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Anomalous hyperfine coupling and nuclear magnetic relaxation in Weyl semimetals

The electron-nuclear hyperfine interaction shows up in a variety of phenomena including e.g. NMR studies of correlated states and spin decoherence effects in quantum dots. Here we focus on the hyperfine coupling and the NMR spin relaxation time, $T_1$ in Weyl semimetals. Since the density of states in Weyl semimetals varies with the square of the energy around the Weyl point, a naive power counting predicts a $1/T_1T\sim E^4$ scaling with $E$ the maximum of temperature ($T$) and chemical potential. By carefully investigating the hyperfine interaction between nuclear spins and Weyl fermions, we find that while its spin part behaves conventionally, its orbital part diverges unusually with the inverse of energy around the Weyl point. Consequently, the nuclear spin relaxation rate scales in a graphene like manner as $1/T_1T\sim E^2\ln(E/ω_0)$ with $ω_0$ the nuclear Larmor frequency. This allows us to identify an effective hyperfine coupling constant, which is tunable by gating or doping, which is relevant for decoherence effect in spintronics devices and double quantum dots where hyperfine coupling is the dominant source of spin-blockade lifting.