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Photoluminescence-excitation spectra of a doped single
quantum wire near metal-insulator crossover
Toshiyuki Ihara1, Y. Hayamizu1, M.Yoshita1, H. Akiyama1, L. N. Pfeiffer2 and K.W. West2
1
Institute for Solid State Physics, University of Tokyo and CREST, JST, Chiba 2778581, Japan
2
Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, USA
Abstract. We measured photoluminescence-excitation spectra at 5K on an n-type modulation-doped single quantum
wire with a gate to tune electron densities. We found drastic transfer of oscillator strength from excitons to trions. At
higher electron densities, double absorption peaks corresponding to the band edge and the Fermi edge are observed.
These anomalies show bound-state formation and carrier population in inverse-square-root density of states inherent to
one-dimensional systems.
Optical spectroscopy of doped quantum structures
have provided intriguing subjects in fundamental
physics, such as the Burstein-Moss shift between
photoluminescence (PL) and absorption reflecting
Fermi electron distribution and Pauli exclusion
principle, the trion state formed as a bound state of two
electrons and a hole, metal-insulator crossover, Fermiedge singularity and other many-body effects [1]. In
particular, effects of low dimensionality in these
phenomena have attracted strong interests, and
intensive research has been made in two-dimensional
(2D) quantum wells [2].
In 1D quantum wires, there have been several
reports predicting or finding novel 1D features induced
by the inverse-square-root density of state (DOS),
singular 1D Coulomb interactions, and 1D collective
excitation effects [3]. However, the difficulty in
fabrication of high-quality quantum wires has
prevented us from a detailed study on 1D system,
since the band bottom singularity can be easily
smoothed by sample disorders. In addition, the small
volumes of quantum wire make it difficult to measure
the absorption or excitation spectra that directly reflect
the oscillator strength. Therefore, many of the subjects
of fundamental interests are still left open, and most of
the earlier predictions and findings need experimental
verification or further confirmation.
Recently, we improved the quality of T-shaped
GaAs
quantum
wires,
and
measured
photoluminescence excitation (PLE) spectra of nondoped multiple quantum wires with high spectral
resolutions [4]. We observed the pronounced OS
concentration into the lowest bound state, as well as
the reduction of the absorption at the continuum state,
i.e., the 1D DOS divergence does not appear at the
continuum absorption edge. We interpreted this feature
as a result of Coulomb interaction between an electron
and a hole, which is consistent of the earlier theoretical
predictions [5].
On another front, we also fabricated a high-quality
n-type modulation doped quantum wire with a gate to
tune the density of one-dimensional electron gas. In
the previous paper, we demonstrated the evolution of
PL spectra during metal-insulator crossover where a
trion PL peak evolves to a broad PL peak due to bandto-band transition [6].
In this letter, we report on the PL and PLE spectra at
various electron densities (ne) in an n-type doped
single quantum wire with a gate. The PLE spectra
show a drastic OS transfer from excitons to trions with
increasing ne from zero, which can be interpreted as a
nature of 1D system where the OS concentrates into
the lowest bound state. At higher ne, we observed the
metal-insulator crossover where the trion peak evolves
to the typical single absorption onset of the band-toband transition. In this crossover region, we found a
double absorption peak structure corresponding to
Fermi edge at low temperature and inverse-square-root
divergence of 1D DOS at band edge.
The sample structure of n-type doped GaAs
quantum wire is illustrated in the inset of Fig.1. The Tshaped quantum wire is formed at the cross sectional
area of 14nm Al0.07Ga0.93As - Al0.33Ga0.67As quantum
well (stem well) and 6 nm GaAs - Al0.45Ga0.55As
quantum well (arm well). The modulation doping of Si
at the spacer distance of 100nm from the stem well
results in the formation of 2D electron gas with the
density of 1x10^11cm-2 in the stem well. By applying
DC gate voltage (Vg) to the gate layer on the top of
arm well relative to 2D electron gas in the stem well,
we can tune the electron concentrations in 1D wire and
also in 2D arm well. The detailed conformation of this
sample is shown in ref. [6].
In our micro-PL and PLE measurements, the
excitation light from a continuous wave Titaniumsapphire laser was polarized to (001) direction, which
was perpendicular to the wire axis, and was focused
into a 1 m spot by a 0.5 numerical aperture objective
lens on the top (110) surface of the sample. The
emission to the direction of (001) was detected by a
0.5 numerical aperture objective lens via a polarizer of
(-110) direction so as to cut the intense laser scattering.
