Bi-directional LEEM and eV-TEM spectroscopy on a graphene-hBN heterostack

Van der Waals heterostacks can exhibit emergent properties as a result of the coupling between the individual layers stacked. Here we focus on heterostacks of graphene and hBN, and study both coherent electron resonances (or unoccupied states) and inelastic losses. For this, we measure electron reflection and transmission spectra of the stack, as a function of electron energy. Special attention is paid to the symmetry upon flipping the heterostack, i.e., whether the electrons are first incident on the graphene or on the hBN surface: whereas electron reflection may be sensitive to sample orientation, electron transmission should not. Experimentally, we compare LEEM (reflection) and eV-TEM (transmission) IV spectra measured on free-standing graphene-hBN heterostacks with either the graphene or hBN side facing the LEEM objective lens. Resonances and inelastic loss are first modeled with the help of a simple wave interference toy model inspired by optics. More advanced calculations are performed to obtain the spatially resolved density of unoccupied states in the heterostack. We relate these calculations to the measured spectra, taking into account the finite probing depth of the reflected electron beam.