Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale.

Charge transport measurements form an essential tool in condensed matter physics. The usual approach is to contact a sample by two or four probes, measure the resistance and derive the resistivity, assuming homogeneity within the sample. A more thorough understanding, however, requires knowledge of local resistivity variations. Spatially resolved information is particularly important when studying novel materials like topological insulators, where the current is localized at the edges, or quasi-two-dimensional (2D) systems, where small-scale variations can determine global properties. Here, we demonstrate a new method to determine spatially-resolved voltage maps of current-carrying samples. This technique is based on low-energy electron microscopy (LEEM) and is therefore quick and non-invasive. It makes use of resonance-induced contrast, which strongly depends on the local potential. We demonstrate our method using single to triple layer graphene. However, it is straightforwardly extendable to other quasi-2D systems, most prominently to the upcoming class of layered van der Waals materials.

Gateless patterning of epitaxial graphene by local intercalation.

We present a technique to pattern the charge density of a large-area epitaxial graphene sheet locally without using metallic gates. Instead, local intercalation of the graphene-substrate interface can selectively be established in the vicinity of graphene edges or predefined voids. It provides changes of the work function of several hundred meV, corresponding to a conversion from n-type to p-type charge carriers. This assignment is supported by photoelectron spectroscopy, scanning tunneling microscopy, scanning electron microscopy and Hall effect measurements. The technique introduces materials contrast to a graphene sheet in a variety of geometries and thus allows for novel experiments and novel functionalities.