Confining graphene plasmons to the ultimate limit

Abstract

Graphene plasmons have recently attracted a great deal of attention because of their tunability, long lifetime, and high degree of field confinement in the vertical direction. Nearby metal gates have been shown to modify the graphene plasmon dispersion and further confine their electric field. We study the plasmons of a graphene sheet deposited on a metal, in the regime in which metal bands do not hybridize with massless Dirac fermion bands. We derive exact results for the dispersion and lifetime of the plasmons of such hybrid system, taking into account metal nonlocalities. The graphene plasmon dispersion is found to be acoustic and pushed down in energy towards the upper boundary of the intraband graphene particle-hole continuum, thereby strongly enhancing the vertical confinement of these excitations. Landau damping of such acoustic plasmons due to particle-hole excitations in the metal gate is found to be surprisingly weak, with quality factors exceeding Q = 10 2 .Introduction.-Recently, the fundamental properties of graphene plasmons and hybrid plasmon-phonon polaritons in graphene encapsulated in hexagonal boron nitride (hBN) have been studied in an extensive manner [1][2][3]. In encapsulated graphene, plasmons have record-high lifetimes approaching 1 ps both in the mid-infrared [4] and Terahertz (THz) [5,6] spectral ranges, while at the same time displaying strong vertical confinement.The plasmon dispersion relation in graphene can be engineered not only by coupling them to standing Fabry-Pérot phonon polariton modes of hBN slabs [7], but also by placing metal gates nearby. These have been shown to play two vital roles. On the one hand, when shaped in the form of split gates, the associated p-n junctions allow to detect plasmons electrically thanks to the photothermoelectric effect [8]. On the other hand, they screen the long-range tail of the electron-electron interaction potential, yielding acoustic plasmon modes [9-11] whose associated electric field is tightly confined to the small volume between the metal gate and graphene [5]. The latter is typically filled with an hBN spacer, which can be thinned down to a single layer or even removed. The modification of the plasmon dispersion from the usual unscreened √ q

Quantum effects in the acoustic plasmons of atomically thin heterostructures: publisher’s note

“…Additionally, the frequency dependence of the plasmon width also changes severely with metal thickness, going from a reduction to an increase with increasing frequency as the gold layer is made thicker, again indicating a complex evolution of metal screening with this geometrical parameter. It is remarkable that acoustic plasmons exist even by directly depositing the graphene on the metal without spacing, which corroborates a recent prediction of this effect [24], and defies the intuition that metal screening can quench the graphene response. At low mid-IR frequencies, the acoustic plasmons are predicted to exhibit smaller lifetimes as the film thickness increases; thicker metal films are thus providing more efficient screening and less relative weight of the field inside the metal, where the intrinsic inelastic rate is larger than in the graphene alone (cf.…”

“…1), or also in graphene and a metal surface, emerging as a low-energy branch in the energy-momentum dispersion diagram [23]. In contrast to the intuition that metal screening quenches the graphene response, an acoustic plasmon branch has been predicted to manifest itself even when graphene is directly deposited on the metal without a spacer [24]. For atomic-scale graphene-metal separations, the nonlocal nature of the optical response in both the metal and graphene layers plays an important role, demanding a rigorous theoretical treatment to accurately describe the dispersion and lifetime of acoustic plasmons [25].…”

A theory of electrodynamic response for bounded metals: Surface capacitive effects

“…This underlies the incorrect conclusion drawn by Harris 85 and calls into question many other works such as Ref. 99 . That Eq.…”

Quantum Nanophotonics in Two-Dimensional Materials

“…For AGPs in GDM structures, this shift can be substantial at small graphene-metal separations and is also responsible for the slowdown of the AGPs' velocity 8,10 . Moreover, as the graphene-metal separation t is reduced, the nonlocal description predicts plasmon velocities asymptotically approaching electron velocity vF, but without ever surpassing (falling below) it 8,10,157 . This is in stark contrast to the local-response prediction which allows the AGP's dispersion to fall inside the prohibited graphene's intraband electron-hole continuum.…”