A. Appendix: Electron-phonon coefficients

The electron-phonon coefficients g are defined as

$$\bf q \bf k \left(\vphantom{{\hbar\over 2M\omega_{{\bf q}\nu}}}\right. {\hbar\over 2M\omega_{{\bf q}\nu}} \left.\vphantom{{\hbar\over 2M\omega_{{\bf q}\nu}}}\right)^{{1/2}}_{} \bf k {dV_{SCF}\over d {\hat u}_{{\bf q}\nu}} \hat{\epsilon}_{{{\bf q}\nu}}^{} \bf k \bf q$$ (1)

The phonon linewidth γ_{$\bf q$ν} is defined by

$$\bf q \bf q \sum_{{ij}}^{} \int {d^3k\over \Omega_{BZ}} \bf q \bf k \bf q \bf k \bf q$$ (2)

while the electron-phonon coupling constant λ_{$\bf q$ν} for mode ν at wavevector $\bf q$ is defined as

$$\bf q {\gamma_{{\bf q}\nu} \over \pi\hbar N(e_F)\omega^2_{{\bf q}\nu}}$$ (3)

where N(e_F) is the DOS at the Fermi level. The spectral function is defined as

$${1\over 2\pi N(e_F)} \sum_{{{\bf q}\nu}}^{} \bf q {\gamma_{{\bf q}\nu}\over\hbar\omega_{{\bf q}\nu}}$$ (4)

The electron-phonon mass enhancement parameter λ can also be defined as the first reciprocal momentum of the spectral function:

$$\sum_{{{\bf q}\nu}}^{} \bf q \int {\alpha^2F(\omega) \over \omega}$$ (5)

Note that a factor M^-1/2 is hidden in the definition of normal modes as used in the code.

McMillan:

$${\Theta_D \over 1.45} \left[\vphantom{ {-1.04(1+\lambda)\over \lambda(1-0.62\mu^*)-\mu^*}}\right. {-1.04(1+\lambda)\over \lambda(1-0.62\mu^*)-\mu^*} \left.\vphantom{ {-1.04(1+\lambda)\over \lambda(1-0.62\mu^*)-\mu^*}}\right]$$ (6)

or (better?)

$${\omega_{log}\over 1.2} \left[\vphantom{ {-1.04(1+\lambda)\over \lambda(1-0.62\mu^*)-\mu^*}}\right. {-1.04(1+\lambda)\over \lambda(1-0.62\mu^*)-\mu^*} \left.\vphantom{ {-1.04(1+\lambda)\over \lambda(1-0.62\mu^*)-\mu^*}}\right]$$ (7)

where

$$\left[\vphantom{ {2\over\lambda} \int {d\omega\over\omega} \alpha^2F(\omega) \mbox{log}\omega }\right. {2\over\lambda} \int {d\omega\over\omega} \left.\vphantom{ {2\over\lambda} \int {d\omega\over\omega} \alpha^2F(\omega) \mbox{log}\omega }\right]$$ (8)