Rigid muffin-tin approximation for the electron-phonon interaction in transition metals Page: 2 of 10
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The electron phonon matrix element gik'k is defined in terms of
ak'k by
g . (k' - k)I h (2)
a -ask'-k
where e3(q) is a phonon polarization vector, wiq is a phonon frequency
and Ua is the atomic mass. The absolute square of gjk'k determines the
transition rate between Bloch state k and k, due to the presence of a
phonon of wave vector k' - k and polarization j. In principle, the
energy of the Bloch state $k should differ from that of state 4k' by
wjk'-k, but phonon energies are usually small on an electronic struc-
ture scale so in practice both of the states, k and k' can be taken to
be at the Fermi energy for most transition metal systems.
Most of the experimentally observable quantities related to the
electron-phonon interaction can be viewed as averages over the Fermi
surface of I gjk'k 2. The mass enhancement parameter which gives the
electron-phonon enhancement of the specific heat and which enters the
Mctillan (1968) equation for the superconducting transition temperature
is given by
X = N(0) , 6(E 'k 23)
k' k
where N(0) is the (siagle-spin) Fermi energy density of states. A quan-
tity very similar to A determines the high temperature electrical
resistivity. For temperatures greater than the Debye temperature, the
resistivity is given rather accurately by a relaxation time approximation
3
= " 2 '(4)
2e2N(0)<v >T
ep
where <v=> is the :ean square Fermi velocity and where the electron-
phonon lifetime Tep is determined by the transport version of A
h/T = 2nk T A , (5)
ep B tr
Y 8(e )8(E )(v - v ,
tr 2 'c, k k k k (6)
k' k
Other electron-phonon properties can be written in terms of more
restricted averages over I oak'k 2 as will he shown in Sect. 3.
The question "How well does the ITA work?" is answered in part by
Table I which shows values of A as calculated using the %MTA and as
deduced from experiment for various transition tetals. Overall the
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Butler, W. H. Rigid muffin-tin approximation for the electron-phonon interaction in transition metals, article, January 1, 1980; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1055878/m1/2/: accessed June 9, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.