Super van Hove singularities in graphene-like materials

We discuss the crossover from weak to strong correlations in Dirac materials by analyzing the excitonic insulator (EI) transition in a paradigmatic family of ‘slow’ graphenes. We consider the exciton modes at Q = (0, 0) and (π, 0), and show that pristine graphene is free of an excitonic instability. When the band structure is compressed, a gap opens first in a Q = (π, 0) EI phase before a Q = (0, 0) EI phase is triggered when the bands are further compressed. The gap in the Q = (π, 0) phase dominates over that in the the Q = (0, 0) phase throughout the band compression process. Interestingly, we find the presence of high order van Hove singularities¹ in both the EI phases driven by the interaction-induced changes in the band structure. Our study suggests that two-dimensional slow graphenes could provide a novel platform for exploring the physics of EI phases and high order van Hove singularities.

[1].Noah F. Q. Yuan, Hiroki Isobe, Liang Fu, Magic of high order van Hove singularity. arXiv:1901.05432