tc superconductors, revealing how instantons influence vortex condensation and the phases of the system, including confining, Higgs, and phase-separated states.

Contribution

It demonstrates how instantons affect vortex condensation and phase behavior in gauge models of high-Tc superconductors, linking confinement to the absence of the Meissner effect.

Findings

Instantons induce vortex pinning and suppress the Meissner effect.

Vortex condensation always occurs at integer filling due to instantons.

Phase separation occurs in strong coupling and low filling regimes.

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 $a_{\mu}$ 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 $a_\mu$ is absent, although $a_{\mu}$ is massive. This state is essentially the same as the confining phase of the pure gauge model. Away from integer filling, a ``magnetic field'' $\mu$ (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.