(1.566eV) and broad peak at higher energy (1.570eV).
At Vg=0.7V, we observe a broad absorption onset
(FE) that has long tail at low-energy side. The
absorption of the arm well is so large that we cannot
remove its low-energy tail at 1.580eV.
In the PL spectra at low ne (0-0.15V), we observed
sharp excitonic emission at the energy of both X and
X-. As ne increases, X- evolves into the broad PL peak
whose low energy shoulder (BE) shows red-shift. We
have demonstrated the evolution of PL spectra in a
previous paper [6].
In order to give a rough assignment of the spectral
structure at high ne, we make a theoretical calculation
of free particle approximation, neglecting the manybody interaction. We take into account joint density of
state (Dj), Fermi distribution for electrons (fe) and
holes (fh), and Lorenzian convolution with
phenomenological broadening (L). Using these terms
on the effective mass approximation, the emission (I)
and absorption (A) spectra are given by following
equations.
I     D1j D   f e  e  f h  h L   E g   d
A    D1j D  1  f e  e L   E g   d
where
FIG. 1 Normalized experimental (a) and theoretical
(b) spectra of photoluminescence (PL:dotted lines)
and PL excitation (PLE:solid lines) for 1D quantum
wire at various electron density.
Note we have checked that this experimental setup
does not change the lineshape of optical spectra shown
in this paper, but significantly reduces the background
noise of PLE spectra.
Fig.1 (a) shows the normalized PL (dotted lines) and
PLE (solid lines) spectra at various gate voltages (Vg)
measured on 1D quantum wire at 5K. At first, we
demonstrate the evolution of PLE spectra with
increasing ne. At Vg=0V, where ne is very low, we
observe a sharp absorption peak at 1.569eV (X) with
FWHM of 0.9meV, which is assigned as neutral
excitons. The splitting of X peak is probably due to the
inhomogeneous monolayer fluctuations of the stem
well. As ne increases with applying gate voltage, X
moves to higher energy showing drastic quenching.
Instead, a new absorption peak (X-) appears at almost
2meV below X, which we assigned as negatively
charged excitons (trions). At Vg=0.2V, X becomes
undetectable, and asymmetric X- peak completely
dominates the PLE spectrum. At much higher Vg, a
new broad peak appears from the high-energy tail of
X-, which results in a characteristic double peak
structure (0.35V) of sharp onset at the lowest energy
 e ,  h are
the kinetic energy of electrons and
holes, respectively, and    e   h  (1  me / mh ) e .
We assumed the band gap energy (Eg) as a constant,
and calculated the spectra as a function of photon
energy (  ).
Fig.1 (b) shows the normalized emission (dotted
lines) and absorption spectra (solid lines) calculated
for 1D system at various electron density with the
parameter of =0.2meV, me=0.067m0, and
mh=0.105m0, and Te=Th=8K. The electron density
was calculated by following relation.
ne   De1D  e  f e  e d e  
1

2me
2
1
e
f e  e d e
While the emission peak stays at band edge (the
energy of Eg), the absorption spectra show dramatic
evolution from the sharp peak at band edge at low ne
(5.2x104) to the broad onset at Fermi edge of 8K at
high ne (5.8x105).
The good agreements between measured PLE and
calculated absorption spectra lead us to the following
conclusion: First, the FE onset observed at high ne
(0.7V) corresponds to the absorption at Fermi edge at
low temperature (5K). Next, the low energy shoulder
of PL peak (BE) at high ne, which evolves smoothly
from X- peak, corresponds to band edge. Finally, the
double peak observed at the crossover region (0.35V)
corresponds to the coexistence of absorption at band
edge and Fermi edge. We believe this is the first
observation of the characteristic double peak feature
corresponding 1D DOS singularity and Fermi edge.
Note that these interpretations have been confirmed
by the measurement of temperature dependence of
optical spectra. In that experiment, we found that, as
the temperature increases, FE onset loses its amplitude
FIG. 2 (a) The position of peaks, (b) X - X- energy
gap and Fermi energy, and (c) PLE maximum
intensity
measured for 1D wire are plotted as a
function of gate voltage. The same plots for 2D arm
well are shown in (d), (e) and (f).
and the absorption at band edge appears, i.e., BursteinMoss shift disappears. The temperature dependence of
PLE spectra will be reported elsewhere.
