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arXiv · 2406.15712

Construction and Accuracy of Electronic Continuum Models of Incommensurate Bilayer 2D Materials

Xue Quan·Alex Watson·Daniel Massatt
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Abstract

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.

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Xue Quan, Alex Watson, Daniel Massatt. 2024-06-22. Construction and Accuracy of Electronic Continuum Models of Incommensurate Bilayer 2D Materials. https://arxiv.org/abs/2406.15712

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