Unconventional Fermi surface in two-dimensional systems of Dirac fermions

TL;DR

This paper investigates the low-energy behavior of two-dimensional Dirac fermions, revealing unconventional Fermi surface properties and quasiparticle characteristics depending on the decay rate exponent, with implications for systems with long-range interactions.

Contribution

It identifies distinct regimes of Fermi surface and quasiparticle existence in 2D Dirac fermions based on the decay rate exponent, highlighting unusual behavior in systems with long-range interactions.

Findings

No sharp Fermi surface and no quasiparticles for 0<x<1/2

Sharp Fermi surface but no quasiparticles for 1/2≤x≤1

Both sharp Fermi surface and quasiparticles for x>1

Abstract

At the low energy regime, the decay rate of two-dimensional massless Dirac fermions due to interactions can be written as $\mathrm{Im}\Sigma(\omega) \propto |\omega|^{x}$ at zero temperature. We find that the fermion system has: I) no sharp Fermi surface and no well-defined quasiparticle peak for $0<x<1/2$; II) a sharp Fermi surface but no well-defined quasiparticle peak for $1/2\leq x\leq 1$; III) both sharp Fermi surface and well-defined quasiparticle peak for $x>1$. In the presence of long-range gauge/Coulomb interaction or certain massless boson mode, the system exhibits unusual behavior belonging to class II.