Extended Kohler$^,$s Rule of Magnetoresistance

TL;DR

This paper extends Kohler's rule to account for thermally-induced changes in carrier density, revealing new insights into the electronic structure of topological semimetals, superconductors, and semiconductors through magnetoresistance analysis.

Contribution

The authors introduce an extended Kohler's rule incorporating temperature-dependent carrier density, providing a new method to analyze electronic bandstructure and magnetoresistance scaling.

Findings

Magnetoresistance in TaP follows the extended Kohler's rule with temperature-dependent carrier density.

Application to BaFe₂(As₁₋ₓPₓ)₂ clarifies the scaling behavior of normal-state magnetoresistance.

Validation of the extended rule in InSb demonstrates its broad applicability.

Abstract

A notable phenomenon in topological semimetals is the violation of Kohler$^,$s rule, which dictates that the magnetoresistance $MR$ obeys a scaling behavior of $MR = f(H/\rho_0$), where $MR = [\rho_H-\rho_0]/\rho_0$ and $H$ is the magnetic field, with $\rho_H$ and $\rho_0$ being the resistivity at $H$ and zero field, respectively. Here we report a violation originating from thermally-induced change in the carrier density. We find that the magnetoresistance of the Weyl semimetal, TaP, follows an extended Kohler$^,$s rule $MR = f[H/(n_T\rho_0)]$, with $n_T$ describing the temperature dependence of the carrier density. We show that $n_T$ is associated with the Fermi level and the dispersion relation of the semimetal, providing a new way to reveal information on the electronic bandstructure. We offer a fundamental understanding of the violation and validity of Kohler$^,$s rule in terms of different temperature-responses of $n_T$. We apply our extended Kohler$^,$s rule to BaFe$_2$(As$_{1-x}$P$_x$)$_2$ to settle a long-standing debate on the scaling behavior of the normal-state magnetoresistance of a superconductor, namely, $MR$ ~ $tan^2\theta_H$, where $\theta_H$ is the Hall angle. We further validate the extended Kohler$^,$s rule and demonstrate its generality in a semiconductor, InSb, where the temperature-dependent carrier density can be reliably determined both theoretically and experimentally.