Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems

TL;DR

This paper investigates the interlayer hybridization mechanisms in graphene quasicrystals and bilayer graphene systems, revealing symmetry-dependent hybridization rules and their effects on electronic properties through theoretical analysis and optical spectra verification.

Contribution

The study provides a comprehensive symmetry-based framework for understanding interlayer hybridization in twisted and untwisted bilayer graphene, including quasicrystalline structures, which was previously not well understood.

Findings

Hybridization rules depend on symmetry group (D6h, D6, D6d).

Weak hybridization near Fermi level due to energy gap between Dirac bands.

Electron-hole asymmetry in hybridization strength at high energies.

Abstract

The incommensurate 30$^{\circ}$ twisted bilayer graphene (BG) possesses both relativistic Dirac fermions and quasiperiodicity with 12-fold rotational symmetry arising from the interlayer interaction [\href{https://science.sciencemag.org/content/361/6404/782}{Ahn et al., Science \textbf{361}, 782 (2018)} and \href{https://www.pnas.org/content/115/27/6928}{Yao et al., Proc. Natl. Acad. Sci. \textbf{115}, 6928 (2018)}]. Understanding how the interlayer states interact with each other is of vital importance for identifying and subsequently engineering the quasicrystalline order in the layered structures. Herein, via symmetry and group representation theory we unravel the interlayer hybridization selection rules governing the interlayer coupling in both untwisted and twisted BG systems. Compared with the only allowed equivalent hybridization in $D_{6h}$ untwisted BG, $D_6$ twisted BG permits equivalent and mixed hybridizations, and $D_{6d}$ graphene quasicrystal allows both equivalent and non-equivalent hybridizations. The energy-dependent hybridization strengths in graphene quasicrystal and $D_6$ twisted BG show two remarkable characteristics: (i) near the Fermi level the weak hybridization owing to the relatively large energy difference between Dirac bands from top and bottom layers, and (ii) in high-energy regions the electron-hole asymmetry of hybridization strength with stronger interlayer coupling for holes, which arises from the non-nearest-neighbor interlayer hoppings and the wave-function phase difference between paring states. These hybridization-generated band structures and their hybridization strength characteristics are verified by the calculated optical conductivity spectra. Our theoretical study paves a way for revealing the interlayer hybridization in van der Waals layered systems.