TY - JOUR
T1 - Localized description of superconductivity in narrow-band metals
AU - Birnboim, A.
AU - Gutfreund, H.
PY - 1974
Y1 - 1974
N2 - A localized description of superconductivity in narrow-band metals, proposed by Appel and Kohn, is applied to the calculation of the phonon-exchange vertex in three transition metals. The essence of this description is the formulation of the equation for the vertex function in the Wannier representation and the assumption of a contact interaction, in which the two electrons in a Cooper pair scatter together from site to site. The value of the vertex function at =0 plays the same role in determining Tc as the coupling parameter in the BCS or McMillantheory. The phonon-exchange vertex is calculated for V, Nb, and Ta, assuming that the d electrons occupy the threefold degenerate 25 band. The calculation makes use of tabulated atomic wave functions and potentials, and of measured phonon frequency distributions. The electron-phonon interaction is described within the so-called modified tight-binding approximation, in which the zeroth-order electron wave functions follow adiabatically the vibrating ions. The values of the phonon-exchange vertex at =0 are compared with given by McMillan and correct orders of magnitude are obtained with reasonable screening of the atomic potentials. The validity of the contact approximation is checked numerically.
AB - A localized description of superconductivity in narrow-band metals, proposed by Appel and Kohn, is applied to the calculation of the phonon-exchange vertex in three transition metals. The essence of this description is the formulation of the equation for the vertex function in the Wannier representation and the assumption of a contact interaction, in which the two electrons in a Cooper pair scatter together from site to site. The value of the vertex function at =0 plays the same role in determining Tc as the coupling parameter in the BCS or McMillantheory. The phonon-exchange vertex is calculated for V, Nb, and Ta, assuming that the d electrons occupy the threefold degenerate 25 band. The calculation makes use of tabulated atomic wave functions and potentials, and of measured phonon frequency distributions. The electron-phonon interaction is described within the so-called modified tight-binding approximation, in which the zeroth-order electron wave functions follow adiabatically the vibrating ions. The values of the phonon-exchange vertex at =0 are compared with given by McMillan and correct orders of magnitude are obtained with reasonable screening of the atomic potentials. The validity of the contact approximation is checked numerically.
UR - http://www.scopus.com/inward/record.url?scp=5344269987&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.9.139
DO - 10.1103/PhysRevB.9.139
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AN - SCOPUS:5344269987
SN - 0163-1829
VL - 9
SP - 139
EP - 146
JO - Physical Review B
JF - Physical Review B
IS - 1
ER -