We derive a Landau-Ginzburg description of semionic superconductors. On a fundamental level the lagrangian of the system involves two vector potentials: the ordinary electromagnetic potential and a potential that describes the statistical interaction between semions. The Goldstone pole in the current correlator of the semionic gas (which was discovered in a mean field expansion by Fetter et al.) occurs when the polarization-induced Chern-Simons mass term for the statistical vector potential exactly cancels the bare term responsible for the statistics. We speculate about reasons why this cancellations should hold beyond the lowest order in the mean field expansion. When the cancellation occurs, it is possible to rewrite the system in terms of a standard Landau-Ginzburg order parameter. We derive the effective long wavelength description of the dynamics of this order parameter interacting with the electromagnetic field. Apart from the sort of anisotropies one might expect in any theory of superconductivity of layered materials, we find a time reversal violating term in the electromagnetic field lagrangian which may be the distinguishing feature of the anyonic theory of superconductivity.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics