A simple derivation of moiré-scale continuous models for twisted bilayer graphene

Abstract

We provide a formal derivation of a reduced model for twisted bilayer graphene (TBG) from Density Functional Theory. Our derivation is based on a variational approximation of the TBG Kohn-Sham Hamiltonian and asymptotic limit techniques. In contrast with other approaches, it does not require the introduction of an intermediate tight-binding model. The so-obtained model is similar to that of the Bistritzer-MacDonald (BM) model but contains additional terms. Its parameters can be easily computed from Kohn-Sham calculations on single-layer graphene and untwisted bilayer graphene with different stackings. It allows one in particular to estimate the parameters $w_{\mathrm{AA}}$ and $w_{\mathrm{AB}}$ of the BM model from first-principles. The resulting numerical values, namely $w_{\mathrm{AA}}=w_{\mathrm{AB}}\simeq 126$ meV for the experimental interlayer mean distance are in good agreement with the empirical values $w_{\mathrm{AA}}=w_{\mathrm{AB}}=110$ meV obtained by fitting to experimental data. We also show that if the BM parameters are set to $w_{\mathrm{AA}}=w_{\mathrm{AB}}\simeq 126$ meV, the BM model is an accurate approximation of our reduced model.

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• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Moiré amplification of highly tunable shift current response in twisted trilayer graphene
• Classically forbidden regions in the chiral model of twisted bilayer graphene. With an appendix by Zhongkai Tao and Maciej Zworski
• Magic distances in twisted bilayer graphene
• A Scalable Two-Level Domain Decomposition Eigensolver for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains