Spatial distribution of the electric current and field in atomic-scale conductors

This paper uses a tight-binding scattering formalism to calculate the spatial distribution of the electric current and field in small phase-coherent conductors. The calculation is simple and efficient, allowing one to obtain: simultaneous pictures of the current density and the local potential and field in a wide range of atomic-scale structures. The use of the method is illustrated by two examples. The first shows the formation of a resistivity dipole across an extended obstacle. The second is conduction through a double: constriction, where we compare the current and potential distributions at and off resonance. The current pattern at resonance is related to the wavefunction of the quasibound state responsible for the resonance. Off resonance, large internal closed currents are found inside the double constriction. At resonance the potential drops are concentrated at the entrances to the constriction, while off resonance essentially all of the potential drop occurs in the interior of the double constriction.