Fast nuclear spin relaxation rates in tilted cone Weyl semimetals: Redshift factors from Korringa relation

Abstract

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.

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