Extended Kohler’s Rule of Magnetoresistance

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