Non-invasive nanoscale potentiometry and ballistic transport in epigraphene nanoribbons

The recent observation of non-classical electron transport regimes in two-dimensional materials has called for new high-resolution non-invasive techniques to locally probe electronic properties. We introduce a novel hybrid scanning probe technique to map the local resistance and electrochemical potential with nm- and $mu$V resolution, and we apply it to study epigraphene nanoribbons grown on the sidewalls of SiC substrate steps. Remarkably, the potential drop is non uniform along the ribbons, and $mu$m-long segments show no potential variation with distance. The potential maps are in excellent agreement with measurements of the local resistance. This reveals ballistic transport in ambient condition, compatible with micrometer-long room-temperature electronic mean free paths.