The dynamical dielectric function of a double-layer system made of mono – layer graphene (MLG) and GaAs quantum well with separation of and homogenous dielectric background at zero temperature is investigated. The results were used to calculate the plasmon dispersion modes and damping rate of the structure and compare to those of similar double layer systems.
An Giang University Journal of Science – 2019, Vol 6, 39 – 48 PLASMON DISPERSION IN GRAPHENE – GaAs SYSTEM AT ZERO TEMPERATURE Nguyen Van Men1, Dong Thi Kim Phuong2 An Giang University Information: Received: 29/09/2017 Accepted: 18/11/2017 Published: 02/2019 Keywords: Damping rate, dynamical dielectric function, plasmon dispersion modes, random – phase – approximation ABSTRACT The dynamical dielectric function of a double-layer system made of mono – layer graphene (MLG) and GaAs quantum well with separation of and homogenous dielectric background at zero temperature is investigated The results were used to calculate the plasmon dispersion modes and damping rate of the structure and compare to those of similar double layer systems Calculations are done within random – phase – approximation (RPA) and taking into account the layer-thickness of two – dimensional – electron gas (2DEG) In addition, the analytical expressions of plasmon frequencies are found out by using approximation expansion with the first order of response and Coulomb bare interaction functions The results show that the plasmon modes and damping rate of the structure depend considerably on separation, 2DEG layer-thickness, the dielectric constant of contacting media, and carrier densities However, the dependence of two branches in plasmon on these properties is not similar INTRODUCTION Plasmon excitations in many-electron systems have been studied a long time ago and have been used to create plasmatic devices such as wave guide, data memory, optical converter, etc (Maier, 2007; Ho Sy Ta, 2017) The dynamical dielectric function and plasmon dispersion relation are two many important -body quantities in such structures (Vazifehshenas et al, 2010) Therefore, it can be seen that the dielectric function and plasmon mode of 2DEG were calculated both within and without correlation (Nguyen Quoc Khanh, 1996; 2001; Nguyen Quoc Khanh & Ngo Minh Toan, 2003) Besides, dielectric function and plasmon dispersion of MLG and bilayer graphene (BLG) were considered by Hwang & Sarma (2007; 2009; 2010) and by Rajdeep Sensarma, Hwang, and Sarma (2012) In addition, double layer structures Graphene, a single 2D sheet of carbon atoms in a honeycomb lattice, attracts a lot of attention of many theoretical and experimental researchers in recent years, both for its unique electronic properties (Castro Neto et al, 2009; Sarma et al, 2010) as well as for possible technological application (Geim et al, 2007; Wie et al, 2017) Quasi-particle excitations in graphene have a linear dispersion (in comparison with parabolic dispersion of ordinary 2DEG) at low energies and are described by the massless Dirac equation (Sarma, 2010) Because of this different property, the plasmon of double-layer systems consisting of MLG would be predicted to have lots of significant differences from those of single layer one 39 An Giang University Journal of Science – 2019, Vol 6, 39 – 48 mode and damping rate of MLG-2DEG systems including the thickness of 2DEG sheet that have not been paid enough attention by physicists have been studied in recent years such as DLG with homogenous dielectric background at finite temperature (Dinh Van Tuan & Nguyen Quoc Khanh, 2013), DLG with non homogeneous dielectric background at a finite temperature (Badalyan & Peeters, 2012), plasmon modes of double-layer structures consisting of MLG and very thin 2DEG sheet at zero temperature (Principi et al, 2012) Principi and coworkers (2012) have shown that long-range Coulomb interactions between massive electrons and massless Dirac fermions lead to a new set of optical and acoustic intra-subband plasmons Finally, recent researches relevant to graphene have studied by Ph.D students in Viet Nam (Ho Sy Ta, 2017) and in India (Digish, 2015) shows the interest of material scientists in graphene To our knowledge, although collective excitations of such chiral-nonchiral double-layer structures (MLG – 2DEG as an example) may have interesting properties, calculations for plasmon Because of the above reasons, in this paper, we consider a double-layer system consisting of doped MLG and GaAs quantum well, separated by a spacer of width d assuming that 2DEGs in MLG and GaAs are electrically isolated (Gamucci et al, 2014) We investigate the plasmon dispersion relation and damping rate at zero temperature using the RPA dielectric function, taking into account the thickness of the 2DEG layer THEORY The considered double-layer system is made of a MLG flake placed onto modulation-doped GaAs/SiO2 heterostucture hosting a 2DEG, with the effective electron mass m* in the GaAs quantum as shown in Fig z SiO2 κ Spacer d SiO2 SiO2 MLG z = d+w z=w κ κ2D GaAs κ Figure A MLG-2DEG double-layer system immersed in a three-layered dielectric medium with the background dielectric constants κ According to dielectric formalism, the plasmon dispersion relation of an electronic system can be obtained from the zeroes of dynamical dielectric function (Sarma & Madhukar, 1981; Hwang & Sarma, 2009) ε ( q, ω p − iγ ) = 40 (1) An Giang University Journal of Science – 2019, Vol 6, 39 – 48 decay rate are determined from the following equations (Tanatar & Davoudi, 2003; Vazifehshenas et al, 2010) Where ω p is the plasmon frequency at a given wave-vector q , and γ is the damping rate of plasma oscillations However, in case of weak damping ( γ