Resistivity of a Non-Galilean–Invariant Fermi Liquid near Pomeranchuk Quantum Criticality

Abstract

We analyze the effect of the electron-electron interaction on the resistivity of a metal near a Pomeranchuk quantum phase transition (QPT). We show that umklapp processes are not effective near a QPT, and one must consider both interactions and disorder to obtain a finite and T dependent resistivity. By power counting, the correction to the residual resistivity at low T scales as AT((D+2)/3) near a Z=3 QPT. We show, however, that A=0 for a simply connected, convex Fermi surface in 2D, due to the hidden integrability of the electron motion. We argue that A>0 in a two-band (s-d) model and propose this model as an explanation for the observed T((D+2)/3) behavior.