Quantitative reliability of Migdal-Eliashberg theory for strong electron-phonon coupling

Details Quantitative reliability of Migdal-Eliashberg theory for strong electron-phonon coupling Quantitative reliability of Migdal-Eliashberg theory for strong electron-phonon coupling

2011-05-13

arxiv.org/abs/1105.2833v3

Phys. Rev. B 84 (2011), 184531

Physics

Condensed Matter

Superconductivity

6 pages, 4 figures; extended version with added references

Scientific paper

10.1103/PhysRevB.84.184531

We reassess the validity of Migdal-Eliashberg (ME) theory for coupled electron-phonon systems for large couplings $\lambda$. Although model calculations have found that ME theory breaks down for $\lambda\sim 0.5$, it is routinely applied for $\lambda>1$ to strong coupling superconductors. To resolve this discrepancy it is important to distinguish between {\em bare} parameters, used as input in models, and {\em effective} parameters, derived from experiments. We show explicitly that ME gives accurate results for the critical temperature and the spectral gap for large effective $\lambda$. This provides quantitative theoretical support for the applicability of ME theory to strong coupling conventional superconductors.

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