Validation of SK-TB parametrization for TBG with out-of-plane relaxation

Ascertain the validity of the Slater–Koster tight-binding parametrization that yields a monolayer velocity V_MLG = 1.09×10^6 ms^−1 for twisted bilayer graphene when out-of-plane atomic relaxation is included, by benchmarking its band structures against density-functional theory across relevant twist angles.

Background

To match experimental Fermi velocities and van Hove singularities, the authors employ an SK-TB model with adjusted V_ppπ^0. While successful for rigid (unrelaxed) bilayers and STM comparisons, they note uncertainty regarding its validation when vertical relaxation is present.

Resolving this would ensure the model’s reliability for realistic TBG samples, where relaxation substantially modifies interlayer coupling and may impact flat-band isolation and bandwidths.