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 PL and 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 T in 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 PL and photoluminescence excita-
tion PLE spectra 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
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PHYSICAL REVIEW B 15 OCTOBER 1998-II VOLUME 58, NUMBER 16
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