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      Minimal model for low-energy electronic states of twisted bilayer graphene

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          Abstract

          We introduce a physically motivated minimal model for the electronic structure of twisted bilayer graphene (tBLG), which incorporates the crucial role of lattice relaxation. Our model, based on \(k \cdot p\) perturbation theory, combines the accuracy of DFT calculations through effective tight-binding Hamiltonians with the computational efficiency and complete control of the twist angle offered by continuum models. The inclusion of relaxation significantly changes the bandstructure at the first magic-angle twist corresponding to flat bands near the Fermi level (the "low-energy" states), and eliminates the appearance of a second magic-angle twist. We argue that the minimal model for the low-energy states of tBLG consists of ten bands, necessary to capture the changes in electronic states as a function of twist angle. We also provide information on the nature of these bands through their wavefunctions, which is closely tied to the features of the atomic relaxation.

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          Twisted Bilayer Graphene: Moiré with a Twist

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            Structural and electron diffraction scaling of twisted graphene bilayers

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              Strain Solitons and Topological Defects in Bilayer Graphene

              Spontaneous symmetry-breaking, where the ground state of a system has lower symmetry than the underlying Hamiltonian, is ubiquitous in physics. It leads to multiply-degenerate ground states, each with a different "broken" symmetry labeled by an order parameter. The variation of this order parameter in space leads to soliton-like features at the boundaries of different broken-symmetry regions and also to topological point defects. Bilayer graphene is a fascinating realization of this physics, with an order parameter given by its interlayer stacking coordinate. Bilayer graphene has been a subject of intense study because in the presence of a perpendicular electric field, a band gap appears in its electronic spectrum [1-3] through a mechanism that is intimately tied to its broken symmetry. Theorists have further proposed that novel electronic states exist at the boundaries between broken-symmetry stacking domains [4-5]. However, very little is known about the structural properties of these boundaries. Here we use electron microscopy to measure with nanoscale and atomic resolution the widths, motion, and topological structure of soliton boundaries and topological defects in bilayer graphene. We find that each soliton consists of an atomic-scale registry shift between the two graphene layers occurring over 6-11 nm. We infer the minimal energy barrier to interlayer translation and observe soliton motion during in-situ heating above 1000 {\deg}C. The abundance of these structures across a variety samples, as well as their unusual properties, suggests that they will have substantial effects on the electronic and mechanical properties of bilayer graphene.
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                Author and article information

                Journal
                10 January 2019
                Article
                1901.03420
                d4801e30-5f95-47df-8988-9e3c32ea5f98

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                5 pages, 4 figures (supplementary material: 9 pages, 1 figure)
                cond-mat.mes-hall

                Nanophysics
                Nanophysics

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