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We study the influence of strong spin-orbit interaction on the formation of flat bands in relaxed twisted bilayer WSe$_2$. Flat bands, well separated in energy, emerge at the band edges for twist angles ($theta$) close to 0$^o$ and 60$^o$. For $theta$ close to 0$^o$, the interlayer hybridization together with a moir{e} potential determines the electronic structure. The bands near the valence band edge have non-trivial topology, with Chern numbers equal to +1 or $-$1. We propose that this can be probed experimentally for twist angles less than a critical angle of 3.5$^o$. For $theta$ near 60$^o$, the flattening of the bands arising from the K point of the unit cell Brillouin zone is a result of atomic rearrangements in the individual layers. Our findings on the flat bands and the localization of their wavefunctions for both ranges of $theta$ match well with recent experimental observations [1,2].
The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave
Twisted bilayer graphene provides a new two-dimensional platform for studying electron interaction phenomena and flat band properties such as correlated insulator transition, superconductivity and ferromagnetism at certain magic angles. Here, we pres
The crystal structure of a material creates a periodic potential that electrons move through giving rise to the electronic band structure of the material. When two-dimensional materials are stacked, the twist angle between the layers becomes an addit
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
Spin-orbit coupling in graphene can be increased far beyond its intrinsic value by proximity coupling to a transition metal dichalcogenide. In bilayer graphene, this effect was predicted to depend on the occupancy of both graphene layers, rendering i