Renormalization of the Drude conductivity by the electron-phonon interaction.

It is commonly believed that the Drude conductivity is not renormalized by many-body interactions. To the contrary, we show that for impure metals the Drude conductivity is decreased by a temperaturedependent factor proportional to the electron-phonon coupling l. We demonstrate this effect by both the linear response and the quantum transport approaches. This effect, while comparable to the bare Drude conductivity, will be masked by the large temperature dependence of electron-phonon scattering. We expect such many-body corrections to other transport coefficients.