Phase diagram of the quantum electrodynamics of two-dimensional and three-dimensional Dirac semimetals

Abstract

We study the quantum electrodynamics of two-dimensional (2D) and three-dimensional (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 $N\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}4$ 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.