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In order to analytically capture and identify peculiarities in the electronic structure of silicene, Weaire-Thorpe(WT) model, a standard model for treating three-dimensional (3D) silicon, is applied to silicene with the buckled 2D structure. In the original WT model for four hybridized $sp^3$ orbitals on each atom along with inter-atom hopping, the band structure can be systematically examined in 3D, where flat (dispersionless) bands exist as well. For examining silicene, here we re-formulate the WT model in terms of the overlapping molecular-orbital (MO) method which enables us to describe flat bands away from the electron-holesymmetric point. The overlapping MO formalism indeed enables us to reveal an important difference: while in 3D the dipersive bands with cones are sandwiched by doubly-degenerate flat bands, in 2D the dipersive bands with cones are sandwiched by triply-degenerate and non-degenerate (nearly) flat bands, which is consistent with the original band calculation by Takeda and Shiraishi. Thus emerges a picture for why the whole band structure of silicene comprises a pair of dispersive bands with Dirac cones with each of the band touching a nearly flat (narrow) band at $Gamma$. We can also recognize that, for band engineering, the bonds perpendicular to the atomic plane are crucial, and that a ferromagnetism or structural instabilities are expected if we can shift the chemical potential close to the flat bands.
Interactions between stacked two-dimensional (2D) atomic crystals can radically change their properties, leading to essentially new materials in terms of the electronic structure. Here we show that monolayers placed on an atomically flat substrate ca
We present electronic structure calculations of twisted double bilayer graphene (TDBG): A tetralayer graphene structure composed of two AB-stacked graphene bilayers with a relative rotation angle between them. Using first-principles calculations, we
Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moir{e} superlattice. Such superlattices are known to host bulk valley currents at tiny angles ($alp
We study the effect of twisting on bilayer graphene. The effect of lattice relaxation is included; we look at the electronic structure, piezo-electric charges and spontaneous polarisation. We show that the electronic structure without lattice relaxat
The charge susceptibility of twisted bilayer graphene is investigated in the Dirac cone, respectively random-phase approximation. For small enough twist angles $thetalesssim 2^circ$ we find weakly Landau damped interband plasmons, i.~e., collective e