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Validity of Kohler's rule in the pseudogap phase of the cuprate superconductors

We report in-plane resistivity ($ρ$) and transverse magnetoresistance (MR) measurements in underdoped HgBa$_2$CuO$_{4+δ}$ (Hg1201). Contrary to the longstanding view that Kohler's rule is strongly violated in underdoped cuprates, we find that it is in fact satisfied in the pseudogap phase of Hg1201. The transverse MR shows a quadratic field dependence, $δρ/ρ_o=a H^{2}$, with $a(T)\propto T^{-4}$. In combination with the observed $ρ\propto T^2$ dependence, this is consistent with a single Fermi-liquid quasiparticle scattering rate. We show that this behavior is universal, yet typically masked in cuprates with lower structural symmetry or strong disorder effects.