Evanescent channels and scattering in cylindrical nanowire heterostructures

TL;DR

This paper develops a formalism to analyze scattering in cylindrical nanowire heterostructures, revealing how evanescent channels influence tunneling and resonant transmission, with applications to various quantum nanostructures.

Contribution

It extends the R-matrix formalism to cylindrical coordinates and demonstrates how evanescent channels affect scattering and resonance phenomena in nanowire heterostructures.

Findings

Evanescent channels cause specific dips in tunneling coefficients.

Resonant transmission peaks are linked to poles of the scattering matrix.

Cylindrical symmetry removes Cartesian selection rules.

Abstract

We investigate the scattering phenomena produced by a general finite-range nonseparable 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 nanocylinder.