Correlated Fractional Dirac Materials

Fractional Dirac materials (FDMs) feature a fractional energy-momentum relation $E(\vec{k}) \sim |\vec{k}|^{\alpha}$, where $\alpha \; (<1)$ is a real noninteger number, in contrast to that in conventional Dirac materials with $\alpha=1$. Here we analyze the effects of short- and long-range Coulomb repulsions in two- and three-dimensional FDMs. Only a strong short-range interaction causes nucleation of a correlated insulator that takes place through a quantum critical point. The universality class of the associated quantum phase transition is determined by the correlation length exponent $\nu^{-1}=d-\alpha$ and dynamic scaling exponent $z=\alpha$, set by the band curvature. On the other hand, the fractional dispersion is protected against long-range interaction due to its nonanalytic structure. Rather, a linear Dirac dispersion gets generated under coarse graining, and the associated Fermi velocity increases logarithmically in the infrared regime, thereby yielding a two-fluid system. Altogether, correlated FDMs unfold a rich landscape accommodating unconventional emergent many-body phenomena.