Finite temperature dynamical polarization and plasmons in gapped graphene

Abstract

In this study we report our numerical results on finite temperature non-interacting dynamical polarization function, plasmon modes and electron energy loss function of doped single layer gapped graphene within the random phase approximation. We find that the interplay of linear energy band dispersion, chirality, bandgap and temperature endow single layer gapped graphene with strange polarizability behaviour which is a mixture of 2DEG, single layer and bilayer graphene and as a result the plasmon spectrum also manifests strikingly peculiar behaviour. The plasmon dispersion is observed to be suppressed till temperatures up to ~ , similar to the gapless graphene case but beyond a reversal in trend is seen in gapped graphene, for all values of band gap. This behaviour is also corroborated by the density plots of electron energy loss function. The opening of a small gap also generates a new undamped plasmon mode which is found to disappear at high temperatures. The plasmonic behaviour of gapped graphene is further found to be hugely influenced by the substrate on which the gapped graphene sheet rests, which signifies the need for a careful substrate selection in the making of desirable graphene based plasmonics devices.

A theoretical study of collective plasmonic excitations in double-layer silicene at finite temperature

“…Furthermore, the frequency of the optical branch decreases with increasing temperature and reaches a minimum value around T = 0.4T F but after that it bounces off at higher temperatures. The behavior of optical plasmons for this studied DLS is similar to the plasmon dispersion of SLGG where the plasmon frequencies follow first a decreasing and then an increasing trend with a minimum at T ∼ 0.5T F for all band gap values 45 and similar to the double-layer graphene at small wave vectors. 56 Recently, it has been shown that the temperature-dependent plasmons of SLS, SLG and singlelayer n-doped and p-doped molybdenum disulfide can also exhibit such a behavior.…”

“…4 and 5 suggests that when the temperature increases from T = 0.5T F to T = T F , similar to the case of SLGG at finite temperature, 45 the boundaries are changed only slightly such that the extent of SPE gap decreases by temperature very slowly; this can be explained by the fact that single-particle transitions are more probable at higher temperatures. 45 Moreover, in panels (a,b,d) of Figs. 4 and 5, the interband boundaries are not discernible beforeq 0.25 but for values after that, that seems to be consistent with Eq.…”

“…40 The extrinsic (doped) finite-temperature plasmons of SLS have also been studied: as temperature increases from T = 0, the plasmon energy first lowers, reaching to a minimum value and then bounces back in both cases of SLS and SLGG. 42,45 Similar calculations were performed at zero temperature when both electric and magnetic (exchange) fields were applied. 46 It is worth pointing out that an exchange field can be induced by positioning ferromagnetic adatoms 47 on the surface or by employing a ferromagnetic substrate.…”

Plasmon modes in double bilayer graphene heterostructures

“…and several values of potential bias. It is seen from the figure that the potential bias, leading to an energy gap in BLG layer, decreases remarkably plasmon frequencies of both branches as in the case of gapped graphene systems [35][36][37][38][39][40]. In addition, the interband SPE continuum edge increases with increase in the potential bias.…”

Finite-temperature Coulomb Excitations in Extrinsic Dirac Structures

“…However, at finite temperature, the conduction band would receive thermally induced doping in both cases. 70,71 In graphene, with zero energy band gap, this density is enhanced as n T 2 and the plasmon dispersion behaves like Ω 2 p qT .…”