WIAS Preprint No. 1376, (2008)

Evanescent channels and scattering in cylindrical nanowire heterostructures


  • Racec, Paul N.
  • Racec, Roxana
  • Neidhardt, Hagen

2010 Mathematics Subject Classification

  • 47A40 35Q40 35P25 58J50

2008 Physics and Astronomy Classification Scheme

  • 72.10.Bg 73.23.Ad 73.40.-c 73.63.-b


  • Nanowire, scattering, mesoscopic transport, resonances, evanescent states




We investigate the scattering phenomena produced by a general finite range non-separable potential in a multi-channel two-probe cylindrical nanowire heterostructure. The multi-channel current scattering matrix is efficiently computed using the R-matrix formalism extended for cylindrical coordinates. Considering the contribution of the evanescent channels to the scattering matrix, we are able to put in evidence the specific dips in the tunneling coefficient in the case of an attractive potential. The cylindrical symmetry cancels the ''selection rules'' known for Cartesian coordinates. If the attractive potential is superposed over a non-uniform potential along the nanowire, then resonant transmission peaks appear. We can characterize them quantitatively through the poles of the current scattering matrix. Detailed maps of the localization probability density sustain the physical interpretation of the resonances (dips and peaks). Our formalism is applied to a variety of model systems like a quantum dot, a core/shell quantum ring or a double barrier, embedded into the nano-cylinder.

Appeared in

  • Phys. Rev. B., 79 (2009) pp. 155305/1--155305/14.

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