Phase diagram of the Quantum Electrodynamics of 2D and 3D Dirac semimetals

TL;DR

This paper investigates the phase diagrams of 2D and 3D Dirac semimetals using Schwinger-Dyson equations, revealing strong-coupling instabilities, exciton condensation in 2D, and non-Fermi liquid behavior in 3D.

Contribution

It provides a self-consistent analysis of the phase diagrams of Dirac semimetals, identifying critical couplings and novel non-Fermi liquid phases.

Findings

2D Dirac semimetals exhibit exciton condensation at high coupling.

3D Dirac semimetals show dynamical mass generation for N ≤ 4.

3D semimetals display non-Fermi liquid behavior with vanishing quasiparticle weight.

Abstract

We study the Quantum Electrodynamics of 2D and 3D Dirac semimetals by means of a self-consistent resolution of the Schwinger-Dyson equations, aiming to obtain the respective phase diagrams in terms of the relative strength of the Coulomb interaction and the number N of Dirac fermions. In this framework, 2D Dirac semimetals have just a strong-coupling instability characterized by exciton condensation (and dynamical generation of mass) that we find at a critical coupling well above previous theoretical estimates, thus explaining the absence of that instability in free-standing graphene samples. On the other hand, we show that 3D Dirac semimetals have a richer phase diagram, with a strong-coupling instability leading to dynamical mass generation up to N = 4 and a line of critical points for larger values of N characterized by the vanishing of the electron quasiparticle weight in the low-energy limit. Such a critical behavior signals the transition to a strongly correlated liquid, characterized by noninteger scaling dimensions that imply the absence of a pole in the electron propagator and are the signature of non-Fermi liquid behavior with no stable electron quasiparticles.