The calculation we made in this paper neglects the
all kinds of many-body effects. This is why it cannot
reproduce the sharp excitonic absorption peaks due to
bound states (X, X-) observed at low ne. By the same
reason, the theoretical emission spectra at high ne are
inconsistent with the experimental PL spectra where
we observed significant red shift of low energy
shoulder (BE) and broadening with increasing ne. The
red shift of BE shoulder with 2meV from the position
of X- peak corresponds to the shrinkage of band gap
energy due to the many-body effect known as Band
Gap Renormalization [7]. The origin of the increase of
half-width-of-half-maximum of PL peak from 0.5meV
(at 0.2V) to 2meV (at 0.7V) is currently not
understood. We should notice that the sharp emission
peak of calculated spectrum in Fig.1 (b) results from
the small value of  (0.2meV), which is chosen to
reproduce the double absorption peak structure at
Vg=0.35V markedly.
Quantitative plots of experimental results for 1D
system are presented in the left side of Fig.2. The
bottom figure (a) gives the main PLE peak energy of
X (solid circles), X- (solid triangles), FE (solid
squares), and the PL energy of BE shoulder (blank
squares) as a function of gate voltage. Fig.2 (b) plots
the energy separation X-X- (solid inverse-triangles)
and Fermi energy (blank inverse-triangles) estimated
FIG. 3 Normalized experimental (a) and
theoretical (b) spectra of PL (dotted line) and PLE
(solid line) for 2D arm well at various electron
density.
by the calculation from the corresponding electron
density shown in Fig.1 (b) using the following relation.
 2  2 ne 2
Ef 
8me
We also plot the PLE maximum ratio of X (solid
circles), X- (solid triangles) and FE (solid squares) in
Fig.2 (c).
With these results for 1D system in mind, we will
now take a look at the results for 2D system. Since 2D
electron gas is formed in the arm well (one of the
quantum well composing T-shaped quantum wire), we
can measure the optical spectra of 2D system by
changing the position of sample as illustrated in the
inset of Fig.3.
Figure 3 (a) shows normalized PL (dotted lines) and
PLE (solid lines) spectra measured for 2D electron
system in the arm well, and (b) shows the theoretical
calculation of the free particle approximation with
step-functional 2D DOS. In the same way as 1D
system, we plot, in the right side of Fig.2, (d) the peak
energy of PL and PLE, (e) the X,X- splitting and
Fermi energy, and (f) ratio of PLE maximum value as
a function of gate voltage.
From the PLE spectra measured for 2D system, we
found following: First, there are always two absorption
peaks in the presence of 2D electron gas (at Vg=0.30.8V): the peak which evolves from X and that from
X-. As ne increases, the OS transfers gradually from X
to X-, and the splitting of X and X- increases
nonlinearly from 1.5meV to 8meV. Second, the
evolution from X- to FE occurs smoothly by single
peak with increasing ne. FE shows typical
asymmetrical peak line shape that is not consistent of
the free-particle calculation shown in the top line of
Fig.3 (b).
These results for 2D system, especially the
asymmetrical peak at FE, remind us the many-body
enhancements known as Fermi edge singularity.
Indeed, the observed evolution of optical structures is
analogous to the numerical calculation including FES
effect and also electronic spin effect [8]. The fact that
these FES theories appear to agree with the measured
optical properties of 2D electron system has been
verified by several experiments by other groups [9].
In 1D system, however, the evolution of PLE
spectra shows a slightly different story. Now, let us
discuss the difference between results of 1D system
and those of 2D system, focusing on the PLE spectra.
The sharp excitonic peaks (X, X-) observed at low
ne for both 1D and 2D system show interesting
differences of dimensionality. In 1D system, we
observe drastic OS transfer from X to X- with
increasing ne, and X- completely dominates the PLE
spectrum at 0.2V. In 2D system, on the contrary, X
peak is still detectable at high ne, and there are no
ranges of ne where X- completely dominates the
spectrum. This difference is observed for the first time
and provides us an answer to the fundamental
question ”How are the bound states formed in the
presence of 1D (2D) electron gas? ” as discussed
below.
In theoretical terms, the exciton has to be orthogonal
to all the lower-lying three-particle states [10]. As ne
increases, the available unoccupied states for the
exciton formation decrease due to phase-space filling.
This occurs significantly in 1D system, because the
amount of DOS at large wave number is small due to
the inverse-square-root divergence feature. Thus, X of
1D system loses its intensity drastically with
increasing ne compared to that of 2D system. In other
words, the enhancement of OS of trion state in 1D
system can be interpreted as the OS concentration into
the lowest ground state resulted from 1D DOS
singularity.
