Transcript Biexciton formation at high magnetic field in (Cd,Mn)Te

Biexcitonic Faraday Rotation in GaAs / AlGaAs Quantum wells
H-255
Y Hashimoto*, T Kuroda, F Minami
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
*Present address: Graduate school of Science and Technology, Chiba University, Chiba 263-8522, Japan
e-mail: [email protected]
Abstract
The polarization rotation introduced by the resonant pulse excitation is
investigated in nonmagnetic GaAs quantum wells. The Faraday rotation
signal is resolved both in spectral and temporal domain, showing a clear
excitonic and biexcitonic resonance profile. The Faraday rotation spectra
are well reproduced by a calculation based on the multiple transition
model, in which the two-exciton complex of singlet and triplet geometry
are taken into account. The resonance energies
of the two-exciton states,
半導体量子井戸における
extracted through the present fitting, are consistent with results of spin光誘起励起子ファラデー回転
dependent nonlinear absorption.
橋本　佑介 , 黒田　隆 ,
Why the biexciton state induce the
Faraday rotation ?

Assuming the situation under +
polarized excitation. Then, the + (left
picture) and - (right picture) polarized
component of probe beam cause a
transition forming the antibonding (2x)
and bonding biexciton (Bx), respectively.
This difference generates the
remarkable circular dichroism and
induce the Faraday rotation.


1
1
G
南　不二雄
Fitting to the experimental data
By use of spin selective photo-excitation, a remarkable nonlinear
birefringence due to resonant creation of bonding and
antibonding biexcitons is induced.




1
1
1
1
G
G
1
2
2



n w 

w


(
w
)


1
1
2 (w) 

2
~ w   w  i w   
1
2

w
n
0n
2
]
e
e
r
g
e
d
[
n
o
i
t
a
t
o
Faraday R
0.4
0.2
0.1
0.0
100
80
60
40
-0.1
Intensity [arb.u.]
Absorption
0.6
0.4
0.2
hh
lh
0.0
1.56
1.57
1.58
Energy [eV]
1.59
nm]
794
Polarization of Pump beam

:

:
50
100
200
Delay Time [ps]
Temporal profile of the PIFR is
shown. In this figure the probe energy
is tuned to be just below the hh
exciton line. Occurrence of the
symmetric profile with respect to the
pump polarization supports that the
signal originates from the photoinduced magnetic momenta.
Excellent agreement
-0.1
1.560 1.565 1.570 1.575 1.580
Energy [eV]
f
hh exciton ()
hh exciton ()
bounded two exciton
unbounded two exciton
f 0
f 0
0.025 × f
0.013 × f
0
0
g
w 0 [eV]
g0
g0
g0
g0
1.5716
1.5716
1.5688
1.5734
0.3
0.8
0.2
0.6
0.1
0.0
-0.1
150
: A fit considering the
single exciton and biexciton
The Biexcitonic Faraday rotation
Dw0=0.016[meV]
The parameter used in the fit
considering the exciton and
bieciton (
)
Spectral profile at t = 6ps
Rotation [degree]
0
On the other hand,
0.0
Optical Density
gth [
Temporal profile in the hh exciton resonance
Rotation [Arb. u]
mirror
Probe
The absorption spectrum of the present
sample at 5 K is indicated, together with
the spectrum of the pump pulse and that
of the spectrally narrowed probe one for
comparison. The pump spectrum covers
the hh exciton absorption.
0
-20
792
: A fit considering only
the single exciton
0.1
ps
elen
Sample : GaAs (8nm) / Al0.3Ga0.7As (10nm) ×20
multiple quantum wells
Light source : Mode-locked femtosecond Ti-sapphire laser
Detection : Balancing Photo-diodes
Accuracy : Less than the 10-2 degree
20
790
Wav
0
2c
(n  n )
: experiment
: calculation
0.2
e[
Probe beam
(linear polarized)
788
De
la
786
0.3
]
Sample in 5K
For the probe pulse, we inserted
a wavelength variable spectral
filter of Fourier-transformlimited type (left picture), so
that the band width was
narrowed down to 1/30 of the
laser output. The probe energy
was varied above the hh exciton
resonance region.
wl
Not match
yT
im
Polarization beam splitter
Pump
Line Width
Fitting results
0.3
Balancing unit
F  
Rotation [degree]
Faraday rotation
by the optical pumping
Pump beam
(circularly polarized)
mirror
probe beam
fn
The fitting parameter
exciton :
Extracted from the
transmission spectrum
f0, g0, w00
biexciton :
g : the value of exciton g0
w0, f : free parameter
n-
Temporal and spectral resolved Faraday rotation
OUT
lens
Amplitude
n+
Photo-induced Faraday rotation measurement
slit
G
Result & Discussion
Experimental Set Up
grating
1
 w2  iw gn
Resonance wavelength
Although photo-induced Faraday
rotation (PIFR) has been observed
in a number of semiconductor
materials, such as diluted magnetic
systems and nonmagnetic quantum
structures , an origin of the PIFR
has not been fully clarified.
Therefore, we performed a detail
study of PIFR induced by the
excitonic nonlinearrity.
2X
BX
1
東京工業大学理工学研究科
Motivation

2X
BX
0.4
Pump beam : 
Probe beam : 
: With Excitation
: Without Excitation
0.2
0.0
1.560
1.565
1.570
1.575
Energy [eV]
The spectrally profile of the PIFR at
6ps is displayed. The FR signal
emerges only at the exciton resonance
region, and becomes negligible when
the probe energy is far from the
exciton. This fact indicates that the
dominant origin for the FR is the
excitonic nonlinearity.
-0.2
1.560
: hh exciton
: bounded two exciton
1.565
1.570
1.575
1.580
To confirm the formation of the biexciton states,
transient absorption measurements were performed.
An example of the transient absorption spectrum at t =
6 ps with counter-circularly polarized pumping and
probing is shown. A fit considering the single exciton
and biexciton gives the value of 2.8±0.6meV for the
binding energy of the bonding biexciton, which agrees
well with the parameter given by the analysis of FR
spectra (2.8±0.2meV).
Energy [eV]
conclusions
We observed the biexcitonic Faraday rotation in semiconductor quantum wells. The spectral
profile shows the a good agreement with the calculation, where the formation of the
bonding, and antibonding biexciton are taken into account.