Theoretical study reveals rate of electron thermal relaxation in heated metals, highlighting strong links to electron-phonon coupling and superconductivity mechanisms.
If electrons in a metal are heated to a temperature Tₑ greater than the lattice temperature TL, the electron-phonon interaction causes temperature relaxation dTₑ/dt=γT(TL-Tₑ) which is rapid for TL>θD. A formula γT=3{}{λ}〈ω²〉/{π}k_BTₑ is derived, where {λ}〈ω²〉={η}/M is an important parameter in the theory of superconductivity. Quantitative agreement with recent experiments is good.
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Philip B. Allen (1987) studied this question.
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