Band-edge divergence and Fermi-edge singularity in an n-type doped quantum wire. Toshiyuki Ihara Ph.D student of Akiyama group in Institute for Solid State Physics, University of Tokyo and CREST, JST, Chiba , Japan ’06 EPFL Switzerland

Members in Akiyama Laboratory 秋山 英文 Hidefumi AKIYAMA 吉田 正裕 Masahiro YOSHITA 劉 舒曼 Liu Shu-man 安東 頼子 Yoriko ANDO 伊藤 弘毅 Hirotake ITOH 井原 章之 Toshiyuki IHARA 稲田 智志 Satoshi INADA 岡田 高幸 Takayuki OKADA 岡野 真人 Makoto OKANO 宗像 孝光 Takamitsu MUNAKATA

Recent research topics 1D many-body systems Firefly (Lightning bug) T-wire Laser Quantum wire laser action by electro- and optical-excitation Optical response of low-dimensional many-body systems Bioluminescence quantum-efficiency measurement

What is T-shaped quantum wire ? Benefit Size controllability High quality Weak point Small confinement Difficult fabrication T-shaped quantum wire is made of two quantum wells (Arm well & Stem well) grown by molecular beam epitaxy

Our experiments on quantum wires Micro-PL and resonant PLE measurements Waveguide transmission measurements Lasing by electro- and optical- excitation Single / Multi T-wire with optical waveguide n-type doped single T-wire with FET structure sample measurement

Our experiments on quantum wires Micro-PL and resonant PLE measurements Waveguide transmission measurements Lasing by electro- and optical- excitation Single / Multi T-wire with optical waveguide n-type doped single T-wire with FET structure sample measurement

Band edge and Fermi edge in the optical spectra “Band-edge peak” and/or “Fermi-edge peak” appears in the spectra !? Without many-body effectsWith Fermi-edge singularity effect G. D. Mahan, Phys. Rev. 153, 882 (1967). Both experimental and theoretical investigations have reported since early 90’s.

Sample structure of n-type doped T-wire ＜ fabrication ＞ MBE with cleaved edge overgrowth method ＜ size of wire ＞ 14 x 6nm x 4mm(single) ＜ doping ＞ ① Si modulation doping ② FET gate structure →tunable electron density ＜ measurement ＞ Temperature-elevated micro-PL spectra & resonant PLE spectra

Result at high electron density High electron density : 6x10 5 cm -1 Cryostat temperature : 5K (Estimated temperature : 10K) ’04 T. Ihara et. al. We observed the Fermi-edge absorption onset with small FES enhancement

Comparison with Oberli ’ s experiments D. Y. Oberli et al, Physica E 11, 224 (2001).

What if we change temperature and electron density ? Higher temperature Lower temperature Band-edge absorption ? Band gap renormalization ? Metal-Insulator crossover ? Bound states ? 1D screening ? Low density Band-edge absorption ? Fermi edge singularity ? Band edge & Fermi edge induced by 1D DOS and Pauli Blocking

Results : PL and PLE spectra at various temperature - Same energy with PL peak. - Good agreements with calculations. - Characteristic of 1D electron systems Temperature high low A sharp absorption peak (BE) appears. Fermi-edge absorption onset (FE) appears. Sharp absorption peak at 50K Band-edge absorption peak induced by 1D DOS divergence !! T=50K (k B T/E f ～ 1) non-degenerate 1DEG T=5K (k B T/E f ～ 0.1) degenerate 1DEG ※ Electron density : 6x10 5 cm -1

Results : PL and PLE spectra at various electron density at T=5K Sharp band-edge absorption appears at n e = 1.5x10 5 cm -1 ～ 3x10 5 cm -1 Discrete symmetrical peaks appear only at low densities ( n e < 1.5x10 5 cm -1 ) Electron density high low n e =6x10 5 cm -1 ～ 3x10 5 cm -1 degenerate 1DEG (k B T/E f < 0.5) -Fermi edge absorption onset -Band edge emission -Band gap renormalization n e =3x10 5 cm -1 ～ 1.5x10 5 cm -1 non-degenerate 1DEG (k B T/E f > 0.5) Sharp band-edge absorption n e < 1.5x10 5 cm -1 Discrete peaks of bound states

Summary 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. When the dense 1D electron gas is degenerate at a low temperature, we observe a band-edge emission peak and a Fermi-edge absorption onset with small FES effect. Further investigations - Trion / Band-edge problem - PL and PLE measurement at lower temperature ( ～ 1K) - Contrast with 2D electron systems.