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

Disorder such as impurities and dislocations in Weyl semimetals (SMs) drives a quantum critical point (QCP) where the density of states at the Weyl point gains a non-zero value. Near the QCP, the asymptotic low energy singularities of physical quantities are controlled by the critical exponents $\nu$ and $z$. The nuclear spin-lattice relaxation rate, which originates from the hyperfine coupling between a nuclear spin and long-range orbital currents in Weyl fermion systems, shows intriguing critical behavior. Based on the self-consistent Born approximation 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 scaling behavior of $(T_1T)^{-1}$ is also confirmed by the self-consistent $T$-matrix approximation, where a remarkable temperature dependence of $\mu(T)$ could play an important role. We hope these results of $(T_1T)^{-1}$ will serve as an impetus for exploration of the disorder-driven quantum criticality in Weyl materials.