The effect of electron-electron interactions on the Peierls transition in metals with strong nesting of Fermi surfaces

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Abstract
It is well known that periodic lattice distortions can occur in metallic systems due to the cut-off of the electron distribution at the Fermi surface. One-dimensional models of materials with strong nesting of Fermi surfaces in three dimensions are commonly employed to investigate such a Peierls transition involving a soft phonon of amplitude u. Calculations which take account of single-particle electronic energies only always give a lowering in energy Ubs from the distortion proportional to u2 ln u, and consequently always predict a phase transition at a low enough temperature. This is in disagreement with the results of Halperin and Rice (1968) and of Chan and Heine (1973). The authors show very simply that if the electrostatic interaction between the electrons is included, then Ubs infinity -u2 and so whether or not the phase transition occurs depends upon the balance between this term and the normal quadratic forces. They conclude that the Frohlich Hamiltonian is inappropriate for the discussion of this problem.

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