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