Construction and Accuracy of Electronic Continuum Models of Incommensurate Bilayer 2D Materials
<|reference_start|>Construction and Accuracy of Electronic Continuum Models of Incommensurate Bilayer 2D Materials: 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 moir\'{e} 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.<|reference_end|>
@article{quan2024construction,
    title={Construction and Accuracy of Electronic Continuum Models of
  Incommensurate Bilayer 2D Materials},
    author={Xue Quan, Alex Watson, Daniel Massatt},
    journal={arXiv preprint arXiv:2406.15712},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.15712},
    primaryClass={math-ph cs.NA math.MP math.NA}
}