Self-consistent determination of the electron excitation spectrum under inelastic scattering

Establish the correct electronic excitation spectrum of electrons confined in a quantum well by performing self-consistent calculations that fully account for inelastic electron–phonon interactions, using nonequilibrium Green’s function methods combined with density functional theory or, potentially, GW calculations, in order to determine whether the proposed coherence-length criterion correctly distinguishes confined from bulk-like electronic states.

Background

The paper proposes that electronic dimensionality is controlled by the relationship between the electron phase-coherence length and the geometric confinement length. When the coherence length exceeds the well thickness, electrons are expected to retain phase information long enough to form standing waves and behave as a lower-dimensional electron gas; when it is shorter, collisional broadening is expected to merge the confined states into a bulk-like continuum.

These conclusions are presented as conjectures or educated guesses rather than as results derived from a fully self-consistent treatment. The unresolved task is to calculate the electronic excitation spectrum while incorporating the full inelastic electron–phonon self-energy, potentially together with density-functional or GW electronic structure, so that the proposed confinement criterion can be tested rigorously.