Absence of small magic angles for disordered tunneling potentials in twisted bilayer graphene
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929248732708864 |
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| author | Becker, Simon Oltman, Izak Vogel, Martin |
| author_facet | Becker, Simon Oltman, Izak Vogel, Martin |
| contents | We consider small random perturbations of the standard high-symmetry tunneling potentials in the Bistritzer-MacDonald Hamiltonian describing twisted bilayer graphene. Using methods developed by Sjöstrand for studying the spectral asymptotics of non-selfadjoint pseudo-differential operators, we prove that for sufficiently small twisting angles the Hamiltonian will not exhibit a flat band with overwhelming probability, and hence the absence of the so-called \textit{magic angels}. Moreover, we prove a probabilistic Weyl law for the eigenvalues of the non-selfadjoint tunneling operator, subject to small random perturbations, of the Bistritzer-MacDonald Hamiltonian in the chiral limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12799 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Absence of small magic angles for disordered tunneling potentials in twisted bilayer graphene Becker, Simon Oltman, Izak Vogel, Martin Mathematical Physics Spectral Theory We consider small random perturbations of the standard high-symmetry tunneling potentials in the Bistritzer-MacDonald Hamiltonian describing twisted bilayer graphene. Using methods developed by Sjöstrand for studying the spectral asymptotics of non-selfadjoint pseudo-differential operators, we prove that for sufficiently small twisting angles the Hamiltonian will not exhibit a flat band with overwhelming probability, and hence the absence of the so-called \textit{magic angels}. Moreover, we prove a probabilistic Weyl law for the eigenvalues of the non-selfadjoint tunneling operator, subject to small random perturbations, of the Bistritzer-MacDonald Hamiltonian in the chiral limit. |
| title | Absence of small magic angles for disordered tunneling potentials in twisted bilayer graphene |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2402.12799 |