Predicting Tc for MgB2
Neglecting non-linear cross
terms, the electron-phonon coupling constant lambda
for our anharmonic phonon is approximately given by
lambda = N(Ef)
( B'2 Sumn (n|Q|0)2/(En-E0 )
+ B'4 Sumn (n|Q2|0)2/(En-E0 )
where N(Ef) is the total density of states at the Fermi energy and
equal to 0.69 states/eV/cell. En
and |n> are the eigenvalues and eigenfunctions of the oscillator E2g
in its adiabatic potential shown
in Fig.~2b.
B'2 and B'4 are the first and second-order
EP coupling, respectively, and obtained from expansion of
D(u) .
Q is the normal coordinate which is related to
boron displacement u via a normalization constant.
We calculate a total electron-phonon coupling
lambda = 0.92.
Using the McMillan expression for Tc and taking a typical value for
mu* = 0.15 with the renormalized phonon energy
of E2g mode, we obtain a Tc of 38.77 K, in excellent agreement
with experiment.
Within the above approximation, the non-linear
EP coupling increases Tc by about 10%.
Our preliminary calculations of lambda
including other non zone-center phonons indicates that the numbers will not
change significantly.
Therefore we conclude that MgB2
is a conventional
electron-phonon superconductor in the strong-coupling regime.