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

Abstract

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.

Low-energy band structure in Bernal stacked six-layer graphene: Landau fan diagram and resistance ridge

“…crossings [18][19][20][21][22][26][27][28]43]. This complexity arises from the fact that the low-energy band structure of the AB-stacked hexlayer graphene consists of three bilayer bands -7 - [3,[5][6][7][8]22,44].…”

Tight-binding model and direct-gap/indirect-gap transition in single-layer and multilayer MoS2

“…Crucial to the development of the theoretical analysis in graphene is also the fact that model Hamiltonians for multilayer graphenes can be built using the single-layer TB description as a fundamental block and just adding additional interlayer hopping terms. [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] Different stacking orders can also be easily investigated. The advantage of such a TB description with respect to first-principles calculations is that it provides a simple starting point for the further inclusion of many-body electron-electron effects by means of quantum field theory (QFT) techniques, as well as of the dynamical effects of the electron-lattice interaction.…”

Screening in multilayer graphene

“…Although a recent theoretical work investigates systems in which the stacking of the layers is partly Bernal and partly rhombohedral, 1 so far, most of the effort has been put into understanding either completely Bernal or completely rhombohedral stacked multilayer samples. These two systems behave very differently.…”