Temperature of superconducting transition for very strong coupling in antiadiabatic limit of Eliashberg equations

Abstract

It is shown that the famous Allen -- Dynes asymtotic limit for superconducting transition temperature in very strong coupling region $T_c>\frac{1}{2\pi }\sqrt{\lambda }{\Omega }_0$ (where $\lambda \gg 1$ - is Eliashberg - McMillan electron - phonon coupling constant and ${\Omega }_0$ - the characteristic frequency of phonons) in antiadiabatic limit of Eliashberg equations ${\Omega }_0/D\gg 1$ ($D\sim E_F$ is conduction band half-width and $E_F$ is Fermi energy) is replaced by $T_c>(2{\pi }^4{)}^{-1/3}(\lambda D{\Omega }_0^2{)}^{1/3}$, with the upper limit for $T_c$ given by $T_c<\frac{2}{{\pi }^2}\lambda D$.

4 pages, 2 figures

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