Short-range impurity in a saddle-point potential: Conductance of a microjunction

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Abstract
The conductance G of the two-dimensional electron gas in the presence of an impurity in the central cross section of the split-gate constriction is calculated. The confining potential of the constriction is assumed to be a saddle-point potential, and the impurity is assumed to be short range. It is found that for attractive impurity potentials a quasibound state exist below the band bottom of each transverse subband. If the energy of this bound state is far from the threshold energy, then one observes resonant reflection and a narrow downward dip in G vs the Fermi energy E. When the bound state is near the threshold, one observes resonant transmission and a narrow peak in G vs E.