Fast nuclear spin relaxation rates in tilted cone Weyl semimetals: Redshift factors from Korringa relation
Spin lattice relaxation rate is investigated for 3D tilted cone Weyl semimetals (TCWSMs). The nuclear spin relaxation rate is presented as a function of temperature and tilt parameter. We find that the relaxation rate behaves as $(1-ζ^2)^{-α}$ with $α\approx 9$ where $0\le ζ< 1$ is the tilt parameter. We demonstrate that such a strong enhancement for $ζ\lesssim 1$ that gives rise to very fast relaxation rates, is contributed by the combined effect of a new hyperfine interactions arising from the tilt itself, and the anisotropy of the ellipsoidal Fermi surface. Extracting an effective density of states (DOS) $\tildeρ$ from the Korringa relation, we show that it is related to the DOS $ρ$ of the tilted cone dispersion by the "redshift factor" $\tildeρ=ρ/\sqrt{1-ζ^2}$. We interpret this relation as NMR manifestation of an emergent underlying spacetime structure in TCWSMs.