Evanescent modes and scattering in quasi-one-dimensional wires

Abstract

We calculate the current transmission amplitudes and electrical conductance as a function of Fermi energy for electrons scattering from a single defect in a quasi-one-dimensional wire. In a confined geometry the scattering boundary conditions couple propagating modes in the wire to nonpropagating or evanescent modes. Therefore, the applied steady current causes localized or evanescent modes to build up around any defects in the wire. These extra stored electrons strongly affect the scattering boundary conditions for the propagating modes whenever the Fermi energy approaches either a new quasi-one-dimensional subband or a quasi-bound-state splitting off of the higher confinement subbands. We show that the presence of evanescent modes can lead to either perfect transparency or perfect opaqueness for the scattering modes, even in the presence of scattering defects. For the special case of a \ensuremath{\delta}-function scatterer in the wire we analytically obtain the scattering amplitudes. We also numerically examine a finite-range scatterer.