Electronic structure of 30∘ twisted double bilayer graphene

Abstract

The electronic structures of 30 • twisted double bilayer graphene, which loses the translational symmetry due to the incommensurate twist angle, are studied by means of the tight-binding approximation. We demonstrate the interlayer decoupling across the 30 • twisted interface in the vicinity of the Fermi level from various electronic properties, including the density of states, effective band structure, optical conductivity, and Landau-level spectrum. However, at Q points, the interlayer coupling results in the appearance of new Van Hove singularities in the density of states, new peaks in the optical conductivity and, importantly, the 12-fold-symmetry-like electronic states. The k-space tight-binding method is adopted to explain this phenomenon. The electronic states at Q points show charge distribution patterns more complex than the 30 • twisted bilayer graphene due to the symmetry decrease. These phenomena also appear in the graphene monolayer on the AB-stacked graphene bilayer with a 30 • twist angle.

Lattice relaxation, mirror symmetry and magnetic field effects on ultraflat bands in twisted trilayer graphene

“…When consider the magnetic field, the hopping t ij has a phase term which defined by Peierls substitution [37,38]. This full tight-binding model is accurate enough for both twisted bilayer and multilayer graphene systems [35,39].…”

Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems

“…Numerical simulations indicate that a fractal feature happens for the sliding force and the low friction appears as a result of the quasicrystalline structure [23]. The vertical pressure and electric field can be utilized to tune the quasicrystalline electronic states [27]. The numerical calculations show that quasicrystalline electronic states can also exist in 30 • twisted double bilayer graphene system [28].…”

“…Introduction.-Besides the emergent correlated effects [1][2][3][4][5][6][7][8][9][10][11] in slightly twisted bilayer graphene, the recently discovered quasicrystal [12,13] in 30 • incommensurately twisted bilayer graphene has also attracted considerable interest in both experiment [12][13][14][15][16][17][18][19][20] and theory [21][22][23][24][25][26][27][28][29]. Several synthetic methods, including chemical vapor deposition and carbon segregation from the bulk during high temperature annealing, have been used to successfully grow graphene quasicrystal on SiC [12,14], Pt [13], Cu [18][19][20] and Cu-Ni alloy [15] substrates.…”

“…The vertical pressure and electric field can be utilized to tune the quasicrystalline electronic states [27]. The numerical calculations show that quasicrystalline electronic states can also exist in 30 • twisted double bilayer graphene system [28]. All of these peculiar physical properties make graphene quasicrystal quite distinctive from graphene monolayer.…”

High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems

“…It's interesting to investigate the consequence of such enlarged rotation symmetries in the LA-THBs. Though their single-particle properties have been studied [52][53][54][55][56][57][58][59][60], physical properties driven by electron-electron (e-e) interaction have not been studied. Here we propose to use these materials to generate symmetry-protected highangular-momentum (HAM) topological superconductivities (TSCs), absent in crystalline materials.…”