Space Charge in Nanostructure Resonances

In quantum ballistic propagation of electrons through variety of nanostructures, resonance in the energy-dependent transmission and reflection probabilites generically is associated with (1) a quasi-level with a decay lifetime, and (b) a bulge in electron density within the structure. It can be shown that, to a good approximation, a simple formula in all cases connects the density of states for the latter to the energy dependence of the phase angles of the eigenvalues of the S-matrix governing the propagation. For both the Lorentzian resonances (normal or inverted) and for the Fano-type resonances, as a consequence of this eigenvalue formula, the space charge due to filled states over the energy range of a resonance is just equal (for each spin state) to one electron charge. The Coulomb interaction within this space charge is known to distort the electrical characteristics of resonant nanostructures. In these systems, however, the exhcange effect should effectively cancel the interaction between states with parallel spins, leaving only the anti-parallel spin contribution.