Abstract:
We propose a superconductivity theory of two-band nonadiabatic systems with
strong electron correlations in the linear approximation in nonadiabaticity.
Assuming a weak electron–phonon interaction, we obtain analytic expressions
for the vertex and “intersecting” functions for each of the two bands. With
the diagrams involving intersections of two electron–phonon interaction
lines taken into account (which means going beyond the Migdal
theorem), we determine mass operators of the Green's functions and use
them to derive the basic equations of the superconductivity theory for
two-band systems. We find an analytic expression for the superconducting
transition temperature $T_{\mathrm{c}}$
that differs from the expression in the case
of the standard two-band systems by an essential renormalization of
the relevant quantities that results from the nonadiabaticity effects and strong
electron correlations. We study the dependence of $T_{\mathrm{c}}$ and of the
isotopic coefficient $\alpha$ on the Migdal parameter $m= \omega_0/\varepsilon_{\mathrm{F}}$
and show that accounting for the overlap of energy bands on the Fermi surface
and for the nonadiabaticity effects at small values of the transferred
momentum $(q\ll2p_{\mathrm{F}})$ allows obtaining high values of $T_{\mathrm{c}}$ even for
the weak electron–phonon interaction.
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