Abstract
Current theories of high temperature superconductivity are based on the behavior of the ideal (2+1)-dimensional anyon gas at finite density. The anyon gas can be described using fundamental fermionic or bosonic matter in interaction with a topologically massive statistical gauge field. If the renormalized Chern-Simons coefficient at zero density takes the values γR(0)=N/2π, the anyon gas is a superfluid, and if the fundamental matter is electrically charged, it behaves like a superconductor. In this article we analyze an ideal anyon gas composed of two anyonic species, each associated with fundamental matter that has different (fermionic and bosonic) statistics. For supersymmetric values of the masses and couplings, no exotic statistics can occur when the system is in a superconducting state at finite density. However, semionic superconductivity can be achieved when the supersymmetry is very softly broken by a fundamental boson-fermion mass splitting.
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