Critical optical properties of AA-stacked multilayer graphenes

Abstract

The band structures and optical properties of AA-stacked multilayer graphenes are calculated by the tight-binding model and gradient approximation. For a nL-layer AA-stacked graphene, there are nL peaks at both low and middle frequencies. The threshold energy of odd-layer graphene is much lower than that of even-layer graphene for nL<10. The differences in the electronic structures and optical properties between the odd and even layers are reduced with increasing nL. When nL grows to 30 (200), the spectra of 2D graphene are almost identical to those of 3D graphite at middle (low) frequencies.

Feature-Rich Magnetic Quantization in Sliding Bilayer Graphenes

“…There are only two categories of absorption peaks arising from intragroup optical vertical excitations. Intergroup excitations are forbidden because of the special relationships among the wave functions of the two Dirac cone structures 42 . Two threshold peaks, associated with the four LLs nearest to E F , occur at ω = 0.05 eV, and the other intragroup excitation peaks come into existence at ω ≥ 0.63 eV.…”

Introduction

“…Such peaks are also observed for other stacked graphene, as well as being a critical characteristic of sp 2 -bonding carbon systems. In a uniform perpendicular magnetic field = B B z 0 , the Landau level (LL) spectrum behaves in the same way as several groups of monolayer-like spectra [126,153,183]. Responsible for each Dirac cone, the quantized LLs of each group are characterized by a set of single quantum modes, and their energies can be described by a square root dependence on B 0 .…”

“…In AA-stacked graphene, all the graphene sheets are identically stacked along the z direction [126,153]. The low-energy band structure consists of several monolayerlike massless Dirac cones [78][79][80]153], which are exactly located at the two valleys K and K′, while the energies of the Dirac points shift away from the Fermi energy due to the vertically projected geometry.…”

“…The low-energy band structure consists of several monolayerlike massless Dirac cones [78][79][80]153], which are exactly located at the two valleys K and K′, while the energies of the Dirac points shift away from the Fermi energy due to the vertically projected geometry. The absorption spectrum is, in general, a superposition of monolayer-like spectra, because only the vertical excitations of intra-Dirac-cones are permitted, regardless of the external electric and magnetic fields [153,183]. However, the stacking effect gives rise to an optical gap for the even-layer configurations, which is a forbidden optical transition zone resulting from free carriers in the Dirac cones.…”

“…Responsible for each Dirac cone, the quantized LLs of each group are characterized by a set of single quantum modes, and their energies can be described by a square root dependence on B 0 . Therefore, the magneto-absorption spectrum consists of several monolayer-like spectra with delta-function-like absorption peaks following the optical selection rule of Δ = ± n 1 [153,183]. A forbidden transition region and a discontinuous threshold frequency would be revealed for all the bilayer-like intragroup LL transitions, as the Fermi level ( = E 0 F ) deviates from the Dirac point.…”