Interacting chiral electrons at the 2D Dirac points: a review.

Pseudo-relativistic chiral electrons in 2D graphene and 3D topological semimetals, known as massless Dirac or Weyl fermions, constitute various intriguing topics in modern condensed-matter physics. Among these electron-electron Coulomb-interaction effects are particularly unique and attract great attentions since the interaction between the chiral electrons is not screened and remains long-ranged, in contrast to its screened and short-ranged property in conventional correlated materials. In graphene the long-range interaction has been shown to induce an anomalous logarithmic renormalization of velocity and, at strong coupling, even led to predictions of exotic phase transitions with a spontaneous mass acquisition. The layered organic material α-(BEDT-TTF)2I3under pressure provides an excellent testing ground for this type of interaction effects where, unlike graphene, a 2D massless-Dirac-fermion phase appears directly next to a correlated insulating phase. In this review we give an overview of our recent progress on the understanding of the interacting chiral electrons in 2D, placing particular emphasis on graphene and α-(BEDT-TTF)2I3. We first review the current experimental and theoretical understandings of the interaction effects in graphene, turn attentions to the status of α-(BEDT-TTF)2I3and highlight its relevance to and difference from graphene. The second half of this review focusses on nuclear magnetic resonance (NMR) experiments and associated model calculations in the latter system; they provide unprecedented opportunities to resolve the momentum dependence of spin excitations and correlations influenced by strong electronic interactions around the band-crossing Dirac points (valleys) at and near the charge neutrality. The observations of an anisotropic reshaping of a tilted Dirac cone and various orthodox electron correlation effects as well as precursor fluctuations of an incipient instability towards intervalley excitonic condensate shall be reviewed and discussed.