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We present a tight-binding calculation of a twisted bilayer graphene at magic angle $thetasim 1.08^circ$, allowing for full, in- and out-of-plane, relaxation of the atomic positions. The resulting band structure displays as usual four narrow mini bands around the neutrality point, well separated from all other bands after the lattice relaxation. A thorough analysis of the mini-bands Bloch functions reveals an emergent $D_6$ symmetry, despite the lack of any manifest point group symmetry in the relaxed lattice. The Bloch functions at the $Gamma$ point are degenerate in pairs, reflecting the so-called valley degeneracy. Moreover, each of them is invariant under C$_{3z}$, i.e., transforming like one-dimensional, in-plane symmetric irreducible representation of an emergent $D_6$ group. Out of plane, the lower doublet is even under C$_{2x}$, while the upper doublet is odd, which implies that at least eight Wannier orbitals, two $s$-like and two $p_z$-like for each of the two supercell sublattices AB and BA are necessary, probably not sufficient, to describe the four mini bands. This unexpected one-electron complexity is likely to play an important role in the still unexplained metal-insulator-superconductor phenomenology of this system.
We present a systematic study of the low-energy collective modes for different insulating states at integer fillings in twisted bilayer graphene. In particular, we provide a simple counting rule for the total number of soft modes, and analyze their e
The flat bands of magic-angle twisted bilayer graphene (MATBG) host strongly-correlated electronic phases such as correlated insulators, superconductors and a strange metal state. The latter state, believed to hold the key to a deeper understanding o
The electronic properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, in particular when the two layers are rotated relative to each other by a small angle. TBG has recently attracted a great
Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron-electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when $ pm 1, pm 2, pm 3$ e
We study theoretically many-body properties of magic-angle twisted bilayer graphene for different doping levels. Our investigation is focused on the emergence, stability, and manifestations of nematicity of the ordered low-temperature electronic stat