Similarity renormalization of the electron--phonon coupling

Details Similarity renormalization of the electron--phonon coupling Similarity renormalization of the electron--phonon coupling

1996-09-06

arxiv.org/abs/cond-mat/9609065v2

Physics

Condensed Matter

Superconductivity

17 pages, LaTeX2e, uses AMS-fonts, 5 ps-figures included. Replaced by a completely revised version that contains several new r

Scientific paper

10.1002/andp.19975090305

We study the problem of the phonon-induced electron-electron interaction in a solid. Starting with a Hamiltonian that contains an electron-phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitely. The effective interactions are calculated to second order in the electron-phonon coupling. It is shown that the effective interaction between two electrons forming a Cooper pair is attractive in the whole parameter space. For a simple Einstein model we calculate the renormalization of the electronic energies and the critical temperature of superconductivity.

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