Scattering resonances in two-dimensional crystals with application to graphene

Abstract

We address the band-structure of two-dimensional crystals above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the in-plane and perpendicular motions, as elucidated by the analysis of an exactly solvable model. Some of the resonances turn into true bound states at highsymmetry k vectors. Ab initio scattering theory verifies the existence of the resonances in realistic graphene and shows that they lead to a total reflection of the incident electron below and total transmission above the resonance energy.

Mapping unoccupied electronic states of freestanding graphene by angle-resolved low-energy electron transmission

“…4 in Ref. [18]). We therefore conclude that this is the first experimental observation of this scattering resonance in freestanding graphene.…”

“…Ab initio calculations show the existence of discrete states immersed in the continuous spectrum above the vacuum level [18,19]. Only recently, the existence of a special kind of scattering resonance in graphene originating from a strong coupling of the in-plane and perpendicular motions was predicted [18]. Ab initio scattering theory [18,20] predicts that such resonances lead to a sharp transition from high to low transmission of an incident electron above, respectively, below, the resonance energy.…”

“…Only recently, the existence of a special kind of scattering resonance in graphene originating from a strong coupling of the in-plane and perpendicular motions was predicted [18]. Ab initio scattering theory [18,20] predicts that such resonances lead to a sharp transition from high to low transmission of an incident electron above, respectively, below, the resonance energy. Measurements of the electronic structure above the vacuum level of single and multilayer graphene on SiC have been reported in a low-energy electron microscopy (LEEM) study based on the measuring principle of VLEED [21].…”

Time-dependent density functional theory of coupled electronic lattice motion in quasi-two-dimensional crystals

“…Thereby, the acoustic plasmon in graphene does not exist as an isolated excitation, but it is rather bound into a combined plasmonphonon mode. We show that the coupling provides a mechanism for the bidirectional energy exchange between the electronic and the ionic subsystems with fundamentally, as well as practically, important implications for the lattice cooling and heating by electrons in graphene.Known for its extraordinary properties and vast potential applications [1], graphene -a two-dimensional crystal comprised of a honeycomb lattice of carbon atomscontinues to receive much attention as it reveals new remarkable features [2][3][4][5][6][7]. For one of the recent findings, an acoustic plasmon (APl) (plasmon with linear wave-vector dispersion) has been predicted theoretically in an extrinsic free-standing monolayer graphene [7].…”

“…Known for its extraordinary properties and vast potential applications [1], graphene -a two-dimensional crystal comprised of a honeycomb lattice of carbon atomscontinues to receive much attention as it reveals new remarkable features [2][3][4][5][6][7]. For one of the recent findings, an acoustic plasmon (APl) (plasmon with linear wave-vector dispersion) has been predicted theoretically in an extrinsic free-standing monolayer graphene [7].…”