The crossover region from X- to FE reflects the
difference of DOS more directly. In 1D system, we
observe a characteristic double peak structure
corresponding band bottom singularity and Fermi edge.
In 2D system, the evolution from X- to FE occurs
smoothly by single peak with increasing ne, which is
consistent with the fact that band bottom of the stepfunctional 2D DOS does not have such a sharp
singularity as 1D case.
It is surprising that we succeed to observe the
divergence feature of 1D DOS so clearly in the optical
spectrum. To our knowledge, the 1D DOS singularity
has not been observed directly in experiments so far,
because this anomaly could disappear due to the
inhomogeneous broadening, and also due to the
Coulomb interaction between electron and hole [5].
Indeed, because of the Coulomb-induced origin, the
PLE spectrum measured for non-doped quantum wires
of high quality shows a reduction of the absorption at
the continuum state, i.e., the Sommerfeld factor is less
than 1 in 1D system [4]. We guess that the screening
effect of Coulomb interaction due to the doped
electron gas plays an important role for the
observation of 1D DOS without Coulomb-induced
modification.
Equally striking is that Fermi edge enhancement due
to many-body effects in 1D system seems weaker than
that in 2D system. In other words, the PLE spectra of
1D system at high ne show good agreement with the
free-particle calculation, while those of 2D system are
not consistent. This result contrasts with the widely
used interpretation that the FES effect should become
significant in 1D system due to larger many-body
interaction induced by 1D confinement and also due to
smaller hole recoil effects [11]. It is currently unclear
for us what causes the weak FES effect in 1D system.
We need further investigations.
In summary, we measured the PL and PLE spectra
on an n-type doped single quantum wire with a gate to
tune the electron density. We observed drastic OS
transfer from excitons to trions with increasing ne,
which results from 1D character that OS concentrates
into the lowest bound state. Furthermore, we found
characteristic double peak structure near metalinsulator crossover. We interpret this double peak
corresponds to the coexistence of Fermi edge and the
inverse-square-root divergence of 1D DOS at the band
edge, and confirm this conclusion by the comparison
with free-particle calculation and also with the results
for 2D system.
This work was partly supported by a Grant-in-Aid
from the Ministry of Education, Culture, Sports,
Science, and Technology, Japan.
[1]未定
[2]未定
[3]未定
[4] Akiyama et al. App. Phys. Lett. 82, 379 (2003), Itoh et al.
App. Phys. Lett. 83, 2043 (2003).
[5] Ogawa et al. Phys. Rev. B 43, 14325 (1991), Rossi et al.
Phys. Rev. Lett. 76, 3642 (1996).
[6] Akiyama et al. Solid State Commun. 122, 169 (2002).
[7]未定
[8] Hawrylak et al. Phys. Rev. B 44, 3821 (1991), Takagiwa
et al. J. Phys. Chem. Solids 63, 1587 (2002).
[9] Huard et al. Phys. Rev. Lett. 84, 187 (1999), Yusa et al.
Phys. Rev. B 62, 15390 (2000), Kaur et al. Phys. Status
Solidi B 178, 465 (2000).
