Magneto-electronic properties of rhombohedral trilayer graphene: Peierls tight-binding model

Research highlights: RHtriangle Three groups of Landau levels of ABC-stacked trilayer graphene are obtained. RHtriangle They are strongly affected by the stacking configuration and interlayer interactions. RHtriangle Based on the wave function characteristics, an effective quantum number is defined. RHtriangle Three sets of effective quantum numbers are used to index the Landau levels. RHtriangle These quantum numbers are useful for defining the optical selection rules. - Abstract: Magneto-electronic properties of rhombohedral (ABC-stacked) trilayer graphene are investigated by the tight-binding (TB) model with all important interlayer interactions taken into account. A numerical strategy, band-like matrix, is applied to solve the huge Hamiltonian matrix and thus the eigenvalues and eigenvectors of Landau levels (LLs) are well defined. Based on the characteristics of the wave functions, the LLs are divided into three groups. These LLs are strongly affected by the stacking configuration and interlayer interactions. The LL spectra do reflect the main features of the zero-field subbands, i.e., the existence of three LL groups, specified onset energies of the three groups, and asymmetric electronic structure. In an ABC-stacked structure, the LL wave functions are each composed of six magnetic TB Bloch functions for six sublattices. Each magnetic TB Bloch function exhibits the spatial symmetry, localization feature, and oscillation modes. Three sets of effective quantum numbers are defined to index the LLs of the three groups based on the oscillation modes in specific sublattices. These effective quantum numbers are useful for defining the optical selection rules of the optical absorption spectra.