Band-edge divergence and Fermi-edge singularityBand-edge divergence and Fermi-edge singularity

in an n-type doped quantum wire.in an n-type doped quantum wire.

Toshiyuki IharaToshiyuki Ihara Ph.D student of Akiyama groupPh.D student of Akiyama group

in Institute for Solid State Physics, University of Tokyo and CREST, JST, Chiba in Institute for Solid State Physics, University of Tokyo and CREST, JST, Chiba 2778581, Japan2778581, Japan

’’06 08/02 @ EPFL Switzerland06 08/02 @ EPFL Switzerland

Members in Akiyama Members in Akiyama LaboratoryLaboratory

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 topicsRecent 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

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What is T-shaped quantum wire ?What is T-shaped quantum wire ?

BenefitSize controllability

High quality

Weak point Small confinement Difficult fabrication

T-shaped quantum wireis made of two quantum wells

(Arm well & Stem well)grown by

molecular beam epitaxy

Our experiments on Our experiments on quantum wiresquantum 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 Our experiments on quantum wiresquantum 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 spectraBand edge and Fermi edge in the optical spectra

“Band-edge peak” and/or “Fermi-edge peak” appears in the spectra !?

Without many-body effects With Fermi-edge singularity effect

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G. D. Mahan, Phys. Rev. 153, 882 (1967).

5.0

Both experimental and theoretical investigations have reported since early 90’s.

Sample structure of n-type doped T-wireSample structure of n-type doped T-wire＜ fabrication ＞

MBE with cleaved edge overgrowth method

＜ size of wire ＞

14 x 6nm x 4mm(single)

＜ doping ＞

①Si modulation doping②FET gate structure→tunable electron density

＜ measurement ＞

Temperature-elevated micro-PL spectra & resonant PLE spectra

Result at high electron Result at high electron densitydensityHigh electron density : 6x105 cm-1

Cryostat temperature : 5K(Estimated temperature : 10K)

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We observed the Fermi-edge absorption onset with small FES enhancement

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

What if we change temperature and electron What if we change temperature and electron density ?density ?

Higher temperature

Lower temperatureBand-edge absorption ?

Band gap renormalization ?Metal-Insulator crossover ?

Bound states ?1D screening ?

Low density

Band-edge absorption ?

Fermi edge singularity ?

Band edge & Fermi edgeinduced by 1D DOS and

Pauli Blocking

Results : PL and PLE spectra at various Results : PL and PLE spectra at various temperaturetemperature

- Same energy with PL peak. - Good agreements with calculations.- Characteristic of 1D electron systems

Tem

pera

ture

high

low

A sharp absorptionpeak (BE) appears.

Fermi-edge absorption onset (FE) appears.

Sharp absorption peak at 50K

Band-edge absorption peak induced by 1D DOS divergence !!

T=50K (kBT/Ef ～ 1)non-degenerate 1DEG

T=5K (kBT/Ef ～ 0.1)degenerate 1DEG

※ Electron density : 6x105 cm-1

Results : PL and PLE spectra at various electron density at Results : PL and PLE spectra at various electron density at T=5KT=5K

Sharp band-edge absorption appears at ne = 1.5x105cm-1 ～ 3x105cm-1

Discrete symmetrical peaks appear only at low densities (ne < 1.5x105cm-1 )

Ele

ctro

n de

nsity

high

low

ne=6x105cm-1 ～ 3x105cm-1

degenerate 1DEG (kBT/Ef < 0.5)

-Fermi edge absorption onset-Band edge emission-Band gap renormalization

ne=3x105cm-1 ～ 1.5x105cm-1

non-degenerate 1DEG (kBT/Ef > 0.5)

Sharp band-edge absorption

ne < 1.5x105cm-1

Discrete peaks of bound states

SummarySummary

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.