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

TL;DR

This paper analyzes the electronic band structure of multilayer graphenes with mixed Bernal and rhombohedral stacking, revealing localized states, characteristic band types, and optical features arising from stacking faults.

Contribution

It introduces a general scheme to understand the electronic structure of arbitrary stacking configurations in multilayer graphene, highlighting the role of finite Bernal sections.

Findings

Low-energy eigenstates are localized in Bernal sections.

Spectrum includes linear, quadratic, and cubic bands.

Characteristic optical absorption edges are identified.

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 corresponding characteristic photon frequencies.