Skip to Main content Skip to Navigation
Theses

Fonctions d'onde locales dans le formalisme des liaisons fortes

Abstract : The energy band interpolation is a well known problem in solid state theory. It is often disconnected from the consideration of wavefunctions, in particular in the very popular k.p and tight-binding approaches. However, the local wavefunction is also important since the matrix elements of different operators in real space constitute the basic ingredient to evaluate many physical observables. This is particularly true when one tries to evaluate interactions (in particular, short range interactions) between quansi-particles. In the empirical tight binding method, the single-electron wavefunctions are developed on a basis of orbitals whose spatial form is not taken into account in the construction of the Hamiltonian. This work adresses this theoretical problem that remained open since the pioneering work of Slater and Koster (1954). We take as a starting point a basis of atomic orbitals (in practice, Slater orbitals) with adjustable screening coefficients. We calculate the overlap matrix between the different functions of the basis and obtain a new, orthogonal basis using the Löwdin orthogonalization procedure. The projections of the Hamiltonian eigenstates on the new basis give the electronic Bloch functions, which are then used to compute the momentum matrix elements in real space, that are iteratively compared with their k-space counterpart. This method allows a self-consistent fitting of the screening coefficients of starting atomic orbitals, therefore complements the tight-binding theory with a description of local wavefunctions. Our results compare satisfactorily with results of ab initio and empirical pseudo-potential calculations. Beyond semiconductor nanostructures, this work is a fundamental step toward modeling many-body effects from post-processing wave-functions within the Slater and Koster theory. A first test of this approach was made by computing the fine structure of excitons in bulk GaAs. We have calculated the dispersion of exciton fine structure, treating on equal footing all the ingredients of the problem, from details of the single particle dispersions (valence band warping, electron and hole spin splittings) to direct and exchange Coulomb interactions. Our results are in very good agreement with experimental values of exciton binding energy and longitudinal-transverse splitting.
Complete list of metadatas

Cited literature [85 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00826049
Contributor : Ramzi Ben Chamekh <>
Submitted on : Monday, May 27, 2013 - 4:30:38 PM
Last modification on : Thursday, December 10, 2020 - 10:51:55 AM
Long-term archiving on: : Wednesday, August 28, 2013 - 2:45:10 AM

Identifiers

  • HAL Id : tel-00826049, version 1

Citation

Ramzi Ben Chamekh. Fonctions d'onde locales dans le formalisme des liaisons fortes. Science des matériaux [cond-mat.mtrl-sci]. Université Pierre et Marie Curie - Paris VI, 2012. Français. ⟨tel-00826049⟩

Share

Metrics

Record views

859

Files downloads

5018