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Disorder such as impurities and dislocations in Weyl semimetals (SMs) drivesa quantum critical point (QCP) where the density of states at the Weyl pointgains a non-zero value. Near the QCP, the asymptotic low energy singularitiesof physical quantities are controlled by the critical exponents $\nu$ and $z$.The nuclear spin-lattice relaxation rate, which originates from the hyperfinecoupling between a nuclear spin and long-range orbital currents in Weyl fermionsystems, shows intriguing critical behavior. Based on the self-consistent Bornapproximation for impurities, we study the nuclear spin-lattice relaxation rate$1/T_1$ due to the orbital currents in disordered Weyl SMs. We find that$(T_1T)^{-1}\sim E^{2/z}$ at the QCP where $E$ is the maximum of temperature$T$ and chemical potential $\mu(T)$ relative to the Weyl point. This scalingbehavior of $(T_1T)^{-1}$ is also confirmed by the self-consistent $T$-matrixapproximation, where a remarkable temperature dependence of $\mu(T)$ could playan important role. We hope these results of $(T_1T)^{-1}$ will serve as animpetus for exploration of the disorder-driven quantum criticality in Weylmaterials.

Nuclear spin relaxation rate near the disorder-driven quantum critical point in Weyl fermion systems