Interacting Dirac liquid in three-dimensional semimetals

TL;DR

This paper theoretically investigates the properties of the three-dimensional interacting Dirac liquid, revealing distinct behaviors at intrinsic and extrinsic doping levels, and predicts observable spectral features such as plasmarons.

Contribution

It provides analytical and numerical analysis of the self-energy, spectral function, and quasiparticle properties of the 3D Dirac liquid using Hartree-Fock and RPA methods, highlighting novel features.

Findings

Intrinsic Dirac liquid exhibits unusual Fermi liquid properties similar to graphene.

Extrinsic Dirac liquid behaves as a standard Landau Fermi liquid.

Spectral function shows a plasmaron sideband and breakdown of Fermi liquid at high energies.

Abstract

We study theoretically the properties of the interacting Dirac liquid, a novel three-dimensional many-body system which was recently experimentally realized and in which the electrons have a chiral linear relativistic dispersion and a mutual Coulomb interaction. We find that the "intrinsic" Dirac liquid, where the Fermi energy lies exactly at the nodes of the band dispersion, displays unusual Fermi liquid properties similar to graphene, whereas the "extrinsic" system with finite detuning or doping behaves as a standard Landau Fermi liquid. We present analytical and numerical results for the self-energy and spectral function based on both Hartree-Fock and the random phase approximation (RPA) theories and compute the quasiparticle lifetime, residue, and renormalized Fermi velocity of the extrinsic Dirac liquid. A full numerical calculation of the extrinsic RPA spectral function indicates that the Fermi liquid description breaks down for large-energy excitations. Furthermore, we find an additional plasmaron quasiparticle sideband in the spectral function which is discontinuous around the Fermi energy. Our predictions should be observable in ARPES and STM measurements.