PIERS ONLINE, VOL. 4, NO. 2, 2008 263 Hydrostatic Pressure and Magnetic Field Effects on the Exciton States in Vertically Coupled GaAs-(Ga, Al) As Quantum Dots M. E. Mora-Ramos 1 , A. H. Rodr´ ıguez 2 , S.Y.L´opez 3 , and C. A. Duque 4,5 1 Universidad Aut´onoma del Estado de Morelos, Ave. Universidad 1001, 62209 Cuernavaca, M´ exico 2 Universidad Aut´onoma de la Ciudad de M´ exico, Plantel Iztapalapa, M´ exico DF, M´ exico 3 Facultad de Educaci´on, Universidad de Antioquia, AA 1226, Medell´ ın, Colombia 4 Instituto de F´ ısica, Universidad de Antioquia, AA 1226, Medell´ ın, Colombia 5 Instituto de F´ ısica, Unicamp, CP 6165, Campinas-SP, 13083-970, Brazil Abstract— The variational procedure, in the effective-mass and parabolic-band approxima- tions, is used in order to investigate the combined effects of hydrostatic pressure and in-plane- direction-applied magnetic field on the exciton states in vertically coupled GaAs-(Ga, Al) As quantum dots. Calculations are performed for two cylindrical-shape quantum dots. The exciton envelope wave function is obtained through a variational procedure using a hydrogenic 1s-like wave function and an expansion in a complete set of trigonometric functions for the electron and hole wave functions. The anticrossing effects on the dispersion with applied magnetic field and hydrostatic pressure of the photoluminescence peaks associated with direct and indirect excitons have been considered. 1. INTRODUCTION A symmetric/asymmetric coupled double quantum well (DQW) is made of two identical/different quantum wells (QW) that are separated by a thin barrier. For the symmetric case, in flat-band conditions, i.e., without applied electric field in the growth direction of the heterostructure, the eigenfunctions of the DQW have well-defined symmetries. These are broken in the asymmetric case. In this case, only transitions between electron and hole states with the same symmetry are optically allowed. Whenever the maximum probability of the electron and hole wave functions are distributed in the same well, the transitions are known as spatially direct transitions. The intensity of these optical transitions is essentially given by the overlap integral of the electron and hole single-particle envelope wave functions and temperature-dependent populations of electrons and holes in the subbands. Also, it is certainly necessary to take into account the electron-hole (e − h) Coulomb interaction for an appropriate description of the optical transitions in semiconducting heterostructures. Of course, effects of the e − h Coulomb interaction are essential whenever the fine structure of the optical spectra shows features which are within the range of the exciton binding energy. On the other hand, the application of hydrostatic pressure results in changes of the dielectric constant and of band structure parameters such as the energy gap and the conduction band mass. This may result in modifications of the interband optical transitions in GaAs-based QW’s (see Ref. [1], and references therein). By applying an in-plane magnetic field in coupled QWs, it is possible to induce strong changes in the excitonic-related photoluminescence (PL) spectra due to field-induced displacement of the interwell exciton dispersion in momentum space, which leads to a transition from the momentum- space direct exciton ground state to the momentum-space indirect exciton ground state [2–4]. The indirect exciton lifetime in coupled DQW heterostructures under applied magnetic fields has been studied by Butov et al [2–4] and they attribute the observed results to an increase in the magnetoexciton mass. Also, Butov et al [2–4] have studied long-lifetime indirect excitons in coupled QWs and, at low temperatures and high exciton densities, strong deviations of the indirect exciton PL kinetics from monoexponential PL rise/decay were observed. Parlangeli et al [5] have studied the indirect exciton dispersion in k space by considering the simultaneous effect of in-growth direction applied electric field and in-plane magnetic field in DQW heterostructures and found that the PL spectra increase with the magnetic field following a quadratic behavior. Additionally, they present measurements of the PL peak positions of both direct and indirect excitons in biased GaAs/Ga 1-x Al x As coupled DQWs under in-plane applied magnetic fields. In the present work we are concerned with a theoretical study of the effects of applied hydrostatic pressure and in-plane magnetic fields on the exciton direct and indirect states in GaAs/Ga 1-x Al x As