We have investigated electromigration process at gold nanojunctions as small as several tens of atoms. Junction conductance showed successive drops by one conductance quantum, corresponding to one-by-one removal of gold atoms, only when the junction voltage exceeded certain critical values. The peak position in the histogram of the observed critical voltages agreed with the activation energies for surface diffusion of gold atoms. This fact indicates that the elementary process of electromigration in such small junctions is the self-diffusion of metal atoms driven by microscopic kinetic energy transfer from a single conduction electron to a single metal atom.

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