Superconducting Transition Temperature for Very Strong Coupling in the Antiadiabatic Limit of Eliashberg Equations

It is shown that the famous Allen–Dynes asymtotic limit for superconducting transition temperature in very strong coupling region T_c > \(\frac{1}{{2\pi }}\sqrt \lambda \)Ω₀ (where λ ≫ 1 is Eliashberg–McMillan electron–phonon coupling constant and Ω₀ – the characteristic frequency of phonons) in antiadiabatic limit of Eliashberg equations Ω₀/D ≫ 1 (D ~ E_F is conduction band half-width and E_F is Fermi energy) is replaced by T_c > (2π⁴)^–1/3(λD\(\Omega _{0}^{2}\))^1/3 with the upper limit for T_c given by T_c < \(\frac{2}{{{{\pi }^{2}}}}\)λD.