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 ofMR=f(H/ρ0), whereMR=[ρ(H)−ρ0]/ρ0andHis the magnetic field, withρ(H)andρ0being the resistivity atHand 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 ruleMR=f[H/(nTρ0)], withnTdescribing the temperature dependence of the carrier density. We show thatnTis 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 ofnT. We apply our extended Kohler’s rule toBaFe2(As1−xPx)2to settle a long-standing debate on the scaling behavior of the normal-state magnetoresistance of a superconductor, namely,MR∼tan2θH, whereθHis 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.

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Plain Language Summary

In the presence of a magnetic field, the resistance of an electrical conductor can change. In most cases, this magnetoresistance follows a scaling law known as Kohler’s rule. Violations of Kohler’s rule have often been used as evidence for phase transitions or for emergent new physics. Here, we uncover the violation’s origin—a thermally induced change in the carrier density—and offer a fundamental understanding of the violation and validity of Kohler’s rule in those terms.

We draw our conclusions from magnetoresistance experiments on several types of crystals. One of those crystals, the Weyl semimetal tantalum phosphide (TaP), violates Kohler’s rule. Instead, its magnetoresistance follows a modified form of the rule, which includes a thermal factor that reflects the temperature dependence of the carrier density. We then apply this extended Kohler’s rule to other compounds, thus settling long-standing debate on the scaling behavior of their magnetoresistance.

This work solves puzzles in Kohler’s rule of magnetoresistance, including recent ones in topological semimetals as well as long-lasting debates in cuprate superconductors.