Resistivity of a $2d$ quantum critical metal

TL;DR

This paper calculates the resistivity behavior of a two-dimensional quantum critical ferromagnetic metal near the Curie temperature, revealing a distinct temperature scaling due to magnetic scattering.

Contribution

It provides a detailed RPA-based calculation of resistivity near quantum criticality in 2D, showing a $T^{4/3}$ scaling and confirming agreement with SCR theory.

Findings

Resistivity in 2D scales as $T^{4/3}$ near the quantum critical point.

Resistivity in 3D scales as $T^{5/3}$ near the quantum critical point.

Resistivity due to phonons scales as $T^5$ at low temperatures.

Abstract

We calculate resistivity in the paramagnetic phase just above the curie temperature in a $2d$ ferromagnetic metal. The required dynamical susceptibility in the formalism of resistivity is calculated within the Random Phase Approximation(RPA). The mechanism of resistivity is magnetic scattering in which $s$-band electrons are scattered off the magnetic spin fluctuations of d-band electrons. We use the $s$-$d$ Hamiltonian formalism. We find that near the quantum critical point the resistivity in $2d$ scales as $T^{\frac{4}{3}}$, whereas in $3d$ it scales as $T^{\frac{5}{3}}$. In contrast to it, resistivity due to phonon scattering is given by $T^5$ in low temperature limit as is well known. Our RPA result agrees with the Self-Consistence Renormalisation(SCR) theory result.