Band-edge divergence and Fermi-edge singularity in an
n-type doped T-shaped quantum wire
T. Ihara1, 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 studied photoluminescence-excitation (PLE) spectra of one-dimensional (1D) electron systems in an ntype modulation-doped single quantum wire at various temperatures from 5K to 50K. At low temperature (5K), we
observed a single absorption onset, which corresponds to the Fermi edge of degenerate 1D electron gas. As the
temperature was increased, this Fermi-edge absorption onset disappeared, while another absorption onset appeared at
lower energy, which became a sharp peak at 50K. We assigned this peak to the 1D band-edge absorption induced by the
inverse square root divergence of 1D density of states (DOS).
Keywords: Quantum wires; Electron density of states; Photoluminescence; Fermi-edge singularity
PACS: 73.21.Hb, 73.20.At, 78.67.Lt, 78.55.Cr
INTRODUCTION
SAMPLES AND EXPERIMENTS
Band-edge divergence of one-dimensional (1D)
density of states (DOS) is one of the intriguing
characters of 1D electron systems formed in an n-type
doped quantum wire. One of the earlier theories [1]
predicted that, in the presence of degenerate 1D
electron gas, the optical spectra exhibit a sharp bandedge peak induced by 1D DOS divergence with manybody Coulomb enhancements near the Fermi edge
(Fermi edge singularity; FES). While experimental
investigation of FES has been reported [2], the
appearance of the band-edge divergence has not been
verified yet. In this work, we study the temperatureelevated photoluminescence (PL) and PL-excitation
(PLE) spectra of 1D electron systems formed in an ntype doped T-shaped quantum wire.
Fig.1 shows the sample structure of an n-type
doped GaAs quantum wire. Cleaved-edge overgrowth
with molecular beam epitaxy and growth interrupt
annealing were used to fabricate the single quantum
wire sample with a 14nm x 6nm cross-sectional size
[3]. The electron density of the wire can be tuned by
applying gate voltage (Vg). Micro-PL and PLE
measurements on the wire were performed with a
excitation from cw titanium-sapphire laser with a 1m
spot size. The direction of PL detection was
perpendicular to the laser excitation and their
polarization were orthogonal to each other to improve
signal-to-noise ratio.
RESULTS AND DISCUSSION
FIG. 1 Schematic view of n-type doped quantum
wire sample.
Solid curves in Fig. 2 indicate normalized PLE
spectra at various temperatures in the presence of
dense 1D electron gas. The gate voltage was fixed to
0.7V, which corresponds to the electron density of
about 6 x 105 cm–1 in the quantum wire. At low
temperature (5K), we observed a single absorption
onset at 1.575eV with a long low-energy tail. We
assigned this onset as the Fermi edge (FE), which
separates the occupied and unoccupied state in the
conduction band. A large absorption by the arm well
showed its low-energy tail at around 1.578eV. As the
FIG. 2 Normalized PL (dotted curves) and PLE
(solid curves) spectra of 1D electron gas at various
temperatures. BE and FE corresponds to the band
edge and Fermi edge, respectively.
temperature was increased, the FE onset was smeared
and another absorption onset was formed at 1.565eV.
At 50K, this onset increased its intensity and formed a
sharp peak structure. We assigned this peak to the
band-edge (BE) van Hove singularity induced by the
inverse square root 1D-DOS divergence.
Normalized PL spectra are shown in Fig. 2 by
dotted curves. At 5K, we observed an asymmetrical
broad PL peak at 1.565eV. We assigned this PL peak
to the band-edge emission. The energy gap of 10meV
between PL peak and PLE onset at FE corresponds to
Burstein-Moss shift. As the temperature was increased,
the PL peak shifted to lower energy without any
remarkable change in its lineshape. This red shift with
increasing temperature also appears in bulk GaAs. At
50K, we found that the PL and PLE peak appeared
exactly at the same energy of band edge denoted by
BE.
We also studied electron density dependence of
PLE spectra at low temperature (5K), using the same
sample of a doped quantum wire. The solid curves in
Fig. 3 indicate the normalized PLE spectra at various
Vg. The top line at Vg = 0.7V corresponds to the highdensity, which is the same as the bottom line of Fig. 2.
As we have already mentioned, the single absorption
onset (FE) at Vg = 0.7V corresponds to the Fermi edge.
As the density was decreased, the FE onset shifted to
lower energy. At Vg = 0.35V, band-edge absorption
peak appeared at low-energy side (1.5665eV), and a
characteristic double peak structure was formed. As
the density was further decreased, the Fermi edge peak
merge into the tail of the band-edge peak, and formed
FIG. 3 Normalized PL (dotted curves) and PLE (solid
curves) spectra of 1D electron gas at various gate
voltages.
a single asymmetrical absorption peak structure at Vg
= 0.2V.
The sharp absorption peak (BE) at 50K in Fig. 2
and the double peak structure at 0.35V in Fig. 3 are
surely characteristic of 1D electron systems. As we
have mentioned above, these structures can be
understood by the divergence of 1D DOS. In fact, the
band edge absorption of 2D electron systems exhibits
rather broader lineshape due to the step functional 2D
DOS.
CONCLUSION
Low-temperature PL and PLE spectra are studied
in an n-type modulation-doped T-shaped single
quantum wire with a gate to tune electron densities.
With non-degenerate 1D electron gas, band-edge
absorption exhibits a sharp band-edge-divergence of
1D density of states (DOS). When the dense 1D
electron gas is degenerate at a low temperature, we
observe a Fermi-edge absorption onset.
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