Non Hermitian Tight Binding Bands in Graphene from Tan Bo Model: Strain Effects and Bernal Bilayer Extensions

Abstract

Within the tight binding framework of graphenes π electron nearest neighbors, the Tan Bo model parametrizes transition energies t(dr) based on bond lengths and angles via the Mobius transformation combined with exponential decay. Comparisons between isotropic , geometrically anisotropic , and Slater Koster scales reveal that B = 0 is equivalent to the SK scheme, with L(B) reaching its optimum at Bopt = 0. The Hermitian assembly maintains the Dirac cone at the K point.The Tan Bo geometry dependent transition model and non Hermitian TB assembly scheme developed in this study provide a reproducible single particle benchmark and parameterization reference for future non Hermitian chemical calculations incorporating electron correlation effects in graphene systems.