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

Autor: Mikhail V. Sadovskii
Rok vydání: 2021
Předmět:
Zdroj: JETP Letters. 113:581-585
ISSN: 1090-6487
0021-3640
DOI: 10.1134/s0021364021090034
Popis: It is shown that the famous Allen–Dynes asymptotic limit for the superconducting transition temperature in the very strong coupling region $${{T}_{{\text{c}}}} > \frac{1}{{2\pi }}\sqrt \lambda {{\Omega }_{0}}$$ (where $$\lambda \gg 1$$ is the Eliashberg–McMillan electron–phonon coupling constant and $${{\Omega }_{0}}$$ is the characteristic frequency of phonons) in the antiadiabatic limit of Eliashberg equations $${{\Omega }_{0}}{\text{/}}D \gg 1$$ ( $$D \sim {{E}_{{\text{F}}}}$$ is the half-width of the conduction band and EF is the Fermi energy) is replaced by $${{T}_{{\text{c}}}} > {{(2{{\pi }^{4}})}^{{ - 1/3}}}{{(\lambda D\Omega _{0}^{2})}^{{1/3}}}$$ , with the upper limit $${{T}_{{\text{c}}}} < \frac{2}{{{{\pi }^{2}}}}\lambda D$$ .
Databáze: OpenAIRE