Abstract
The properties of any material are fundamentally determined by its electronic band structure. Each band represents a series of allowed states inside a material, relating electron energy and momentum. The occupied bands, that is, the filled electron states below the Fermi level, can be routinely measured. However, it is remarkably difficult to characterize the empty part of the band structure experimentally. Here, we present direct measurements of unoccupied bands of monolayer, bilayer and trilayer graphene. To obtain these, we introduce a technique based on low-energy electron microscopy. It relies on the dependence of the electron reflectivity on incidence angle and energy and has a spatial resolution ∼10 nm. The method can be easily applied to other nanomaterials such as van der Waals structures that are available in small crystals only.
Highlights
The properties of any material are fundamentally determined by its electronic band structure
The problem of the low count rate in k-resolved inverted photoemission spectroscopy (KRIPES) is overcome in total current spectroscopy[11,12] (TCS) and very-low-energy electron diffraction[13] (VLEED) in which the absorption or reflectivity of low-energy electrons is directly measured, respectively
In contrast to VLEED, where information is obtained from area-averaged diffraction patterns, we acquire the data from real-space low-energy electron microscopy (LEEM) images
Summary
The properties of any material are fundamentally determined by its electronic band structure. In ARPES, a sample is illuminated with photons (from lab ultraviolet-sources or synchrotron radiation) and the energy of the electrons that are released from the material due to the photoelectric effect[3] is measured as a function of the in-plane electron momentum ‘ kjj.
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