Simple derivation of moiré-scale continuous models for twisted bilayer graphene

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