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arXiv 1201.0779cond-mat.mes-hallphysics.plasm-phquant-ph
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磁场中石墨烯的集体激发

Collective excitations in graphene in magnetic field

Pavel A. Andreev

摘要:

研究了单层石墨烯中的集体激发。得到了描述石墨烯中电子集体性质的方程。推导中运用了多粒子量子流体力学方法的基本思想。作为推导的起点,我们使用无质量电子的狄拉克方程,该方程通常用于描述石墨烯中的电子[D. E. Sheehy和J. Schmalian,Phys.Rev.Lett. 99,226803(2007)],其中考虑了库仑相互作用。本文通过推导石墨烯量子流体动力学方程(GQHD)研究了集体激发的色散特性。我们考虑了石墨烯在外部磁场中的情况,磁场与石墨烯样品成一定角度。我们在GQHD方程的线性近似中进行。我们观察到,垂直于石墨烯平面的磁场对集体激发的色散没有影响。对于以一定角度指向石墨烯的磁场,我们获得波色散对系统参数的依赖性:磁场的强度、波矢量、相对于磁场的波传播方向。

英文摘要:

Collective excitations in graphene monolayer are studied. Equations describing collective properties of electrons in graphene are obtained. The basic ideas of the method of many-particle quantum hydrodynamics are used for the derivation. As starting point of the derivation we use the Dirac equation for massless electrons which is usually used for description of electrons in graphene [D. E. Sheehy and J. Schmalian, Phys. Rev. Lett. 99, 226803 (2007)], where the Coulomb interaction is taken into account. We study dispersion properties of collective excitations by means derived here graphene quantum hydrodynamics equations (GQHD). We consider graphene in the external magnetic field which directed at an angle to the graphene sample. We do it in a linear approximation of the GQHD equations. We observe that the magnetic field directed perpendicular to the graphene plane had no influence on dispersion of the collective excitations. For the magnetic field directed at an angle to the graphene we obtain dependence of wave dispersion on system parameters: strength of magnetic field, wave vector, direction of wave propagation relatively to the magnetic field.

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