Correlated Fractional Dirac Materials

Abstract

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.

Published Version in Physical Review Research as a Letter (6 Pages, 3 Figures; Supplemental Material as Ancillary file)

References in corpus (4)

• The electronic properties of graphene
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Merging of Dirac points in a two-dimensional crystal
• Optical conductivity of an interacting Weyl liquid in the collisionless regime

Cited by in corpus (1)

• Quantum geometric tensor in systems with fractional band dispersion