Electronic Spectra of Solids, Impurities and Superstructures with the Recursion and Renormalization Methods

Abstract

The recursion and the renormalization methods have greatly enriched the traditional field of electronic state calculations of periodic and aperiodic materials. After discussing their formal relationship, we present problems where the mentioned iterative procedures provide significant breakthrough. We consider first the application of the recursion method in the reciprocal space for periodic structures, where the unprecedented number of recursions reached allows us to analyze directly the asymptotic region. The recursion method in real space is then discussed and extended to the treatment of large clusters, either regular or with built in foreign atoms or vacancies. Impurity states of arbitrary range can be studied and non-perturbative results concerning ionized substitutional atoms in silicon are here provided for the first time. Localized impurity atoms in the presence of a dynamical Jahn-Teller effect also benefit of the recursion method: several vibronic systems as well as infrared absorption spectrum of transition metal impurities in cubic semiconductors are discussed. Using a mixed real-space reciprocal-space representation, it is shown that layered structures (surfaces, heterostructures, quantum wells and multiple quantum wells) can be studied in a very elegant and economical way with the renormalization method. In particular, we interpret the intrinsic origin of the semiconductor-semimetal transition of InAs — GaSb superlattices.