Effective Lagrangian for a system of nonrelativistic fermions in 2+1 dimensions coupled to an electromagnetic field: Application to anyonic superconductors

Prasanta K. Panigrahi; Rashmi Ray; B. Sakita

doi:10.1103/PhysRevB.42.4036

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Effective Lagrangian for a system of nonrelativistic fermions in 2+1 dimensions coupled to an electromagnetic field: Application to anyonic superconductors

Prasanta K. Panigrahi, Rashmi Ray, B. Sakita

DOI 10.1103/PhysRevB.42.4036 · Physical Review B

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Abstract

We study here, in two spatial dimensions, the effective Lagrangian of nonrelativistic charged fermions in an electromagnetic field. The fermionic integration is performed yielding a one-loop effective action that is evaluated using the inhomogeneity (derivative) expansion technique. The effective Lagrangian involves a Chern-Simons (CS) -like term with a coefficient that is a ‘‘staircase’’ function of B, the magnetic field. We then discuss the application of this effective Lagrangian to a system of anyons, showing that the cancellation of the induced CS term against a CS term included in the beginning to change the fermions to anyons, is favored energetically, together with the expulsion of B from the system of anyons. The cancellation implies the existence of a massless mode. This, together with the fact that B=0, implies superconductivity.