2 + 1 Dimensional Chern-Simons Theory for Landau-Ginzburg Theory

Abstract: In this work, 2 + 1 dimensional Chern-Simons theory have been used in an attempt to describe superconductivity. It was examined if the two defining properties of superconductivity, infinite direct current (DC) conductivity and the Meissner effect, as well as the two characteristic length scales of superconductors, the London penetration depth and the coherence length, could be obtained. Three approaches modelling bulk properties of superconductivity were developed for this purpose. It was found that the London penetration depth could be obtained from a Maxwell-Chern-Simons theory, which explains the Meissner effect too, but not the mechanism responsible for the effect. Infinite DC conductivity was achieved by introducing a Proca mass term. The coherence length was not obtained. Although, the coherence length and the mechanism of the Meissner effect is expected to appear from an edge treatment.