Eur. Phys. J. Appl. Phys. 56, 10105 (2011)
https://doi.org/10.1051/epjap/2011110250

General self-energy-based formulation of levels coupling in quantum confined structures^★

Dipartimento di Elettronica, Politecnico di Torino, Torino 10126, Italy

^a e-mail: marco.vallone@polito.it

Received: 15 June 2011
Accepted: 19 August 2011
Published online: 28 September 2011

Abstract

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.