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 $(1-\zeta^2)^{-\alpha}$ with $\alpha\approx 9$ where $0\le \zeta < 1$ is the tilt parameter. We demonstrate that such a strong enhancement for $\zeta\lesssim 1$ 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) $\tilde\rho$ from the Korringa relation, we show that it is related to the DOS $\rho$ of the tilted cone dispersion by the "redshift factor" $\tilde\rho=\rho/\sqrt{1-\zeta^2}$. We interpret this relation as NMR manifestation of an emergent underlying spacetime structure in TCWSMs.