[10] Esser et al. Phys. Status Solidi B 227, 317 (2001)
[11] Calleja et al. Solid State Commun. 79, 911 (1991)
＜以下、文献選びのためのメモ書き。＞
関連の強い文献。
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3 \\duke\temp\toshi_soft\pdf\Huard_PRL_84_187.pdf
4 \\duke\temp\toshi_soft\pdf\Yusa_PRB_62_15390.pdf
5 \\duke\temp\toshi_soft\pdf\Fritze_PRB_48_4960.pdf
7 \\duke\temp\toshi_soft\pdf\Hawrylak_PRB_44_3821.pdf
8 \\duke\temp\toshi_soft\pdf\Ogawa_PRL_68_3638.pdf
9 \\duke\temp\toshi_soft\pdf\Rodriguez_PRB_47_1506.pdf
10 \\duke\temp\toshi_soft\pdf\Ruckenstein_PRB_35_7551.pdf
11 \\duke\temp\toshi_soft\pdf\Akiyama_SSC_122_169.pdf
15 \\duke\temp\toshi_soft\pdf\Oberli_PhysicaE_11_224.pdf
17 \\duke\temp\toshi_soft\pdf\Takagiwa_JPCS_63_1587.pdf
18 \\duke\temp\toshi_soft\pdf\Kaur_PSSa_178_465.pdf
22 \\duke\temp\toshi_soft\pdf\Skolnick_PRL_58_2130.pdf
25 \\duke\temp\toshi_soft\pdf\Mueller_PRB_42_11189.pdf
27 \\duke\temp\toshi_soft\pdf\Melin_PRL_85_852.pdf
37 \\duke\temp\toshi_soft\pdf\Finkelstein_PRL_74_976.pdf
47 \\duke\temp\toshi_soft\pdf\Delalande_PRL_59_2690.pdf
50 \\duke\temp\toshi_soft\pdf\Ogawa_PRB_43_14325.pdf
51 \\duke\temp\toshi_soft\pdf\Ogawa_PRB_44_8138.pdf
54 \\duke\temp\toshi_soft\pdf\Rossi_PRL_76_3642.pdf
57 \\duke\temp\toshi_soft\pdf\DasSarma_PRL_84_2010.pdf
59 \\duke\temp\toshi_soft\pdf\Rinaldi_PRB_59_2230.pdf
69 \\duke\temp\toshi_soft\pdf\Akiyama_JPCM_10_3095.pdf
90 \\duke\temp\toshi_soft\pdf\Kalt_PRB_40_12017.pdf
145 \\duke\temp\toshi_soft\pdf\Akiyama_APL_82_379.pdf
159 \\duke\temp\toshi_soft\pdf\Itoh_APL_83_2043.pdf
203 \\duke\temp\toshi_soft\pdf\Stebe_PRB_58_9926.pdf
208 \\duke\temp\toshi_soft\pdf\Stebe_SAM_5_545.pdf
255 \\duke\temp\toshi_soft\pdf\Brown_PRB_56_3937.pdf
352 \\duke\temp\toshi_soft\pdf\Esser_PSSb_227_317.pdf
353 \\duke\temp\toshi_soft\pdf\Stopa_PRB_63_195312.pdf
354 \\duke\temp\toshi_soft\pdf\Combescot_SSC_128_273.pdf
357 \\duke\temp\toshi_soft\pdf\esser_PSSa_178_489.pdf
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\\duke\temp\toshi_soft\pdf\Otterburg_PRB_71_033301.pdf
379 \\duke\temp\toshi_soft\pdf\Cox_PRB_69_235303.pdf
393 \\duke\temp\toshi_soft\pdf\Raraport_PSSb_227_419.pdf
396 \\duke\temp\toshi_soft\pdf\Brunhes_PRB_60_11568.pdf
415 \\duke\temp\toshi_soft\pdf\Tischler_PRB_66_081310.pdf
※ そのほか、重要な参考文献の内容
①
Trion は低次元系で束縛エネルギーが増加して、
顕著に観測されるものであり[Stebe208]、一次元
系の方がより観測されやすいという指摘もある
[Combescot354]。
②
Trion を介した Metal-Insulator crossover は、低
次元電子系で顕著に観測されるものであることが
理論的に指摘されている[Stebe208, Combescot354,
Takagiwa17, Esser352, hawrylak7]。実験的には、
量子井戸に形成される二次元電子系で観測されて
いる[Huard3, Yusa4, Kaur18, Finkelstein37, cox379]。
③
多体効果の次元性の影響は興味深く、様々に議
論されている。特に trion 理論・FES 理論が注目
されている。
・一次元の trion の理論 Esser352、
・一次元の FES の理論 Ogawa8, Hawrylak13
・二次元・三次元の trion の理論 Stebe203
・一次元の trion の実験 akiyama11, otterburg365
・ 一 次 元 の FES の 実 験 akiyama11, Oberli15,
calleja12, Fritze5
次元性の影響を調べるに当たって、多体効果が
温度や正孔質量、higher subband に対して非常に
敏感である点は無視できない。これは実験的
[Melin27, Skolnick17, Brown255, Esser357]にも、理
論 的 [Hawrylak7, Ruckenstein10, Mueller25,
Rodigues9]にも指摘されている点である。試料品
質や測定条件をできる限り同じにして 1D・2D を
測定することは重要であると考える。
④
そのほか、
・ Weak BGR in 1D electron system [Cingolani59,
Stopa353]
・2D では X+X-の振動子強度が一定となる実験結
果[Cox379]
・X-の Line shape analysis ：低エネルギー側に多
体効果が現れる[Esser352, Esser357]
などとの関連も興味深い