Model For A Biexciton
Enviado por EduardoLudena • 12 de Enero de 2014 • 5.270 Palabras (22 Páginas) • 268 Visitas
Model for a Biexciton in a Lateral
Quantum Dot Based on Exact Solutions
for the Hookean H2 Molecule.
I. Theoretical Aspects
E. V. LUDEÑA,1 L. ECHEVARRÍA,2 J. M. UGALDE,3 X. LOPEZ,3
A. CORELLA-MADUEÑO4
1Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC,
Apartado 21827 Caracas, Venezuela
2Departamento de Química, Universidad Simón Bolívar, Sartenejas, Caracas, Venezuela
3Kimika Fakultatea, Euskal Herriko Unibertsitatea and Donostia International Physics Center,
Posta Kutxa 1072, 20080 Donostia, Euskadi, Spain
4Departamento de Física, Universidad de Sonora, Apartado Postal 1626 Hermosillo, Sonora, México
Received 15 March 2010; accepted 20 April 2010
Published online 13 January 2011 in Wiley Online Library (wileyonlinelibrary.com).
DOI 10.1002/qua.22818
ABSTRACT: We present here a model for the non-Born-Oppenheimer description of
the biexcitonic complex X2(eehh) trapped in laterally-coupled quantum dot system. We
define a zeroth-order Hamiltonian which allows us, under certain conditions on the
masses and coupling constants, to decouple the problem.We show that the zeroth-order
wavefunctions and energies can be described using the exact solutions for the Hookean
model for the H2 molecule [Ludeña et al., J Chem Phys 2005, 123, 024102]. We also apply
this Hookean model to the description of the excitonic complexes X+
2 (ehh), X−
(eeh), and to
the single exciton X(eh) and analyze the dependence of the total non-Born-Oppenheimer
zeroth-order energies, and binding energies for these sytems with the mass ratio σ. The
general features of the results obtained using this Hookean model agree quite well with
those of more elaborate calculations. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111:
1808–1818, 2011
Key words: biexcitons; lateral quantum dots; Hookean model;
non-Born-Oppenheimer; H2 molecule
Correspondence to: E. V. Ludeña; e-mail: popluabe@yahoo.es
International Journal of Quantum Chemistry, Vol 111, 1808–1818 (2011)
© 2011 Wiley Periodicals, Inc.
MODEL FOR A BIEXCITON
1. Introduction
Coupled semiconductor quantum dots are
novel structures that have attracted much
attention because of their potential applications in
quantum cryptography and quantum computation
[1–5]. Much progress has been achieved in the fabrication
and control of properties of vertically stacked
quantum dots [6–9] as well as of laterally coupled
ones [10–15].Afirst-principle’s theoretical treatment
of these structures (comprising over 5,000 atoms) has
been carried by Jaskolski et at. [16]. For a review
of application of simpler models to lateral quantum
dots in a magnetic field, see Helle et al. [17, 18].
The effects of exciton splitting of two laterally
coupled quantum dots under the influence of an
electric field are of particular interest [19]. This is
due to the important role that an electrically tuned
lateral quantum dot could play in the development
of controllable quantum gates, which are the basic
elements for the realization of quantum computers
[15, 20–22]. On the other hand, it has been experimentally
demonstrated that the type of coupling of
lateral quantum dots has a definite expression in the
photoluminiscence spectrumand, hence, it would be
desirable to attain understanding of this phenomenon
for the purpose of having a voltage-controlled
emission of non-classical light [15, 23]. The latter is
an essential feature in many areas having to do with
the development of opto-electronic devices [24].
The importance of excitons for determining the
optical properties in semiconductor nanocrystals is
already well known [25, 26]. The presence of biexciton
states in semiconductor quantum dots was
experimentally demonstrated (and theoretically corroborated)
by Hu in 1990 [24]. In a single quantum
dot, different pathways leading to the formation of
excitons have been studied [27] and coherent optical
control of biexcitons has been experimentally
achieved [28]. Calculations have been performed to
determine the binding energies of excitonic complexes
as a function of the quantum dot height [29]
and length [30]. Also, the size of quantum dots in
which biexcitons are generated under a two-photon
...