Effect of the hole subband mixing on the spin splitting of heavy-hole excitons in coupled In 0.045 Ga 0.955 As/GaAs double quantum wells T. Wang,* M. Bayer, and A. Forchel Technische Physik, Universita ¨t Wu ¨rzburg, Am Hubland, D-97074, Wu ¨rzburg, Germany Received 6 July 1998 The spin splitting of the parity-forbidden transition hh 12 and ground-state transition hh 11 in a coupled In 0.045 Ga 0.955 As/GaAs double quantum well is investigated by photoluminescence PLand PL excitation spectroscopy in magnetic fields up to 13 T. Our experiment indicated that the spin splitting of hh 12 is reversed compared with that of hh 11 and is larger than that of hh 11 . We report that the spin splitting of hh 12 increases with the decrease of GaAs thickness separating the quantum wells. The hh 12 behavior is confirmed to be due to the strong mixing of the p exciton of hh 12 and the s exciton of the light hole. S0163-18299850440-7 A number of calculation and experiment of the effect of valence-band mixing on the excitons in quantum wells have been reported. 1–11,13,14,16,18,19 Some of the published papers associated with this effect concentrated on the investigation of exciton binding energy. 5,12–17 In addition, there are some papers studying the so-called parity-forbidden transitions, 1–5,9–11,13,14,16,18 but there is no experimental re- sult reporting the spin-splitting of parity-forbidden transition. Only Bauer 1,2,8 gave some theoretical calculation. Further- more, most of these papers just reported the observation of parity-forbidden transition, only a few papers gave some simple assumptions. One of them 13 used modified quantum- well parameters to fit the experimental data, and then as- sumed that the revised quantum-well parameters were due to the effect of hole subband mixing. Another 16 found that the exciton related to the parity-forbidden transition has much smaller exciton binding energy than the ground-state exciton by comparing the energy positions of ground-state transition and parity-forbidden transition with the calculation, and then proposed that the appearance of parity-forbidden transition was due to the hole subband mixing. The authors of Ref. 14 assumed that the appearance of parity-forbidden transition may be due to the presence of electric field. In one word, there is no very convincing experimental evidence for the effect of hole subband mixing. In this paper, we report the spin splitting of the parity-forbidden transition in In 0.045 Ga 0.995 As/GaAs quantum wells, and present a very convincing experimental evidence for the effect of hole sub- band mixing. In order to study the effect of coupling between the heavy-hole and light-hole excitons, we choose the coupled In 0.045 Ga 0.995 As/GaAs double quantum well sepa- rated by nML GaAs barrier based on the following consid- eration. On the one hand, the n =2 heavy-hole subband en- ergy can be adjusted by changing this GaAs barrier thickness. On the other hand, for the case of 0.045% In con- tent, the light-hole state is unconfined; this n ML GaAs bar- rier does not affect the energy of the light hole. It means that the energy separation between the heavy- and light-hole state can be adjusted systematically, which is very important in examining the coupling effect between heavy- and light-hole states. This is difficult to realize in the Al x Ga 1 -x As/GaAs material system. This paper confirms that the appearance of the parity-forbidden transition is due to the strong mixing of the heavy-hole and light-hole exciton. This confirms the theory of Bauer. 1,2,8 The results obtained will provide a very convincing phys- ics basis for the calculation of exciton binding energy and other fields in future, for example, the appearance of high Landau-level transition related to p-type exciton, d-type ex- citon, etc., furthermore, the anticrossing effect. In the near future, we will have another paper related to them. The undoped In 0.045 Ga 0.995 As/GaAs coupled quantum wells separated by thin GaAs spikes were grown by solid source molecular-beam epitaxy on the semi-insulating 001 GaAs substrate. For the two quantum wells a width l w =7.5 nm was chosen in all samples, in which the width l B of the separation barrier was varied. Four different samples were fabricated with barrier widths of 1, 3, 5, and 9 ML of GaAs 1 ML corresponds 0.28 nm. The sample temperature was kept at T =4.2 K by mounting the sample in a LHe cryostat, containing a superconductor solenoid ( B 13 Tin order to perform photoluminescence and photoluminescence excita- tion studies. The direction of the magnetic field is parallel to the growth directions of the samples. The photoexcitation and the collection of the emission were carried out using an optical fiber with a diameter of 200 m. A polarizer and a quarter plate were placed between the outlet of the optical fiber and the sample in order that the spectral were recorded in the + and - polarization. For excitation spectrum a Ti sapphire laser pumped by the Ar + laser was used. The lumi- nescence was dispersed by a double monochromator with a focal length of f =1 m and was detected by a Peltier-cooled GaAs photomultiplier interfaced with a photocounting sys- tem. In order to avoid any many-body effects, only a low excitation power was used. Photoluminescence PLand photoluminescence excita- tion PLEspectra of these samples show an excellent sample quality, for example, Fig. 1 gives the PL and PLE of the sample with the barrier of 9 ML GaAs. The very narrow and high intensity peak corresponds to the ground state la- beled hh 11 ), whose FWHM is only 0.7 meV; the Stokes shift is only 0.1 meV. For the other three samples, the FWHM of ground-state transition are also only 0.7 or below 0.7 meV, the Stokes shifts are also about 0.1 meV. The second peak is RAPID COMMUNICATIONS PHYSICAL REVIEW B 15 OCTOBER 1998-II VOLUME 58, NUMBER 16 PRB 58 0163-1829/98/5816/101834/$15.00 R10 183 © 1998 The American Physical Society