Superconductivity in tight-binding approximation Page: 9 of 14
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other terms, where t denotes subband t. By excluding interband
transitions, the other terms consist of (i) terms with V k a a
and I Oka t averaged over the Fermi surface, where ja
measures the coupling of orbitals of different symmetry within a subband
- (e. g. the eg and t2g orbitals in b. c. c. metals); and (ii) :terms with
(JABV k aA aB) cos k.lRAB averaged over the Fermi surface measuring
the second derivatives of the product coupling coefficients aAaB on
different atomic sites A and B in a unit cell, where JAB is the usual
two-center integral. The above terms drop out in the nondegenerate
band model. In fact, they are unimportant compared with the first term.
as can be seen in Table I containing the b. c. c. , h. c. p., and f. c. c.
structures. It is possible that either the second derivative terms
are small when averaged over the Fermi surface, or they almost cancel
with the interband transitions. Such possibilities are under investigation.
To supplement the above argument, it is perhaps useful to compare
our calculations to those of reference 11. We made use of the Bloch
formulation of electron-phonon interaction. Different Bloch sums were
set up for orbitals of different symmetry and for each atomic site in a
unit cell. Orbitals of different symmetry were mixed in the process of
diagonalizing the Hubbard Hamiltonian. When we computed the electron-
phonon interaction, adiabatic electron orbitals which follow the ion
motion were assumed, and each subband was treated independently.
Evans et al also used the Bloch formulation but they treated the
d electrons as conduction electrons in the muffin tin potential prescrip-
tion. The five fold degeneracy of the d band was totally ignored and
thus little knowledge concerning the band structure was known. However,
they already obtained reasonable values of 1] compared to the more
accurate results given in reference 12. This demonstrates the relative,
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Poon, S.J. Superconductivity in tight-binding approximation, report, October 1, 1975; United States. (https://digital.library.unt.edu/ark:/67531/metadc863284/m1/9/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.