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

TL;DR

This paper investigates the effective mass of composite fermions in the half-filled Landau level, demonstrating that different definitions lead to finite or divergent results, and employs the temporal gauge to clarify these behaviors.

Contribution

It clarifies the physical meaning of finite versus divergent effective mass definitions and applies the temporal gauge to compute the finite mass within Hartree-Fock approximation, aligning with numerical results.

Findings

Finite effective mass can be computed in the temporal gauge using Hartree-Fock.

Divergence of the effective mass appears at the Fermi surface in RPA calculations.

Temporal gauge reveals the response functions' behavior in the small band mass limit.

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.