Physics Letters A 374 (2010) 4899–4903 Contents lists available at ScienceDirect Physics Letters A www.elsevier.com/locate/pla Temperature effect on plasmon dispersions in double-layer graphene systems T. Vazifehshenas ∗ , T. Amlaki, M. Farmanbar, F. Parhizgar Department of Physics, Shahid Beheshti University, G.C., Evin 1983963113, Tehran, Iran article info abstract Article history: Received 16 August 2010 Received in revised form 10 October 2010 Accepted 12 October 2010 Available online 14 October 2010 Communicated by R. Wu Keywords: Graphene Plasmon Temperature dependent Double-layer We investigate the plasmon dispersion relation and damping rate of a double-layer graphene system consisting of two separated monolayer graphenes with no interlayer tunneling at finite temperature. We use the temperature dependent RPA dielectric function which is valid for graphene systems to obtain the plasmon frequencies and damping rates at different temperatures, interlayer correlation parameters and electron densities and then compare them with those obtained from the zero temperature calculations. Our results show that by increasing the temperature, the plasmon frequencies decrease and the decay rate increases. Furthermore, we find that the behavior of a double-layer graphene system at small and large correlation parameters is different from the conventional double-layer two-dimensional electron gas system. Finally, we obtain that in a density imbalanced double-layer graphene system, the acoustic plasmons are more affected by temperature than the equal electron densities one.  2010 Elsevier B.V. All rights reserved. 1. Introduction Graphene is a sheet of carbon atoms with a thickness of only one atom as a strictly two-dimensional (2D) system. Carbon atoms in graphene arranged on a honeycomb structure which is com- posed of two sublattices [1–5]. The monolayer graphene is a gapless semiconductor and has unusual massless and chiral carriers near the Dirac points, K and K ′ (two equivalent corners of the Brillouin zone) where the band structure of graphene is linear. This is different from the parabolic relation of conventional two-dimensional electron gas (2DEG) systems [1]. Graphene can be doped chemically or electri- cally to be either n-type or p-type material [3]. The novel proper- ties of graphene not only attract the attention of many theoretical and experimental researchers, but also make it a good candidate for technological applications [6,7]. Many-body properties of graphene have been studied exten- sively [8,9]. The dynamical dielectric function and plasmon dis- persion relation are two important many-body quantities in such structures [10–12]. Plasmons are the quanta of collective excita- tions of the electronic systems which can affect the response of systems to the applied fields. The plasmon dispersion relation in double-layer system differs significantly from the single layer one. Two branches, acoustic and optical, are appeared due to the in phase and out of phase electron oscillations in two layers, respec- tively [13]. The double-layer graphene (DLG) is a system consisting of two separate parallel single layer graphenes (SLG) which are placed * Corresponding author. Tel.: +98 21 29902784; fax: +98 21 22431666. E-mail address: t-vazifeh@cc.sbu.ac.ir (T. Vazifehshenas). close together to make an effective interaction between them but far enough to prevent the electron tunneling, similar to the con- ventional double-layer 2DEG systems. The DLG is different from bi- layer graphene (BLG) system in which two coupled single graphene layers stacked as in graphite and interlayer tunneling should be considered. As in the conventional double-layer 2DEG systems, many-body phenomena like the Coulomb drag due to the inter- layer electron–electron interactions can be occurred [14,15]. The Coulomb drag rate has been calculated for the DLG system and its behavior compared to the conventional double-layer 2DEG sys- tem [16]. In this Letter, we investigate the plasmon dispersion of a DLG system in which the two graphene layers separated by a nanome- ter distance d. The plasmon modes of a DLG at zero temperature have been obtained by Hwang and Das Sarma [17]. In this work, all calculations are done at finite temperature and the results com- pared with the zero temperature ones. Considering the correlation parameter, k F d, where k F is the Fermi wave vector, we discuss the interlayer correlation effects on the plasmon dispersion relation of a DLG at finite temperature. We put an upper limit on the temper- ature T = 0.2T F ( T F is the Fermi temperature) to ensure that the effect of phonons is negligible [18]. We also study the damping rate of plasmons at finite temperature. In addition, the plasmon frequencies and decay rate of a DLG system with different electron densities of layers are calculated at both zero and finite temper- ature and compared with those obtained from the equal electron density system. 2. Theory We consider two parallel doped graphene layers with the elec- tron densities, n 1 and n 2 . Throughout of this Letter, we set ¯ h = 1. 0375-9601/$ – see front matter  2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2010.10.026