Superconductivity in the Anyon Model

Two dimensional world of quantum particles is not limited to bosons and fermions. There may exist particles consistent with the laws of Physics of a more general nature called anyons. Two-particle wavefunction anyons acquires any phase under the exchange of a pair. One has to look at 'surface' phenomena on an anyon hunt. It has been suggested that anyons may be present in the layered high temperature superconductors. Our focus will be on a special case of anyons which may be considered half-way between bosons and fermions and is called semions. One approach to canonical quantization of an anyon system is assuming that they are composites of fermions and Chern-Simons magnetic flux. Adopting this quantization scheme, the present work studies the linear response of a system of semions. The semions are represented by Schrodinger fermions minimally coupled to Chern-Simons fields with appropriate coupling constant. Charged semions are further coupled to Maxwell fields to study their electromagnetic response. Linear response for the semions on a cylinder is calculated using a gauge invariant, self-consistent time dependent perturbation theory at zero temperature. A diagrammatic method is employed after making a ground state ansatz. It is shown that the Wilson line zero modes are essential to maintain that translational invariance of the system. The phenomenological properties of the system are calculated in terms of three defining parameters. They are the two dimensional charge, mass and density of the fermions. The Meissner effect is shown to operate in the charged system. It is also shown how various dispersion branches may be calculated and the lowest branches are numerically evaluated for both neutral and charged system of semions. The lowest neutral branch supports a linear sound mode near the origin and the charged system is shown to support plasma oscillations.