Quasiparticle theory of collective electron excitations in graphene

In this paper, we develop a new approach for analyzing collective quantum excitations in graphene, based on the quantum multistream model. We explore a range of phenomena, including the energy band structure of collective modes, linear and nonlinear excitations, statistical characteristics, and the linear dielectric response of quasiparticle excitations in graphene. A modified Wigner quasiprobability distribution is derived, enabling the study of phase-space dynamics for linear excitations. Our results reveal that quasiparticle excitations of massless Dirac fermions are governed by three distinct characteristic wavenumbers. Notably, we identify a broad energy bandgap associated with the collective effects, below which quasiparticle excitations become unstable. The thermodynamic analysis, encompassing internal pressure and heat capacity, uncovers several intriguing deviations from the behavior of a conventional Fermi electron gas. Furthermore, we demonstrate that massless Dirac fermions in graphene can sustain both large-amplitude cnoidal waves and solitary structures. By examining the dielectric response within the Lindhard framework, incorporating a quasiparticle energy dispersion that accounts for both single-particle and wave-like contributions, we gain new insights into the frequency-dependent response, loss-function spectrum, and static charge screening, highlighting key differences from the ordinary Fermi gas. This theory offers a unified approach to capturing both the particle-like and wave-like aspects of massless Dirac Fermion excitations, clearly distinguishing their individual contributions to various physical properties. It also extends beyond the conventional many-body theories incorporating the mean field approximations by appropriately linking the single-electron dynamics to collective behavior through the hybrid nature of quasiparticle matter-wave dispersion.