On the residual resistivity near a two dimensional metamagnetic quantum critical point

TL;DR

This paper investigates how impurity scattering affects residual resistivity near a two-dimensional quantum critical point with diverging susceptibility, revealing singular renormalizations and potential experimental signatures.

Contribution

It introduces a novel analysis of impurity-induced resistivity behavior near a 2D quantum critical point, including a squared-logarithmic correction and observable Friedel oscillations.

Findings

Singular renormalization of back-scattering amplitude near criticality

Conversion of logarithmic to squared-logarithmic correction in conductivity

Impurities induce observable Friedel oscillations

Abstract

The behavior of the residual (impurity-dominated) resistivity is computed for a material near a two dimensional quantum critical point characterized by a divergent $q=0$ susceptibility. A singular renormalization of the amplitude for back-scattering of an electron off of a single impurity is found. When the correlation length of the quantum critical point exceeds the mean free path, the singular renormalization is found to convert the familiar `Altshuler-Aronov' logarithmic correction to the conductivity into a squared-logarithmic form. Impurities can induce unconventional Friedel oscillations, which may be observable in scanning tunnelling microscope experiments. Possible connections to the metamagnetic quantum critical end point recently proposed for the material $Sr_{3}Ru_{2}O_{7}$ are discussed.