Exploring graphene superlattices: Magneto-optical properties

Abstract

We present a detailed study of magnetic subbands, wave functions, and transition strengths for graphene superlattices (SLs) subject to a perpendicular magnetic field. It is shown that, for a weak magnetic field, the flat subbands of a SL exhibiting extra Dirac points are grouped into subsets, each of which consists of a singlet subband and a nearly degenerate doublet subband, and one nearly degenerate triplet subband. It was found that the wave functions corresponding to a singlet or to a doublet are always located around the image in real space of the central or extra Dirac points in k-space. The latter properties were explained by assuming that the electron motion is quasi-classical. Our study revealed that, for an intermediate field, the general characteristics of the wave functions are very similar to those of the pristine graphene, while for weak field, their behavior is drastically different. The latter is characterized by rapid oscillations which were understood using the solutions provided by the formalism of Luttinger-Kohn. The study on transition strengths allows us to obtain, for SLs with extra Dirac points in a weak magnetic field and different polarizations, the conditions under which transitions between multiplets are approximately allowed. It was shown that these conditions correspond to an unusual selection rule that is broken when the magnetic field intensity increases from weak to an intermediate value.