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

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