Magneto‐Optical Absorption in Graphene Superlattices: Dirac Point Effects

Abstract

We investigate the effects of Dirac points on the magneto-optical absorption of graphene superlattices (SLs) in a weak perpendicular magnetic field. It is shown that the absorption spectrum exhibits a resonant peak structure whose characteristics depend on the properties and number of these points.For SLs with only one Dirac point, the spectrum consists of resonant peaks satisfying the same selection rule as that for monolayer graphene, except for one of these peaks. For SLs with extra Dirac points, the resonant peaks arise from transition between singlet subbands or between doublet subbands and satisfy a circular polarization and peak intensity dependent selection rule.When a magnetic field is applied perpendicular to the twodimensional plane of graphene, electrons in the system exhibit a quantized energy spectrum consisting of highly degenerate and nonequidistant Landau levels (LLs). [1,2] This quantization provides the theoretical basis for the understanding of a number of interesting phenomena, such as the anomalous integer quantum Hall effect [3] and unusual magneto-optical properties. [4][5][6][7][8] Now, if in addition to the magnetic field, a one-dimensional (1D) periodic potential is applied to monolayer graphene, the above mentioned quantization can be substantially modified, with the corresponding modifications of the transport and magneto-optical properties. Certainly, instead of nonequidistant LLs, electrons in graphene exhibit an energy spectrum consisting of magnetic subbands, [9][10][11] whose general characteristics depend on the magnetic field regime. Three regimes were identified that generate different features in these subbands. They correspond to the cases of strong, intermediate, and weak fields, and can be characterized by the ratio d=l B of the period d of the superlattice (SL) potential to the cyclotron radius l B . In the strong field regime, l B ( d and the SL magnetic subbands and states closely resemble those of pristine graphene, whereas in the intermediate one, l B $ d and the subbands are very dispersive. [9][10][11] The most interesting physical situation arises for the weak field regime, where l B ) d. In this case, the magnetic subbands are essentially flat and the electron motion in the system may be considered as quasiclassical. [11] Within the latter approach, the magnetic field does not alter the band structure, it only quantizes the existing one. Consequently, the properties of the Dirac cones (points) [12][13][14] present in the energy spectrum of the SL in the absence of the magnetic field, including their number, can play an important role in determining the characteristics of the magneto-optical properties associated with the low-lying magnetic subbands. The latter was explored in a recent work, [11] where a detailed study of the magnetic subbands, wave functions, and transition strengths allows us to establish the conditions under which the optical transitions between the magnetic subbands are approximately allowed. In this letter, we expand upon these studies and exp...