Intrinsic plasmons in two-dimensional Dirac materials

Abstract

We consider theoretically, using the random phase approximation (RPA), low-energy intrinsic plasmons for two-dimensional (2D) systems obeying Dirac-like linear chiral dispersion with the chemical potential set precisely at the charge neutral Dirac point. The "intrinsic Dirac plasmon" energy has the characteristic √ q dispersion in the 2D wave-vector q, but vanishes as √ T in temperature for both monolayer and bilayer graphene. The intrinsic plasmon becomes overdamped for a fixed q as T → 0 since the level broadening (i.e. the decay of the plasmon into electron-hole pairs due to Landau damping) increases as 1/ √ T as temperature decreases, however, the plasmon mode remains well-defined at any fixed T (no matter how small) as q → 0. We find the intrinsic plasmon to be well-defined as long as q < k B T e 2 . We give analytical results for low and high temperatures, and numerical RPA results for arbitrary temperatures, and consider both single-layer and double-layer intrinsic Dirac plasmons. We provide extensive comparison and contrast between intrinsic and extrinsic graphene plasmons, and critically discuss the prospects for experimentally observing intrinsic Dirac point graphene plasmons.

Drift-induced modifications to the dynamical polarization of graphene

“…Aside from the mode that was predicted when including the vertex corrections [58], undoped graphene does not support any TM-SPP modes at T = 0 K within the RPA [53]. Here, we numerically show that a high enough drainsource voltage along an undoped graphene channel enables the channel to support specific TM-SPP modes, even for the purely hypothetical case of T = 0 K. More importantly, the numerical results indicate the possibility of the emission of low-energy ( ω 30 meV) and long-wavelength plasmons.…”

Electron polarization function and plasmons in metallic armchair graphene nanoribbons

“…(13) and (18) as well as from Eqs. (14) and (19), for both T = 0 and T = 0 the phase space is redistributed among the inter-band and the intra-band transitions in such a way that it cancels exactly the q 0 and q 2 dependence, inherent in the separate intra-band and inter-band contributions. Strikingly, we find that this cancellation takes place without the long wavelength limit restriction on q and for arbitrary values of T and E F so that the total phase space is…”

“…On the other hand, at finite temperatures [25,28], due to thermally activated electronic transitions, these N 0 passive acoustical modes become separated from the top of the electron-hole continuum and at temperatures of the order of the Fermi energy they behave completely similar to out-of-phase plasmon modes in multilayer structures with equal finite carrier densities in each layer. Intrinsic thermal plasmon modes are formed also in single-layer neutral graphene structures [14,19]. Importantly, in the long wavelength limit these temperature induced inphase and out-of-phase intrinsic plasmon modes in multilayer graphene structures preserve their characteristic square-root and linear energy dispersions, are Landau damped, and disappear at vanishing temperatures.…”

“…Recently plasmons in graphene [13] have been studied in single [14][15][16][17][18][19][20][21] and spatially separated double [22][23][24][25][26][27] and multilayer [28] structures. It was shown that finite temperature can strongly affect the plasmon modes [14,19,25,28].…”

“…It was shown that finite temperature can strongly affect the plasmon modes [14,19,25,28]. Particularly, at zero temperature in Coulomb-coupled N -layer unbalanced graphene structures there exists only one inphase optical plasmon mode and N − N 0 − 1 out-of-phase acoustical modes [22,25,28] (here N 0 is the number of neutral graphene layers in such multilayer structures).…”