Scanning tunneling potentiometry, charge transport, and Landauer's resistivity dipole from the quantum to the classical transport regime

Using the nonequilibrium Keldysh formalism, we investigate the spatial relation between the electrochemical potential measured in scanning tunneling potentiometry, and local current patterns over the entire range from the quantum to the classical transport regime. These quantities show similar spatial patterns near the quantum limit but are related by Ohm's law only in the classical regime. We demonstrate that defects induce a Landauer residual resistivity dipole in the electrochemical potential with the concomitant spatial current pattern representing the field lines of the dipole.