G. Pastori Parravicini

Band structure and optical properties of graphite and of the layer compounds GaS and GaSe

SummaryThe band structure of graphite and of the layer compounds GaS and GaSe is computed by using the tight-binding approach in a semi-empirical way. The band structure is related to the basic properties of these compounds and some features of the optical excitation spectrum are explained. We show that the reason why graphite is a semi-metal and GaS and GaSe are semiconductors can be understood in the two-dimensional approximation and is due to the existence of the inversion symmetry in the former case. The absorption edge in GaS corresponds to indirect transitions between the statesΓ1+ andP1+, while in GaSe it corresponds to direct transitions between the statesΓ1+ andΓ3+. Sharp peaks inε2(0,ω) are attributed to saddle point singularities in the joint density of states. The effect on the optical properties produced by a change in the polarization of light is discussed.RiassuntoLa struttura a bande della grafite e dei composti lamellari GaS e GaSe è ottenuta usando l’approssimazione dell’elettrone fortemente legato in forma semi-empirica. La struttura a bande è messa in relazione con le proprietà fondamentali di tali composti ed alcune caratteristiche dello spettro di eccitazione ottica vengono spiegate. Si è mostrato che la ragione per la quale la grafite è un semimetallo, mentre GaS e GaSe sono semiconduttori, può essere capita nella approssimazione bidimensionale; essa è dovuta alla presenza, nel caso della grafite, della simmetria di inversione. Lo spigolo di assorbimento del GaS corrisponde a transizioni indirette tra gli statiΓ1+ eP1+, mentre nel GaSe esso corrisponde a transizioni dirette tra gli statiΓ1+ eΓ3+. Picchi nella funzione dielettricaɛ2(0,ω) sono attribuiti a singolarità nella densità di stati in corrispondenza a punti di sella. L’effetto di un cambiamento della direzione di polarizzazione della luce sulle proprietà ottiche viene discusso.РеэюмеВычисляется эонная структура графита слоистых соединений GaS и GaSe, причем, полузмпирически испольэуется приближение плотной свяэи. Зонная структура свяэывается с основными свойствами зтих соединений, и общясняются некоторые особенности спектра оптических воэбуждений. Мы отмечаем, что причину того, почему графит является полуметаллом, а GaS и GaSe являются полупрово-дниками, можно понять иэ двумерного приближения, и зто обусловлено сушество-ванием обратной симметрии в первом случае. Край поглошения в GaS соответствует непрямым переходам между состояниямиΓ1+ иP1+, тогда как в GaSe край поглошения соответствует прямым переходам между состояниямиΓ1+ иP3+. Острые пики вɛ2 (0,ω) относятся эа счет сингулярностей седловых точек в сочленной плотности состояний, обсуждается зффект для оптических свойств, который обусловлен иэменением поляриэации света.

ENERGY BANDS AND OPTICAL PROPERTIES OF HEXAGONAL BORON NITRIDE AND GRAPHITE.

SummaryThe band structure of hexagonal boron nitride in the two-dimensional approximation is computed using the tight-binding approximation in a semi-empirical way. The results are compared with those of the isoelectronic compound graphite and are shown to be in agreement with the basic experimental data. Three-dimensional band structure calculations have also been performed and the effect of the different spatial structure of boron nitride and graphite lattices on the electronic levels at the saddle point is shown to produce a doublet in the optical excitation spectrum of BN.RiassuntoLa struttura a bande del nitruro di boro esagonale nella approssimazione bidimensionale è calcolata usando il metodo del legame stretto in modo semiempirico. I risultati sono confrontati con quelli del composto isoelettronico grafite e sono in accordo con le proprietà sperimentali fondamentali. La struttura a bande nel caso tridimensionale è pure calcolata e il doppietto nello spettro di eccitazione ottica del BN è attribuito all’effetto della diversa struttura spaziale del nitruro di boro e della grafite sui livelli elettronici al punto sella.РеэюмеПолузмпирическим путем, испольэуя приближение сильной свяэи, вычисляется эонная структура гексагонального нитрида бора в двумерном приближении. Полученные реэультаты сравниваются с реэультатами для иэозлектронного составного графита, и покаэывается, что они согласуются с основными зкспериментальными данными. Также были проведены вычисления трехмерной эонной структуры, и покаэывается, что влияние раэличной пространственной структуры рещеток нитрида бора и графита на злектронные уровни в седловой точке дает дублет в спектре оптического воэбуждения BN.

