Multilayer graphenes with mixed stacking structure: Interplay of Bernal and rhombohedral stacking

We study the electronic structure of multilayer graphenes with a mixture of Bernal and rhombohedral stacking and propose a general scheme to understand the electronic band structure of an arbitrary configuration. The system can be viewed as a series of finite Bernal graphite sections connected by stacking faults. We find that the low-energy eigenstates are mostly localized in each Bernal section, and, thus, the whole spectrum is well approximated by a collection of the spectra of independent sections. The energy spectrum is categorized into linear, quadratic, and cubic bands corresponding to specific eigenstates of Bernal sections. The ensemble-averaged spectrum exhibits a number of characteristic discrete structures originating from finite Bernal sections or their combinations likely to appear in a random configuration. In the low-energy region, in particular, the spectrum is dominated by frequently appearing linear bands and quadratic bands with special band velocities or curvatures. In the higher-energy region, band edges frequently appear at some particular energies, giving optical absorption edges at the corresponding characteristic photon frequencies.