Resistivity of a non-Galilean--invariant Fermi Liquid near Pomeranchuk Quantum Criticality

TL;DR

This paper investigates how electron interactions influence metal resistivity near a Pomeranchuk quantum critical point, highlighting the roles of Umklapp processes, disorder, and Fermi surface geometry in determining temperature dependence.

Contribution

It demonstrates that Umklapp processes are ineffective near the QPT and introduces a two-band model to explain the observed resistivity behavior.

Findings

Resistivity correction scales as T^{(D+2)/3} near a Z=3 QPT.

Hidden integrability causes zero correction in convex 2D Fermi surfaces.

Two-band (s-d) model explains the T^{(D+2)/3} resistivity behavior.

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 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 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.