Selection rules for direct creation of biexcitons by giant two-photon absorption

Abstract The selection rules for direct creation of biexcitons by two-photon absorption processes are discussed on symmetry basis. A detailed analysis is performed for CuCl and CdS crystals, with the energy levels given by Bassani et al. It is found that only Гbiex1 states can be created by giant two-photon absorption when the photons have the same frequency. The polarization dependence is given for the other cases.

A new method for determining excited states of quantum systems

SummaryA new method for computing excited states of a given operatorH is here presented. Our procedure is of particular value when its representation requires an orthonormal basis set of large dimension. In order to obtain the excited state ofH nearest in energy to any chosen trial energyEt, we consider the auxiliary operatorA=(H−Et)2. We show that a reasonable number of relaxations on appropriately generated low-order Krylov subspaces forA is sufficient to produce better and better approximations of its ground state; a high-accuracy final refinement of the ground state ofA is then possible through the standard Lanczos procedure. An important feature of our method is that storage memory limitations, encountered in the conventional determination of all eigenvalues of large systems, are here overcome. As an illustration of the method two significant examples are discussed.

Intensity of two-photon excitonic absorption in two-band and three-band models

Abstract The intensity of two-photon absorption to Wannier excitons is estimated in simplified models. Both two-band and three-band models simultaneously contribute to the optical two-photon spectrum, but it is shown that the two-band model is favoured in crystals with relevant electron-hole interaction. As an example, it is explained why two-photon absorption spectrum in CuCl exhibits 1s, 2p, 3p exciton states.

7th General Conference of the Condensed Matter Division of the European Physical Society

The annual General Conference of the Condensed Matter Division of the European Physical Society has grown into a leading forum for discussion and exchange of the latest scientific developments. The conference series started seven years ago at the initiative of J T Devreese with the Antwerp Conference; it continued with the conferences in Manchester (1982), Lausanne (1983), The Hague (1984), Berlin (1985) and Stockholm (1986). The 7th General Conference was held in Pisa from 7 to 10 April 1987; it was attended by about 900 participants, coming from more than 30 countries of Europe and overseas. The present volume, in two issues T19A and T19B, collects the papers orally presented at the Pisa Conference. The scientific programme contained 90 invited speakers, distributed in plenary lectures, symposia and individual invited talks. The presentation of the papers in this volume follows the pattern of the Conference as closely as possible. The recent explosion of interest in High Temperature Superconductivity motivated, besides the plenary lecture in the programme, the last minute inclusion of an open symposium on this subject. More than forty research groups contributed to this event. The titles of the contributions and the affiliation of the speakers have been included at the end of volume 19B for the benefit of interested readers. Numerous contributions (more than 500), ranging over the entire field of Condensed Matter Physics, were presented in poster sessions. Several poster contributions at the conference (as well as a number of the contributions to the Symposium on High Temperature Superconductivity) will appear as regular articles in Physica Scripta. These articles will later be collected in a Reprint Series of Physica Scripta. We wish to thank the Conference Committees and the individual people who helped in the choice of such stimulating material, and all the contributors to this volume for their cooperation in the timely preparation of manuscripts. A special acknowledgement is also due to the Sponsors, whose generous help has made this manifestation possible.

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.

Conduction bands of solid o—H2 with the molecular O.P.W. method

Abstract The application of the O.P.W. method to closed shell molecular crystals is considered. The non local exchange potentials is included within the zero overlap approximation. The conduction bands of solid o—H2 are obtained at symmetry points of interest and related to the experimental optical absorption spectrum.

Selection rules for indirect transitions and effect of time reversal symmetry

Selection rules for indirect transitions are derived starting from a geometrical interpretation of the Brillouin zone. The effect of time reversal symmetry is included in the procedure. The final results, valid both for single group and double group representations, are presented in a way very convenient for operational applications. The case of diamond lattice is given as a specific example. The comparison between this treatment and previous ones is discussed.

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.