Electronic Excitations in Graphene in the 1–50 eV Range: The π and π + σ Peaks Are Not Plasmons

Abstract

The field of plasmonics relies on light coupling strongly to plasmons as collective excitations. The energy loss function of graphene is dominated by two peaks at ∼5 and ∼15 eV, known as π and π + σ plasmons, respectively. We use electron energy-loss spectroscopy in an aberration-corrected scanning transmission electron microscope and density functional theory to show that between 1 to 50 eV, these prominent π and π + σ peaks are not plasmons, but single-particle interband excitations.

Changing character of electronic transitions in graphene: From single-particle excitations to plasmons

“…As we can see, at these energies the screening factor D(Q,ω) is exactly 1. This means that the mentioned transitions are not screened, i.e., the peaks in S(Q,ω) are pure SP excitations which appear at the same energies as peaks in E 2 (Q,ω) [11,25]. Blue dots in Figs.…”

“…Recently a resolute claim was made [11] that the previously accepted attribution of the two strong structures in the graphene excitation spectra was wrong, and the π and π + σ plasmons are in fact strong single-particle (SP) π → π * and σ → σ * excitations, respectively, with a characteristic Q 2 excitation energy dependence. Another group [12] found strong evidence for 2D plasmon character of π and σ electron excitations, based on the electron energy loss spectroscopy (EELS) experiment showing the √ Q dependent dispersion.…”

Angle-resolved electron energy loss spectroscopy in hexagonal boron nitride

“…Two energy ranges are generally distinguished, with a π plasmon peak in the 6-8 eV range and a σ + π peak at about 25 eV for bulk h-BN and also for graphite [43][44][45][46][47], the position and intensity of the latter peak being strongly dependent on the number of sheets in thin samples. The position of some structures can also be associated with specific interband transitions, particularly if they are correlated with the behavior of ε(q,ω) itself through Kramers-Kronig analyses [43], but some controversy has appeared recently between these two interpretations concerning the nature of the observed signals in 2D systems such as graphene [48][49][50][51]. Actually, deriving well-defined dispersion relations and deciding between the two possibilities is not obvious.…”

Transparency of graphene for low-energy electrons measured in a vacuum-triode setup

“…As electron-transparent gate material, graphene, therefore, opens new possibilities for vacuum-based or gas-based microelectronic devices. For such applications, possible excitations of the graphene, for example, plasmons, and interband excitations 22 caused by the traversing electrons would constitute an unwanted energy loss channel. Patterning of the graphene reduces these losses accordingly.…”