Correlated Fractional Dirac Materials

TL;DR

This paper investigates the effects of Coulomb interactions on fractional Dirac materials, revealing a quantum phase transition to a correlated insulator and the emergence of a two-fluid system with a logarithmically increasing Fermi velocity.

Contribution

It provides a theoretical analysis of how short- and long-range Coulomb interactions influence fractional Dirac materials, identifying a quantum critical point and emergent phenomena.

Findings

Strong short-range interactions induce a correlated insulator phase.

The quantum phase transition has a universality class with specific exponents.

Long-range interactions do not alter the fractional dispersion but generate a linear Dirac dispersion.

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.