Ground state energy of excitons in quantum dot treated variationally via Hylleraas-like wavefunction

Abstract

In this work, the effects of quantum confinement on the ground state energy of a correlated electron–hole pair in a spherical and in a disc-like quantum dot have been investigated as a function of quantum dot size. Under parabolic confinement potential and within effective mass approximation Ritz's variational method is applied to Hylleraas-like trial wavefunction. An efficient method for reducing the main effort of the calculation of terms like rehk exp(−λreh) is introduced. The main contribution of the present work is the introduction of integral transforms which provide the calculation of expectation value of energy and the related matrix elements to be done analytically over single-particle coordinates instead of Hylleraas coordinates.

Basis set effects on the Hartree–Fock description of confined many-electron atoms

“…There are basically two ways to obtain the wavefunction or electron density under these boundary conditions: using a cut-off function on the basis set functions to impose such a confinement (Le Sech and Banerjee 2011, Sarkar et al 2009, van Faassen 2009 or imposing the behaviour on the wavefunction for the numerical solution of the radial equation (Connerade et al 2000, Garza et al 1998. The Hartree-Fock (HF) (Slater 1979) or Kohn-Sham (Kohn and Sham 1965) models are the most popular methods used to obtain the wavefunction and the electron density, although the Hylleras approach has also been used to study two-electron atoms (Aquino et al 2006, Wilson et al 2010, Flores-Riveros et al 2010, Flores-Riveros and Rodríguez-Contreras 2008, Sakiroglu et al 2009.…”

Effects of confined longitudinal and interface optical phonons on excitons in an asymmetric quantum well

“…These properties are closely related to carrier-states and their coupling with phonon modes. Some authors investigated the phonon-modes, exciton-phonons interaction, polaron states and so on [14][15][16][17] in quantum well (QW).In early years, authors usually used bulk-phonon approximation for studying the polaron in QW's [13], and got some reasonable conclusions. But this approximation did not agree with the real physical system when taking account of the strong quantum effects in narrow QW, so the confined longitudinal optical (LO) phonons and interface optical (IO) phonons modes were introduced for studying the exciton-phonons interaction [18,19], and it is more appropriate for doing a research on the quantum systems.…”

“…These properties are closely related to carrier-states and their coupling with phonon modes. Some authors investigated the phonon-modes, exciton-phonons interaction, polaron states and so on [14][15][16][17] in quantum well (QW).…”