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

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.

Quantifying electronic band interactions in van der Waals materials using angle-resolved reflected-electron spectroscopy

“…It is well known that for few-layer graphene, the continuous conduction band of graphite splits up into quantized transmission resonances. For a stack of n +1 graphene layers, one can find n such transmission resonances, which lead to n characteristic minima in LEEM-IV curves, thus unambiguously revealing the number of graphene layers272829. These transmission resonances can be viewed in analogy to a tight-binding model where individual transmission resonances correspond to ‘atomic' wave functions and are frequently called ‘interlayer states'1628.…”

Magnetotransport on the nano scale

“…The latter is naturally limited by defects as a source of scattering5101112131415161718. Due to the small spatial extent their influence on transport is often difficult to access.…”

Low-energy electron potentiometry

“…Various materials, on the other hand, show other pronounced features in their IV-curves at higher energies where the electron trajectories are less affected by these distortions. We will demonstrate in the following that those features, instead of the MMT, can be used to determine the local potential, and that this approach leads to better lateral resolution [1]. Figure 9a shows a LEEM image of an area of monolayer, bilayer and trilayer graphene grown on insulating silicon carbide as described in Ref.…”

“…The MMT is present for all materials while clear LEED (Low Energy Electron Diffraction) IV-curves as used in Ref. [1] are not generally available. Consequently, M-LEEP can be applied to a broader range of materials, of which we show two applications in this paper.…”

“…It can consequently be used to perform LEEP experiments on a broader range of material compared to the method described in Ref. [1]. We provide a detailed description of the experimental setup and demonstrate LEEP on workfunction-related intrinsic potential variations on the Si(111) surface and for a metal-semiconductor-metal junction with external bias applied.…”