Extended Kohler’s Rule of Magnetoresistance

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/ρ_{0}), where MR=[ρ(H)−ρ_{0}]/ρ_{0} and H is the magnetic field, with ρ(H) and ρ_{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}ρ_{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 band structure. 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}θ_{H}, where θ_{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.