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

Today, Orion Ciftja and I have made available on the arXiv a preprint reporting our findings on the possibility of Pomeranchuk instabilities in certain quantum Hall devices. What does that mean? It has to do with electrons confined to move in two dimensions and placed under a strong magnetic field. We look at whether under certain conditions the electrons might undergo phase transition in which the distribution of momenta of the electrons changes due to electron-electron interactions, so that they start to move faster in some directions than others. Which direction they choose is random, but once they have decided, they all conform to that choice. So in that sense it is an example of a broken symmetry. This is a problem we have been working on since Orion and I met at SCES’07. Here is the reference:

Does a Fermi liquid on a half-filled Landau level have Pomeranchuk instabilities?
Jorge Quintanilla and Orion Ciftja,
arXiv:0904.0658 [cond-mat.mes-hall].

For the specialists among the readership, here is the abstract:

We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form ν = 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 → ∞ limit.

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