THE THEORY OF ANYONIC SUPERCONDUCTIVITY: A REVIEW

Abstract

Particles in two spatial dimensions with fractional statistics known, generically, as anyons, have been of interest to particle physicists for nearly ten years. A major change in the direction of research occurred when it was discovered that anyons could play a role as quasiparticles in condensed-matter systems. This was originally discovered to be the case in systems exhibiting the Fractional Quantum Hall Effect. The application of anyons to condensed-matter systems received yet another boost when it was discovered by Laughlin that even an ideal gas of anyons was a superfluid and, as a result, a gas of charged anyons would be a superconductor. This led immediately to attempts to explain the superconductivity of high-T{sub c} materials which are layered ceramics in terms of anyons. The main challenge was to find a reasonable model for these materials which has quasiparticles obeying anyonic statistics. The goal of this article is to review the theory of anyonic superconductivity and its possible relation to high-T{sub c} materials. The emphasis in this review is on field-theoretical methods. In this paper the authors explain what an anyon is and how it can be modeled mathematically. The authors discuss the possible relationship between anyons and high-T{sub c}more » materials. The authors review several of the attempts to obtain anyonic quasiparticles from the Hubbard model which is commonly used to describe these materials. The authors describe the mathematical modeling of anyons in terms of their interaction with an Abelian gauge field with a Chern-Simons term. This description of anyons is used extensively in this article. The authors discuss the possible criteria for superconductivity in anyonic systems with particular emphasis on criteria which would be useful in the Chern-Simons description.« less