Observation of Electron Coherence and Fabry–Perot Standing Waves at a Graphene Edge

Abstract

Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry–Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p–n junctions within a graphene superconductor–normal–superconductor structure. By combining superconducting Aharanov–Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p–n–p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.