Ep. Nakhmedov, EFFECT OF ANISOTROPY ON THE ENERGY-GAP AND THE CRITICAL-TEMPERATURE IN A STRONGLY COUPLED LAYERED SUPERCONDUCTOR, Physical review. B, Condensed matter, 54(9), 1996, pp. 6624-6631
The Eliashberg theory is applied to study the critical temperature and
a gap anisotropy of strongly coupled layered superconductors. The ele
ctron-ion pseudopotential, the electron, and the phonon energy spectra
an proposed to be anisotropic in layered crystals with an open Fermi
surface. The anisotropic electron-phonon spectral density [alpha(2)F(z
)](pz) is found to be expanded in cos(np(z)d) functions. Such an expre
ssion for [alpha(2)F(z)](pz) demands the energy gap Delta(p(z),omega)
to present also as an expansion in the harmonic functions. Therefore,
the value of the energy gap along the c axis should display p(z) depen
dence. The value of Delta differs from that obtained by in-plane measu
rements. By using McMillan's method we present each amplitude Delta(n)
(omega) in the harmonic expansion of the energy gap Delta(p(z),omega)
by trial function. The infinite set of coupled homogeneous equations f
or Delta(0), Delta(1), Delta(2),... is obtained, the solution of which
should yield the critical temperature. We estimate only those equatio
ns which include the three amplitudes, Delta(0), Delta(1), and Delta(2
), in the harmonic expansion of the energy gap. An approximate calcula
tion of T-c shows that the critical temperature must be enhanced due t
o the influence of anisotropy.