Validation of the Slater–Koster tight‑binding model for TBG under out‑of‑plane relaxation

Ascertain whether the Slater–Koster tight‑binding parameterization used to simulate twisted bilayer graphene—specifically the model tuned to reproduce a monolayer intraband velocity of approximately 1.09×10^6 ms⁻¹—remains quantitatively accurate when out‑of‑plane atomic relaxation is included, by benchmarking its band structures against density functional theory over relevant twist angles and relaxation amplitudes.

Background

The paper employs a Slater–Koster tight‑binding (SK‑TB) model to paper twisted bilayer graphene and notes that a parameter set matching the experimental monolayer Fermi velocity reproduces many observed features for rigid (flat) bilayers, with or without heterostrain.

However, atomic relaxation—particularly out‑of‑plane modulation—can significantly alter band isolation and gap structure at small angles. The authors explicitly note uncertainty about whether the SK‑TB model has been properly validated against DFT when such relaxation is included, indicating the need for a systematic verification campaign.