Extraordinary Coulomb correlations and incipient excitonic instability of Weyl fermions

In modern solid-state physics, electron correlations constitute major sources of interests in the exploration of novel electronic properties. For Weyl fermion (WF) systems consisted of relativistic massless electrons with nodal dispersion, the interparticle Coulomb interaction has a highly unusual characteristic since its long-range component is unscreened at the band-crossing Weyl nodes due to the vanishing density of states, affecting drastically the nature of WFs as established in quantum electrodynamics. Indeed, exotic phenomena like excitonic mass generation have been predicted in strong coupling. To characterize how strong the interaction can be and identify what kind of emergent Coulomb-induced phenomena it brings about in real materials is among top priorities over experimental challenges of addressing strongly correlated WFs. Here, employing NMR spectroscopy, we show that the anisotropic WFs appearing in a quasi-2D organic conductor possess an extraordinarily strong Coulomb correlation. We find that this characteristic leads to a tremendous enhancement of the NMR index of spin correlations (the Korringa ratio), given by the ratio of the relaxation rate to the square of the spectral shift, by a factor of ~$10^3$ from the values in ordinary metals. Our model calculations based on renormalization-group treatment reveal that the observed enormous spin correlation is a general characteristic of WF systems, arising from the short-wavelength correlations that persist at low energy despite the drastic suppression of the long-wavelength correlations by the running Coulomb coupling. On further cooling, the dynamic spin susceptibility (probed by the relaxation rate) shows a sudden increase, which is identified by model calculations within the ladder approximation as indicating spin-triplet excitonic fluctuations -- precursors to mass generation associated with chiral symmetry breaking.