Measuring the Unoccupied Band Structure with ~10nm Lateral Resolution*

The properties of any material are fundamentally determined by its electronic band structure. But, while the occupied bands below the Fermi level can be routinely measured, it is remarkably difficult to characterize the empty part of the band structure experimentally. We introduce angle-resolved reflected-electron spectroscopy (ARRES), a technique to measure these bands [J. Jobst et al. Nature Commun. 6, 8926 (2015)]. It relies on the dependence of the reflectivity of low-energy electrons on their incidence angle on the sample and their kinetic energy and has a spatial resolution 10nm. We use ARRES to study the unoccupied band structure of van der Waals crystals – custom-built stacks of two-dimensional materials, such as graphene, boron nitride, or transitionmetal dichalcogenides. We show that ARRES can shed light on the interaction between electronic states of individual layers [J, Jobst, et al. Nature Commun. 7, 13621 (2016)], an important step towards tailoring the properties of Van der Waals crystals in a LEGO-like fashion.