Phase-sensitive scanning tunneling potentiometry and the local transport field in mesoscopic systems

A theoretical approach is presented to analyze the local transport field (LTF) and the voltage measured by the scanning tunneling microscope (STM) in a current-carrying mesoscopic system. The phase coherence between an electron wave reflected from a defect and the incident-electron wave leads to Friedel-like oscillations in both the LTF and STM voltage (${\mathit{V}}_{\mathrm{STM}}$). To study this phase-sensitive feature in scanning tunneling potentiometry, we calculate the spatial profile of LTF and ${\mathit{V}}_{\mathrm{STM}}$ for the case of grain boundaries in a thin film and for the case of an impurity near a surface. For the case of a thin film containing grain boundaries within the jellium model, we find that LTF and ${\mathit{V}}_{\mathrm{STM}}$ differ in their spatial variation, but their drops across a grain boundary are of the same order of magnitude. In general, the ${\mathit{V}}_{\mathrm{STM}}$ fluctuates on a larger length scale than the LTF. For the case of a scatterer on a metal surface, the short-range variations of both ${\mathit{V}}_{\mathrm{STM}}$ and the LTF near a surface scatterer are on the order of 1 μV when the current density is on the order of ${10}^7$ A/${\mathrm{cm}}^2$ and the distance d between the STM tip and the metal surface is about 3 Å. Observation of the long-range variation in ${\mathit{V}}_{\mathrm{STM}}$ away from an impurity requires submicrovolt resolution and smaller values of d.