Confinement and Bose condensation in gauge theory of high-Tcsuperconductors

Abstract

The issue of confinement and bose condensation is studied for gauge models of high-$T_c$ superconductors. First the Abelian-Higgs model in $\mathrm{}(2+1)\mathrm{}\mathrm{D},$ 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 result 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 boson density 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.