Local magnetic fields in an anyon superconductor.

Abstract

As has been noted previously, there should be orbital currents and magnetic fields associated with any inhomogeneities in the carrier density \ensuremath{\rho}(r) in anyon models of high-temperature superconductors. For a simple effective-mass model with two species of semions, one can calculate exactly the zero-temperature value of the coefficient \ensuremath{\gamma}, which determines ratio between the current and \ensuremath{\nabla}\ensuremath{\rho}, for IsmallP values of \ensuremath{\nabla}\ensuremath{\rho}. We consider here various situations where \ensuremath{\nabla}\ensuremath{\rho} is IlargeP. For a circularly symmetric localized perturbation, we find constraints on the induced orbital magnetic moment at T=0 which show that the current cannot vanish, if the net inhomogeneity has a magnitude of one electronic charge. We also show that at temperatures above the superconducting transition, the total current at the boundary of a macroscopic sample is determined if the coefficient \ensuremath{\gamma} is known; i.e., in this case the net current is the same as if the density gradients were small. As an intermediate step in our analyses, we review the formulation of the Hartree or Hartree-Fock approximation for an inhomogeneous anyon system. We also introduce a generalized anyon model, where the fictitious charge that couples to the Chern-Simons gauge field is smeared by a Gaussian of width w, for which the Hartree approximation becomes exact in the limit w\ensuremath{\rightarrow}\ensuremath{\infty}.