Spin relaxation in polarized interacting exciton gas in quantum wells
T. Amand, D. Robart, X. Marie, M. Brousseau, P. Le Jeune, and J. Barrau
Laboratoire de Physique des Solides, CNRS URA 74, INSA, Avenue de Rangueil, 31077 Toulouse Cedex, France
Received 10 April 1996
Fast initial decays of both the luminescence intensity and the circular luminescence polarization, under
resonant excitation of high exciton densities typically above 2 10
10
cm
-2
, are reported. These fast decays,
which are not observed in a dense excitonic system with well-defined angular momentum J
z
=1 or
J
z
=-1 , are simultaneously initiated by the increase of the ellipticity of the photogenerating picosecond laser
beam. We show that all the experimental observations support the driving role of the exciton-exciton exchange
interaction in the spin-relaxation mechanism at high density. The theory of the mechanism is developed,
leading to the simulation of luminescence and polarization dynamics for varied photogeneration conditions
intensity and polarization of the laser beam, temperature of the exciton gas. The theory provides an excellent
interpretation of all the very specific features of the experimental data. The dephasing mechanism in polarized
interacting exciton gas is identified. S0163-18299702515-0
I. INTRODUCTION
The optical properties of two-dimensional 2D excitons
in quantum wells QW’s have been the subject of extensive
studies. Ten years ago, Hulin et al. demonstrated that, in
quasi-two-dimensional systems, the exciton energy is renor-
malized to higher values at high densities.
1,2
The blueshift of
the exciton absorption line was shown to be tied to the re-
duced dimensionality of excitons, being well apparent in
GaAs wells of approximately 50 Å wide, but disappearing
rapidly for larger well sizes.
The authors interpreted this effect in terms of a strong
reduction of long-ranged many-body interaction in a 2D sys-
tem, in agreement with the theoretical analysis by Schmitt-
Rink, Chemla, and Miller.
3
It is well documented that in
three-dimensional 3D systems, the excitons absolute en-
ergy remains unchanged, even at high densities. This con-
stant energy is attributed to an almost exact compensation
between two many-body effects acting in opposite direc-
tions: an interparticle attraction which, for bound electron-
hole pairs at T 0 K, is similar to a van der Waals interaction
between atoms, and a repulsive contribution having its origin
in the Pauli exclusion principle acting on the Fermi particles
electrons and holes forming the excitons. It has been ar-
gued by Schmitt-Rink, Chemla, and Miller that the attractive
component, which can be viewed as a long-ranged Coulomb
correlation effect, is strongly reduced in a 2D system, so that
the short-range repulsive part now becomes unbalanced.
A few years ago, in time-resolved luminescence spectros-
copy under circularly polarized and nonresonant laser beam
excitation, an energy splitting has been reported between the
two components of the HH1-E 1 exciton luminescence.
4,5
The component of the same helicity as the pump laser is
always at a higher energy than the other of opposed helicity.
The splitting increases with the exciton density and is
strongly correlated with the time evolution of the spin-
polarization rate of the optically active excitons. These re-
sults were also interpreted in terms of many-body interaction
within the excitonic system. The mutual Pauli repulsion of
excitons photocreated by the
+
polarized laser beam having
the same spin presently, J
z
=+1 excitons is invoked to in-
terpret the blueshift of the
+
polarized luminescence com-
ponent.
More recently, Snelling et al. reported time-resolved mea-
surements of the changes in transmission produced by exci-
tonic saturation at various wavelengths in the vicinity of the
heavy-hole exciton resonance, at room temperature.
6
They
conclude that the two contributions to the exciton saturation
in GaAs quantum wells, i.e., phase-space filling and Cou-
lombic effects, were of similar magnitude.
A clear redshift of the
-
polarized exciton line has been
recognized, in time-resolved absorption
7
and luminescence
8
spectroscopy performed with a
+
polarized beam. This red-
shift indicates the action of an attractive interaction between
the optically active excitons of opposed spins. In a previous
work in resonant excitation conditions, we investigated the
splitting of the exciton luminescence at time t =0
+
i.e., im-
mediately after the laser excitation, when the polarization of
the laser beam was progressively varied from circular to
linear.
9
This led us to the determination of the strengths of
the repulsive and attractive parts of the interaction between
the excitons. The results, which will be useful in this paper,
were close to the predictions of Schmitt-Rink, Chemla, and
Miller.
3
The exciton photoluminescence PL dynamics has been
investigated in resonant excitation conditions in very high
quality GaAs/Al
x
Ga
1 -x
As QWs:
10–12
after a quasi-
instantaneous rise, the luminescence intensity decays over
more than one order of magnitude in a characteristic time of
about 20 ps, followed by a much slower decay in the order of
200 ps. The long decay time is attributed to the radiative
recombination of thermalized excitons. Four contributions
were proposed to interpret the short one: a the radiative free
exciton lifetime;
11,13
b the exciton scattering out of the
J =1, k
0 optically active states to J =1, k
0 optically
nonactive states;
10,11
c the relaxation of the exciton total
angular momentum from the photogenerated |1,1 states to
optically nonactive |2,2 states by hole spin flip;
10,11
d the
recombination of biexcitons.
14,15
PHYSICAL REVIEW B 15 APRIL 1997-I VOLUME 55, NUMBER 15
55 0163-1829/97/5515/988017/$10.00 9880 © 1997 The American Physical Society