Hartree calculation of local magnetic fields in an anyon superconductor

Abstract

We use a modified Hartree approximation to calculate the charge and current distributions induced by the presence of a positive point charge above a plane of positively charged superconducting anyons, at zero temperature. The anyons are taken to have semion statistics, and are treated within a simple two-species effective-mass model. We also consider a geometry where the point charge is partially screened by a second, metallic, plane that does not contain anyons. Applying the results of muon-spin-relaxation experiments in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$, we find that, if the ${\mathrm{CuO}}_{2}$ planes have charge carriers obeying semion statistics, then the magnetic field at the muon site should be in the range 0--25 G, with the actual value depending on the muon location in the crystal.