Effective Mass of Composite Fermions and Fermionic Chern-Simons Theory in Temporal Gauge

Abstract

The definitions of the effective mass of the composite fermion are discussed for the half-filled Landau level problem. In a recent work, Shankar and Murthy show a finite effective mass of the composite fermion by a canonical transformation while the perturbative calculation gives the logarithmic divergence of the effective mass at the Fermi surface. We will emphasize that the different definition of the effective mass has the different physical processes. The finite one could be defined for any momentum of the composite fermion while the divergence only appears at the Fermi surface. We work with the standard Halperin-Lee-Read model but in the temporal gauge. The advantage of this gauge to be employed is that the finite effective mass could be calculated in the Hartree-Fock approximation. Furthermore, it is precisely equal to the result that Shankar and Murthy obtained which is well-fit with the numerical calculation from the ground state energy analysis and a semi-classical estimation. However, if we consider the random phase approximation, one sees that the divergence of the effective mass of the quasiparticle at the Fermi surface emerges again no matter that we work on the temporal or Coulomb gauges. We develop an effective theory where the finite effective mass serves as a `bare' effective mass and show that the same divergence of the RPA effective mass. On the other hand, the correct behavior of the response functions in the small band mass limit could be seen clearly in the temporal gauge since there is a self-interaction among the magnetoplasmons.