Emission of plasmons by drifting Dirac electrons: A hallmark of hydrodynamic transport

Abstract

Direct current in clean semiconductors and metals was recently shown to obey the laws of hydrodynamics in a broad range of temperatures and sample dimensions. However, the determination of frequency window for hydrodynamic phenomena remains challenging. Here, we reveal a phenomenon being a hallmark of high-frequency hydrodynamic transport, the Cerenkov emission of plasmons by drifting Dirac electrons. The effect appears in hydrodynamic regime only due to reduction of plasmon velocity by electron-electron collisions below the velocity of carrier drift. To characterize the Cerenkov effect quantitatively, we analytically find the high-frequency non-local conductivity of drifting Dirac electrons across the hydrodynamic-to-ballistic crossover. We find the growth rates of hydrodynamic plasmon instabilities in two experimentally relevant setups: parallel graphene layers and graphene covered by subwavelength grating, further showing their absence in ballistic regime. We argue that the possibility of Cerenkov emission is linked to singular structure of non-local conductivity of Dirac materials and is independent on specific dielectric environment.The realm of hydrodynamic transport spans at length scales exceeding the particle free path [1]. Experimental demarcation of hydrodynamics and ballistics is conveniently performed by measuring the flow through a pipe between two reservoirs. The flow through wide pipes is limited by viscosity (Poiseuille flow), while in narrower pipes it is limited by particle injection (Knudsen flow). Recently, similar experiments were performed in ultraclean solid-state systems, including thin metal wires [2], Weyl semimetals [3], GaAs-based quantum wells [4], and graphene [5-7]. They have revealed quite a broad window of temperatures and sample dimensions where electrons obey the laws of hydrodynamics [8] but not ballistics, as thought previously [9].While the place for dc hydrodynamic (HD) phenomena on temperature and length scales is established [10,11], the bounds for hydrodynamics on frequency scale are less probed [12]. Generally, electron-electron (e-e) collisions being the prerequisite of HD transport affect neither dc nor ac conductivity in uniform fields, though they may affect the properties of waves in solids -plasmons. Still, the spectra of plasmons in HD and ballistic regimes are almost identical as they are dictated by long-range Coulomb forces insensitive to microscopic details of e-e interactions [13,14]. The character of damping due to e-e scattering in ballistic and HD regimes is different [15,16], still, it is often masked by extrinsic damping.In this Letter, we theoretically reveal a plasmonic phenomenon serving as a hallmark of hydrodynamic transport, and is fully prohibited in collisionless ballistic regime. The effect is emission of plasmons by drifting Dirac electrons or, in other words, Cerenkov plasmon instability of electron drift. Our emphasis on Dirac electron systems, especially graphene, is motivated by numerous observations of hydrodynamic phenomena therein [5][6...

Room-Temperature Amplification of Terahertz Radiation by Grating-Gate Graphene Structures

“…(For a discussion of crossover from the hydrodynamic to the ballistic regime and of the Cherenkov instability in graphene, see Refs. [38,39].) The suggested mechanism should work for any electronic spectrum, but calculations are more compact and physically transparent for parabolic spectrum characterized by the effective mass m. We thus restrict ourselves to the discussion of this case only.…”

“…Recently, some theoretical and experimental studies of grating-gate graphene structures utilizing plasma resonances have been reported [38][39][40]. In particular, the electromagnetic simulations of the graphene gratinggate structures [41] show the possibility of the resonant plasmons strongly coupled to THz radiation even at roomtemperature.…”

Гидродинамические Терагерцовые Плазмоны И Электронный Звук В Графене С Пространственной Дисперсией

“…Проводимость в виде (8) совпадает с проводимостью из [11] в приближении малых q, которое верно для волн с фазовой скоростью больше скорости Ферми. Формула, аналогичная (8) встречается в работах [4,18].…”

“…Плазмоны в гидродинамическом режиме могут возбуждаться постоянным током по черенковскому механизму [4], а также трансформироваться в электронно-дырочные звуковые колебания вблизи точки зарядовой нейтральности [5,6]. Скорость таких электронно-дырочных звуковых колебаний в графене определяется выражением ν F / √ 2, где ν F -скорость Ферми в графене [4,7]. При замедлении гидродинамических плазмонов до скоростей, близких к скорости Ферми, в графене может возникать пространственная дисперсия проводимости.…”

“…4, a и b). Сильная конкуренция между кулоновским и звуковым вкладом в дисперсии происходит по причине экранирования зарядов в графене.…”