Singular Behaviour of Electrons and of Composite Fermions in a Finite Effective Field

TL;DR

This paper investigates the behavior of electrons and composite fermions in finite magnetic fields, revealing potential issues with perturbative approaches and suggesting the need for non-perturbative analysis or indicating possible system instability.

Contribution

It provides a detailed calculation of fermion self-energy in finite fields for both gauge-coupled and phonon-coupled cases, highlighting limitations of perturbation theory in composite fermion spectra.

Findings

Perturbative calculations show unphysical suppression of quasiparticle spectral weight.

Potential resolution may require non-perturbative methods.

System might be inherently unstable under certain conditions.

Abstract

We calculate the self-energy of fermions in Landau level n, in a finite field. Two cases are considered, in which fermions couple either to gauge fluctuations (as in the composite fermion gauge theory) or to phonons, as an example of a Fermi liquid. Perturbative calculations of the composite fermion spectrum show an unphysical suppression of the quasiparticle spectral weight at the composite fermion levels. We argue that this problem might be resolved by a non-perturbative calculation; alternatively, the system might be unstable.