L. Martinelli

Excitons in rare gas atoms and solids

Abstract Excitons in rare gas are described using the integral equation approach and an appropriate semi-empirical simplification of the short-range terms. In the solids, polarization effects are taken into account using a semi-continuum model in analogy with F -centre problem. Reasonable agreement with experiments is obtained for exciton binding energy shifts passing from atoms to crystals.

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

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.

Role of the breathing mode in a strongly coupled Jahn-Teller system

The theoretical absorption spectrum of a vibronic system exhibits two main peaks of different height and width, and, at very strong Jahn-Teller energy, other peaks at higher energies (cone resonances or Slonczewski resonances). Tetrameric cations of the group V elements can be pictured as strongly coupled Jahn-Teller systems; however, high resolution photoelectron spectra available in the literature exhibit only two broad spectral bands. To explain the disappearance of the cone resonances, we have considered a two-mode vibronic model, that, besides a strong linear interaction with the mode , also includes a linear interaction with the total symmetric mode (breathing mode); we have also considered separately off-diagonal second-order effects on the Jahn-Teller system. The analysis has been carried out in the framework of the recursion Lanczos technique, properly implemented. We have verified that the Slonczewski resonances are quenched by the breathing mode, even in the case of moderate coupling; we have then compared our model with the available experimental spectra of group V tetrameric clusters.

Excitons in gaseous and solid neon

The standard integral equation for excitons in crystals is extended to the case of an isolated neon atom. A very simple model Hamiltonian which fits atomic excitation energies is proposed. Then the role of solid state effects in determining solid neon exciton energies is examined.

Renner–Teller Interaction Matrices and Green's Function Formalism

Abstract The general structure of the interaction matrices for the Renner–Teller E ⊗ e vibronic system at any order in the phonon variables and with orbital electronic functions of different symmetry is here determined by means of a simple approach based on the Slater–Koster expressions of two-center integrals and connected to the symmetry group approach. Starting from the case of orbital doublet with p -like functions, through suited canonical transformations in electronic and phonon variables, it is shown that the Renner–Teller problem can be mapped exactly into a set of independent double chains of orthonormal states with interactions between a small number of neighbor states (depending on the order of the interaction considered). The key point of the transformations introduced exploits the axial symmetry of the problem, so the procedure is generally valid also for other symmetries of the orbital functions. Then the Greens function formalism combined with the recursion–renormalization procedure can be efficiently applied to determine with high accuracy the vibronic eigenstates for Renner–Teller systems with interaction matrices expressed in whatever general form.

Core excitons in solid rare gases: Kr-3d and Xe-4d transitions

Abstract Core excitons from 3 d levels of Kr and 4 d levels of Xe are examined within the integral equation formalism both in the isolated atoms and in the crystals. Earlier interpretation that resonances at the interband edge Kr-3 d and Xe-4 d are due to 1 s , 2 p , 3 p excitons is well supported by the present calculation.

Dynamic Jahn-Teller effect in crystals doped with 3d ions

This chapter is devoted to the study of the dynamic Jahn-Teller effect on the optical spectra of 3d-ions impurities in crystals, with particular attention to the theoretical efforts addressed to the interpretation of the experimental results. The presentation assumes that the reader is familiar with the spectroscopic notation for atomic energy levels. In addition, basic concepts and notation of point-group theory are also used. First, we will present a survey of the main experimental and theoretical results according to the electronic configuration. Then we discuss with a tutorial style the main contributions needed to model the optical spectra of the Jahn-Teller active 3d-ions impurities and asimple example is discussed in details. Next we concentrate on the calculation procedures required to address realistic systems. Some applicative examples of the proposed procedure are described in details.

Fine Interactions and the Jahn-Teller Effect in Luminescence of FE 2+ in II-VI Compounds

Infrared luminescence spectra of Fe2+ in II-VI zinc-blende structures show more than 4 unequally spaced lines. To explain such experimental features, we introduce a Jahn-Teller coupling to acoustical phonons of E symmetry. We apply and compare two independent methods: Born-Oppenheimer’s and Lanczos’. Additionally we investigate the role of higher-order corrections such as spin-spin and third-order spin-orbit contributions to accurate calculation of energy levels. Details of the emission spectra of ZnS : Fe 2+, ZnSe : Fe 2+, ZnTe : Fe 2+, and CdTe : Fe 2+ are explained as due to a weak Jahn-Teller coupling which is enhanced when the energy of the coupling phonon is close to the spacing between electronic levels of appropriate symmetry.

Self-trapped excitons in rare-gas dimers and solids

Abstract The excited electron states in isolated rare-gas dimers are described by a model Hamiltonian with appropriate simplifications for the short-range terms. Then the energies of self-trapped excitons are obtained by including solid state effects. The results are compared with the available transient absorption spectroscopy measurements.