Abstract
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.
Highlights
The past years have seen a tremendous increase in available quasi-2D materials, extending from graphene[1] to van der Waals heterostructures[2] and topological insulators[3,4,5]
low-energy electron potentiometry (LEEP) experiments can be combined with Low-Energy Electron Microscopy (LEEM)[14] and Photo Electron Emission Microscopy and Spectroscopy (PEEM) measurements on the same sample in the same microscope
The basic idea behind LEEP is to determine the local potential at each position on a sample from LEEM images, i.e., from the intensity of specularly reflected low-energy electrons (0–100 eV) that are projected onto a pixelated detector[14,15,16,17]
Summary
The past years have seen a tremendous increase in available quasi-2D materials, extending from graphene[1] to van der Waals heterostructures[2] and topological insulators[3,4,5]. Have remarkable physical phenomena such as Dirac-Weyl physics[6,7] and Klein tunneling[8] been observed, these materials offer great opportunities for applications in electronic devices[1,3] To maximize their potential, precise knowledge of the local electron transport properties is essential. Small-scale variations like step edges, grain boundaries and atomic defects can strongly affect global properties To elucidate such local conductance properties, several groups have performed ground-breaking experiments using scanning probe techniques such as Kelvin probe microscopy[10], (four-probe) scanning tunneling microscopy[11] and scanning squid microscopy[12]. This combination forms an extremely powerful set of complementary tools, LEEM allowing one to determine the structure and morphology of 2D materials, PEEM giving access to the electronic band structure, and LEEP providing insight in charge transport on the nanoscale
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