Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems

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.

References in corpus (45)

• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• Graphene bilayer with a twist: electronic structure
• On-surface synthesis of graphene nanoribbons with zigzag edge topology
• Magic Angle Spectroscopy
• Flat Bands in Slightly Twisted Bilayer Graphene
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• Theory of phonon-mediated superconductivity in twisted bilayer graphene
• Commensuration and Interlayer Coherence in Twisted Bilayer Graphene
• Electronic structure of turbostratic graphene
• First direct observation of a nearly ideal graphene band structure
• Topological Superconductivity in Twisted Multilayer Graphene
• Strong coupling phases of partially filled twisted bilayer graphene narrow bands
• Dirac Electrons in a Dodecagonal Graphene Quasicrystal
• Numerical studies of confined states in rotated bilayers of graphene
• Modeling electronic structure and transport properties of graphene with resonant scattering centers
• Quasicrystalline 30° Twisted Bilayer Graphene as an Incommensurate Superlattice with Strong Interlayer Coupling
• Electronic Structure Theory of Weakly Interacting Bilayers
• Theories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene
• Electronic spectrum of twisted graphene layers under heterostrain
• Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• Interlayer interaction in general incommensurate atomic layers
• Quasicrystalline electronic states in 30${}^{\circ }$ rotated twisted bilayer graphene
• Large-area, periodic, and tunable intrinsic pseudo-magnetic fields in low-angle twisted bilayer graphene
• 30${}^{\circ }$-twisted bilayer graphene quasicrystals from chemical vapor deposition
• Interlayer Decoupling in 30° Twisted Bilayer Graphene Quasicrystal
• Dodecagonal bilayer graphene quasicrystal and its approximants
• Identification of superconducting pairing symmetry in twisted bilayer graphene using in-plane magnetic field and strain
• Emergent Localization in Dodecagonal Bilayer Quasicrystals
• Effect of bilayer stacking on the atomic and electronic structure of twisted double bilayer graphene
• Ultrafast unbalanced electron distributions in quasicrystalline 30° twisted bilayer graphene
• Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
• Theory of quantum oscillations in quasicrystals: Quantizing spiral Fermi surfaces
• Pressure and electric field dependence of quasicrystalline electronic states in 30${}^{\circ }$ twisted bilayer graphene
• Electronic structure of 30° twisted double bilayer graphene
• Surfactant-Mediated Epitaxial Growth of Single-Layer Graphene in an Unconventional Orientation on SiC
• Time-evolution patterns of electrons in twisted bilayer graphene
• Polarization-dependent selection rules and optical spectrum atlas of twisted bilayer graphene quantum dots
• $g+ig$ topological superconductivity in the 30${}^o$-twisted bilayer graphene

Cited by in corpus (2)

• Quasicrystalline 30${}^{\circ }$ twisted bilayer graphene: Fractal patterns and electronic localization properties
• Symmetry-directed electronic and optical properties in a two-dimensional square-lattice ZnPc-MOF