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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2406.15712 |
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| _version_ | 1866912390573981696 |
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| author | Quan, Xue Watson, Alex Massatt, Daniel |
| author_facet | Quan, Xue Watson, Alex Massatt, Daniel |
| contents | Single-particle continuum models such as the popular Bistritzer-MacDonald model have become powerful tools for predicting electronic phenomena of incommensurate 2D materials and the development of many-body models aimed to model unconventional superconductivity and correlated insulators. In this work, we introduce a procedure to construct continuum models of arbitrary accuracy relative to tight-binding models for moiré incommensurate bilayers. This is done by recognizing the continuum model as arising from Taylor expansions of a high accuracy momentum space approximation of the tight-binding model. We apply our procedure in full detail to two models of twisted bilayer graphene and demonstrate both admit the Bistritzer-MacDonald model as the leading order continuum model, while higher order expansions reveal qualitative spectral differences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction and Accuracy of Electronic Continuum Models of Incommensurate Bilayer 2D Materials Quan, Xue Watson, Alex Massatt, Daniel Mathematical Physics Numerical Analysis 35Q40 Single-particle continuum models such as the popular Bistritzer-MacDonald model have become powerful tools for predicting electronic phenomena of incommensurate 2D materials and the development of many-body models aimed to model unconventional superconductivity and correlated insulators. In this work, we introduce a procedure to construct continuum models of arbitrary accuracy relative to tight-binding models for moiré incommensurate bilayers. This is done by recognizing the continuum model as arising from Taylor expansions of a high accuracy momentum space approximation of the tight-binding model. We apply our procedure in full detail to two models of twisted bilayer graphene and demonstrate both admit the Bistritzer-MacDonald model as the leading order continuum model, while higher order expansions reveal qualitative spectral differences. |
| title | Construction and Accuracy of Electronic Continuum Models of Incommensurate Bilayer 2D Materials |
| topic | Mathematical Physics Numerical Analysis 35Q40 |
| url | https://arxiv.org/abs/2406.15712 |