Does a Fermi liquid on a half-filled Landau level have Pomeranchuk instabilities?

TL;DR

This paper investigates whether a Fermi liquid at half-filled Landau levels exhibits Pomeranchuk instabilities, finding that susceptibility does not diverge, indicating no spontaneous Fermi surface deformation in typical cases.

Contribution

The study introduces a modified effective interaction and analyzes Fermi surface stability, revealing that Pomeranchuk instabilities do not occur in half-filled Landau levels under typical conditions.

Findings

Susceptibility to Fermi surface deformation remains finite.

System approaches instability only as the Landau level index n tends to infinity.

Infrared divergences are effectively regulated in the analysis.

Abstract

We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form $\nu=2n+1/2$). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the $n \to \infty$ limit.