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 α ≈ 9 where 0 ⩽ ζ < 1 is the tilt parameter. We demonstrate that such a strong enhancement for ζ ≲ 1 that gives rise to very fast relaxation rates, is contributed by a new hyperfine interactions arising from the tilt itself. This can be attributed to the combination of anisotropy of the Fermi surface and an additional part related to the structure of the spacetime: extracting an effective density of states (DOS) $\tilde{\rho }$ from the Korringa relation, we show that it is related to the DOS ρ of the tilted cone dispersion by the 'redshift factor' as $\tilde{\rho }=\rho /\sqrt{1-{\zeta }^2}$. We interpret this relation as NMR manifestation of an emergent underlying spacetime structure in TCWSMs. (paper)