Quantum Interference of Coulomb Interaction and Disorder: Phase Shift of Friedel Oscillations and an Instability of the Fermi Sea

Abstract

We investigate the influence of interference between Coulomb interaction and impurity scattering on the static electronic response $\chi (0,q)$ in disordered metals to leading order in the effective Coulomb interaction. When the transport relaxation time $\tau _{tr}$ is much shorter than the quasiparticle life time, we find a $\mbox{sgn}(2p_F-q)/\sqrt{|2p_F-q|}$ divergence of the polarization function at the Fermi surface ($q=2p_F$). It causes a phase shift of the Friedel oscillations as well as an enhancement of their amplitude. Our results are consistent with experiments and may be relevant for understanding the stability of the amorphous state of certain alloys against crystallization.