Modeling of electronic dynamics in twisted bilayer graphene
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913242738065408 |
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| author | Kong, Tianyu Liu, Diyi Luskin, Mitchell Watson, Alexander B. |
| author_facet | Kong, Tianyu Liu, Diyi Luskin, Mitchell Watson, Alexander B. |
| contents | We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer-MacDonald PDE model, which is periodic with respect to the bilayer's moiré pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes-Thomas estimates. We then provide extensive numerical computations which clarify the range of validity of the Bistritzer-MacDonald model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10430 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modeling of electronic dynamics in twisted bilayer graphene Kong, Tianyu Liu, Diyi Luskin, Mitchell Watson, Alexander B. Mathematical Physics Mesoscale and Nanoscale Physics Numerical Analysis Analysis of PDEs Quantum Physics 81, 65, 35 We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer-MacDonald PDE model, which is periodic with respect to the bilayer's moiré pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes-Thomas estimates. We then provide extensive numerical computations which clarify the range of validity of the Bistritzer-MacDonald model. |
| title | Modeling of electronic dynamics in twisted bilayer graphene |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Numerical Analysis Analysis of PDEs Quantum Physics 81, 65, 35 |
| url | https://arxiv.org/abs/2308.10430 |