Atomic imaging of macroscopic surface conductivity

Scanning tunneling microscopy (STM) enables direct imaging of surface-state bands, through which electrical conduction occurs, confirmed by direct measurements with the four-point probe method. STM images also exhibit voltage drops along a surface due to electrical resistance of the surface states (scanning tunneling potentiometry). Scanning micro-four-point probes and multi-tip STM are newborn techniques for much more direct mapping of the conductivity. Such capability of imaging provides direct insights on carrier scattering at atomic scales.