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Abstract
A model of twisted bilayer graphene has been offered on the base of developed quasi-relativistic approach with high energy [Formula: see text]-Hamiltonian. Monolayer-graphene twist is accounted as a perturbation of monolayer-graphene Hamiltonian in such a way that at a given point of the Brillouin zone there exists an external non-Abelian gauge field of another monolayer. Majorana-like resonances have been revealed in the band structure of model at a magic rotation angle [Formula: see text]. The simulations have also shown that a superlattice energy gap existing at a rotation angle [Formula: see text] vanishes at a rotation angle [Formula: see text].
Highlights
Vector-potentials for these gauge fields are determined by the phases α0 and α±,k, k = 1, 2, 3 of π(pz)-electron wave functions ψpz (r) and ψpz,±δk (r), k = 1, 2, 3 respectively that the exchange interaction Σxrel [3] in accounting of the nearest lattice neighbors for a tight-binding approximation reads18–20
It has been shown an appearance of unconventional superconductivity at a magic rotation angle θM = 1.05◦.1 A feature of the unconventional superconductivity is accompanying insulator states such as flat bands
The interference Moire pattern of electron density appears at magic rotation angles due to coherence of the phase states of commensurately placed monolayers rotated relative to each other.Commensurate arrangement of monolayers relative to each other provides a support of exceptional flatness which has been demonstrated to reduce strain fluctuations, the main source of scattering and the culprit for density inhomogeneities
Summary
Vector-potentials for these gauge fields are determined by the phases α0 and α±,k, k = 1, 2, 3 of π(pz)-electron wave functions ψpz (r) and ψpz,±δk (r), k = 1, 2, 3 respectively that the exchange interaction Σxrel [3] in accounting of the nearest lattice neighbors for a tight-binding approximation reads18–20 3. High-Energy k · p-Hamiltonian for Twisted Bilayer Graphene
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