Influence of Landau level mixing on the properties of elementary excitations in graphene in strong magnetic field
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NANO EXPRESS
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Influence of Landau level mixing on the properties of elementary excitations in graphene in strong magnetic field Yurii E Lozovik1,2* and Alexey A Sokolik1
Abstract Massless Dirac electrons in graphene fill Landau levels with energies scaled as square roots of their numbers. Coulomb interaction between electrons leads to mixing of different Landau levels. The relative strength of this interaction depends only on dielectric susceptibility of surrounding medium and can be large in suspended graphene. We consider influence of Landau level mixing on the properties of magnetoexcitons and magnetoplasmons—elementary electron-hole excitations in graphene in quantizing magnetic field. We show that, at small enough background dielectric screening, the mixing leads to very essential change of magnetoexciton and magnetoplasmon dispersion laws in comparison with the lowest Landau level approximation. PACS: 73.22.Pr; 71.35.Ji; 73.43.Mp; 71.70.Gm. 1 Introduction Two-dimensional systems in strong magnetic field are studied intensively since the discovery of integer and fractional quantum Hall effects [1-3]. For a long time, such systems were represented by gallium arsenide heterostructures with 2D electron motion within each subband [4]. New and very interesting realization of 2D electron system appeared when graphene, a monoatomic layer of carbon, was successfully isolated [5,6]. The most spectacular property of graphene is the fact that its electrons behave as massless chiral particles, obeying Dirac equation. Intensive experimental and theoretical studies of this material over several recent years yielded a plethora of interesting results [7-9]. In particular, graphene demonstrates unusual half-integer quantum Hall effect [6], which can be observed even at room temperature [10]. In external perpendicular magnetic field, the motion of electrons along cyclotron orbits acquires zero-dimensional character and, as a result, electrons fill discrete Landau levels [11]. In semiconductor quantum wells, Landau levels are equidistant and separation between them is determined by the cyclotron frequency ωc = eH/mc. In graphene, due to massless nature of electrons, “ultra* Correspondence: [email protected] 1 Institute for Spectroscopy, Russian Academy of Sciences, Fizicheskaya 5, 142190, Troitsk, Moscow Region, Russia Full list of author information is available at the end of the article
relativistic” Landau levels appear, which are non-equidistant and located symmetrically astride the Dirac point [12,13]. Energies of these levels are 6 En = sign(n) 2 |n|vF /lH , where n = 0, ±1, ±2,..., vF ≈10 m/s is the Fermi velocity of electrons and lH = c/eH is magnetic length, or radius of the cyclotron orbit (here and below we assume ħ = 1). In the case of integer filling, when several Landau levels are completely filled by electrons and all higher levels are empty, elementary excitations in the system are caused by electron transitions from one of the filled Landau levels to one of the empty levels [14]. Such tr
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