We theoretically study the lattice relaxation in the twisted bilayer graphene (TBG) and its effect on the electronic band structure. We develop an effective continuum theory to describe the lattice relaxation in general TBGs, and obtain the optimized structure to minimize the total energy. At small rotation angles < 2 • , in particular, we find that the relaxed lattice drastically reduces the area of AA-stacking region, and form a triangular domain structure with alternating AB and BA stacking regions. We then investigate the effect of the domain formation on the electronic band structure. The most notable change from the non-relaxed model is that an energy gap up to 20meV opens at the superlattice subband edges on the electron and hole sides. We also find that the lattice relaxation significantly enhances the Fermi velocity, which was strongly suppressed in the non-relaxed model. arXiv:1706.03908v1 [cond-mat.mtrl-sci]

Erratum: Lattice relaxation and energy band modulation in twisted bilayer graphene [Phys. Rev. B 96, 075311 (2017)]There is an error in the numerical calculation to solve the self-consistent equation [Eq. (33)] and in graphene's Lamé parameters. As a result, the strain vector u − q was underestimated in the original paper. In the following, we present the corrected tables and figures. These corrections, however, do not affect the qualitative argument and conclusions in the original paper. We adopt graphene's Lamé factors to λ ≈ 3.25 and μ ≈ 9.57 eV/Å 2 [1,2]. The η parameters are updated as Table I. In numerically solving Eq. (33), we consider harmonics within radius |q| 6G M . The corrected values of u − q are presented in Table II. Here, we set the xy coordinates as in Fig. 1 such that G M 1 = (1, 0)G M and G M 2 =

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We theoretically study the electronic structure of small-angle twisted bilayer graphene with a large potential asymmetry between the top and bottom layers. We show that the emergent topological channels known to appear on the triangular AB-BA domain boundary do not actually form a percolating network, but instead they provide independent, perfect one-dimensional eigenmodes propagating in three different directions. Using the continuum-model Hamiltonian, we demonstrate that an applied bias causes two well-defined energy windows which contain sparsely distributed one-dimensional eigenmodes. The origin of these energy windows can be understood using a twoband model of the intersecting electron and hole bands of single layer graphene. We also use the tight-binding model to implement the lattice deformations in twisted bilayer graphene, and discuss the effect of lattice relaxation on the one-dimensional eigenmodes. arXiv:2001.06257v2 [cond-mat.mes-hall]

We present a theoretical study on the electron transmission through the AB-BA stacking boundary in multilayer graphenes. Using the tight-binding model and the transfer matrix method, we calculate the electron transmission probability through the boundary as a function of electron Fermi energy in multilayers from bilayer to five-layer. We find that the transmission is strongly suppressed particularly near the band touching point, suggesting that the electronic conductivity in general multilayer graphenes is significantly interfered by stacking fault. The conductivity suppression by stacking fault is the strongest in the bilayer graphene, while it is gradually relaxed as increasing the number of layers. At a large carrier density, we observe an even-odd effect where the transmission is relatively lower in trilayer and five-layer than in bilayer and four-layer, and this is related to the existence of a monolayer-like linear band in odd layers. For bilayer graphene, we also study the effect of the perpendicular electric field opening an energy gap, and show that the band deformation enhances the electron transmission at a fixed carrier density.