Spectral Function Analysis of Fermi Liquids and of Composite Fermions in a Finite Magnetic Field: Renormalised Gaps

TL;DR

This paper analyzes the quasiparticle spectrum and renormalized energy gaps in Fermi liquids and composite fermions under finite magnetic fields, emphasizing the impact of Landau level quantization on these properties.

Contribution

It introduces a spectral function approach that incorporates Landau level singularities to study renormalized gaps in electron-phonon and composite fermion systems under magnetic fields.

Findings

Landau level structure significantly influences the renormalized gap in composite fermions.

The approach applies to both Debye and Einstein phonons in electron-phonon interactions.

Results are relevant to experimental observations in fractional quantum Hall systems.

Abstract

We consider the self-energy and quasiparticle spectrum, for both electrons interacting with phonons, and composite fermions interacting with gauge fluctuations. In both cases we incorporate the singular structure arising from Landau level quantization in a finite field. This is then used to determine the renormalised gap between the Fermi energy and the first excited states. The electron-phonon problem is treated for both Debye and Einstein phonons. In the case of composite fermions, it is found that the singular Landau level structure strongly affects the renormalised gap in the intermediate coupling regime, which is relevant to experiments on the fractional quantum Hall effect. We compare our findings with measurements of the gap in fractional Hall states with filling fraction nu near nu=1/2.