Plasma Excitations in Graphene: Their Spectral Intensity and Temperature Dependence in Magnetic Field

Abstract

In this paper, we calculated the dielectric function, the loss function, the magnetoplasmon dispersion relation and the temperature-induced transitions for graphene in a uniform perpendicular magnetic field B. The calculations were performed using the Peierls tight-binding model to obtain the energy band structure and the random-phase approximation to determine the collective plasma excitation spectrum. The singleparticle and collective excitations have been precisely identified based on the resonant peaks in the loss function. The critical wave vector at which plasmon damping takes place is clearly established. This critical wave vector depends on the magnetic field strength as well as the levels between which the transition takes place. The temperature effects were also investigated. At finite temperature, there are plasma resonances induced by the Fermi distribution function. Whether such plasmons exist is mainly determined by the field strength, temperature, and momentum. The inelastic light scattering spectroscopies could be used to verify the magnetic field and temperature induced plasmons. Keywords: graphene · Landau level · electronic excitation · random phase approximation · magnetic field · tight-binding model † E-mail: ggumbs@hunter.cuny.edu * E-mail: mflin@mail.ncku.edu.tw 1 Graphene, a flat monolayer of carbon atoms with a honeycomb lattice, is the basic building block for other graphitic materials. It is famous for the linear energy dispersion around the zero Fermi energy, where the electrons can travel thousands of interatomic distances without scattering. Based on the high electron mobility, graphene is a popular candidate for the production of future nanoelectronic elements, such as ballistic transistors, the entire π-magnetoelectronic structure at realistic magnetic field strengths can be solved. The number of charge carriers per area is self conserved during our calculations. Therefore, the accuracy of our results is not constrained by either the energy range or the magnetic field. In the random-phase approximation (RPA), 2 the complete structure of the dielectric function was determined. The single-particle and collective excitations can be precisely identified according to the divergences in the loss function ℑm(−1/ǫ(q, ω)), where q is the in-plane wave vector and ω is the frequency. It should be noted that our discussion is within the condition that q is much smaller than the reciprocal-lattice vector, and the local-field effects 30,31 are neglected in our calculation.The group velocities of the magnetoplasmons in the long wavelength limit are typically positive, and then decrease to negative values as the wave vector is increased. The critical momentum for plasmon damping to occur is clearly established. Our calculations show that this critical wave vector has a strong dependence on the field strength as well as the levels between which the transition takes place. The temperature effects were also investigated and are reported in detail below. We found that the intra-Landau level t...

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