Plasmon properties and hybridization effects in silicene

Abstract

The plasmonic character of monolayer silicene is investigated by time-dependent density functional theory in the random phase approximation. Both the intrinsic (undoped) and several extrinsic (carrier doped or gated) conditions are explored by simulating injection of a probe particle (i.e., an electron or a photon) of energy below 20 eV and in-plane momentum smaller than $1.1\phantom{\rule{0.16em}{0ex}}\AA{}{}^{\ensuremath{-}1}$. The energy-loss function of the system is analyzed, with particular reference to its induced charge-density fluctuations, i.e., plasmon resonances and corresponding dispersions, occurring in the investigated energy-momentum region. At energies larger than 1.5 eV, two intrinsic interband modes are detected and characterized. The first one is a hybridized $\ensuremath{\pi}$-like plasmon, which is assisted by competing one-electron processes involving $s{p}^{2}$ and $s{p}^{3}$ states, and depends on the slightest changes in specific geometric parameters, such as nearest-neighbor atomic distance and buckling constant. The second one is a more conventional $\ensuremath{\pi}\ensuremath{-}\ensuremath{\sigma}$ plasmon, which is more intense than the $\ensuremath{\pi}$-like plasmon and more affected by one-electron processes involving the $\ensuremath{\sigma}$ bands with respect to the analogous collective oscillation in monolayer graphene. At energies below 1 eV, two extrinsic intraband modes are predicted to occur, which are generated by distinct types of Dirac electrons (associated with different Fermi velocities at the so-called Dirac points). The most intense of them is a two-dimensional plasmon, having an energy-momentum dispersion that resembles that of a two-dimensional electron gas. The other is an acoustic plasmon that occurs for specific momentum directions and competes with the two-dimensional plasmon at mid-infrared energies. The strong anisotropic character of this mode cannot be explained in terms of the widely used Dirac-cone approximation. As in mono-, bi-, and few-layer graphene, the extrinsic oscillations of silicene are highly sensitive to the concentration of injected or ejected charge carriers. More importantly, the two-dimensional and acoustic plasmons appear to be a signature of the honeycomb lattice, independently of the chemistry of the group-IV elements and the details of the unit-cell geometry.