2008, Racec, Paul N., Racec, Roxana, Neidhardt, Hagen

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.

2010, Racec, Roxana, Wulf, Ulrich, Racec, Paul Nicolae

We analyze a quantum dot strongly coupled to the conducting leads via quantum point contacts - Fano regime of transport - and report a variety of resonant states which demonstrate the dominance of the interacting resonances in the scattering process in a low confining potential. There are resonant states similar to the eigenstates of the isolated dot, whose widths increase with increasing the coupling strength to the environment, and hybrid resonant states. The last ones are approximatively obtained as a linear combination of eigenstates with the same parity in the lateral direction, and the corresponding resonances show the phenomena of resonance trapping or level repulsion. The existence of the hybrid modes suggests that the open quantum dot behaves in the Fano regime like an artificial molecule quantum point contacts