General self-energy-based formulation of levels couplingin quantum confined structures

The effect of coupling between levels in quantum wells or quantum dots is described in Green’s function formalism. The structure eigenvalues are shown to have a Brillouin-Wigner continued-fraction expression that allows to give a general and intuitive meaning to levels coupling, described in terms of an off-diagonal self-energy. The concept of coupling is linked to a general potential matrix and can be given the same mathematical form for all kinds of coupling (inter- and intra-quantum dot and quantum well), in which off-diagonal self-energy contributions assume each time a different conceptual meaning. Furthermore, the same scheme, based on off-diagonal self-energies, allows to evaluate renormalization contribution due to each structure energy level in a natural and easy way.