Direct observation of locally modified excitonic effect within a moir\'e unit cell in twisted bilayer graphene

Bilayer graphene, forming moir\'e superlattices, possesses distinct electronic and optical properties derived from the hybridization of energy band and the emergence of van Hove singularities depending on its twist angle. Extensive research has been conducted on the global characteristics of moir\'e superlattice induced by long-range periodicity. However, limited attention has been given to the local properties within a moir\'e unit cell, which undoubtedly differ due to the variations in three-dimensional atomic arrangement. Here we demonstrate the highly localized excitations of carbon 1s electrons to unoccupied van Hove singularities in a twisted bilayer graphene using an electron energy loss spectroscopy based on a monochromated transmission electron microscope. The core-level excitations associated with the van Hove singularities show a systematic twist angle dependence which is analogous to the optical excitations. Furthermore, local variations in those core-level van Hove singularity peaks within a moir\'e unit cell have been corroborated for the first time, which can originate from core-exciton lifetimes and band modifications influenced by the local stacking geometry.