English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Eliashberg - McMillan theory of superconductivity is essentially based on theadiabatic approximation. Small parameter of perturbation theory is given by$\lambda\frac{\Omega_0}{E_F}\ll 1$, where $\lambda$ is the dimensionlesselectron - phonon coupling constant, $\Omega_0$ is characteristic phononfrequency, while $E_F$ is Fermi energy of electrons. Here we present an attemptto describe electron - phonon interaction within Eliashberg - McMillan approachin situation, when characteristic phonon frequency $\Omega_0$ becomes largeenough (comparable or exceeding the Fermi energy $E_F$). We consider thegeneral definition of electron - phonon pairing coupling constant $\lambda$,taking into account the finite value of phonon frequency. Also we obtain thesimple expression for the generalized coupling constant $\tilde\lambda$, whichdetermines the mass renormalization, with the account of finite width ofconduction band, and describing the smooth transition from the adiabatic regimeto the region of strong nonadiabaticity. In the case of strong nonadiabaticity,when $\Omega_0\gg E_F$, the new small parameter appears$\lambda\frac{E_F}{\Omega_0}\sim\lambda\frac{D}{\Omega_0}\ll 1$ ($D$ isconduction band half - width), and corrections to electronic spectrum becomeirrelevant. At the same time, the temperature of superconducting transition$T_c$ in antiadiabatic limit is still determined by Eliashberg - McMillancoupling constant $\lambda$, while the preexponential factor in the expressionfor $T_c$, conserving the form typical of weak - coupling theory, is determinedby the bandwidth (Fermi energy). For the case of interaction with a singleoptical phonon we derive the single expression for $T_c$, valid both inadiabatic and antiadiabatic regimes and describing the continuous transitionbetween these two limiting cases.

Electron - phonon coupling in Eliashberg - McMillan theory beyond adiabatic approximation