Theory of thermal relaxation of electrons in metals

Abstract

If electrons in a metal are heated to a temperature ${\mathrm{T}}_{\mathrm{e}}$ greater than the lattice temperature ${\mathrm{T}}_{\mathrm{L}}$, the electron-phonon interaction causes temperature relaxation ${\mathrm{dT}}_{\mathrm{e}}$/dt=${\ensuremath{\gamma}}_{\mathrm{T}}$(${\mathrm{T}}_{\mathrm{L}}$-${\mathrm{T}}_{\mathrm{e}}$) which is rapid for ${\mathrm{T}}_{\mathrm{L}}$>${\mathrm{\ensuremath{\theta}}}_{\mathrm{D}}$. A formula ${\ensuremath{\gamma}}_{\mathrm{T}}$=3\ensuremath{\Elzxh}\ensuremath{\lambda}〈${\mathrm{\ensuremath{\omega}}}^{2}$〉/\ensuremath{\pi}${\mathrm{k}}_{\mathrm{B}{\mathrm{T}}_{\mathrm{e}}}$ is derived, where \ensuremath{\lambda}〈${\mathrm{\ensuremath{\omega}}}^{2}$〉=\ensuremath{\eta}/M is an important parameter in the theory of superconductivity. Quantitative agreement with recent experiments is good.