1140.120.11.120

Y. W. Suen ( 孫允武 ) ,a W. H. Hsieh( 謝文興 ),a,b S. Y. Chang ( 張紓語 ), b

L. C. Lee ( 李良箴 ) , b C. H. Kuan ( 管傑雄 ) , a B. C. Lee ( 李秉奇 ) , c and C. P. Lee ( 李建平 ) c

bDepartment of Physics, National Chung Hsing University, Taichung, Taiwan, R.O.C.

aDepartment of Electrical Engineering, National Taiwan University, Taipei, Taiwan, R.O.C.

cDepartment of Electronics Engineering, National Chiao Tung University, Sinchu, Taiwan, R.O.C

High-Frequency Dynamic Magnetotransport Properties of Quantum Wires

2140.120.11.120

OUTLINES

1. Introduction-- What is edge magnetoplasmon (EMP)?-- Previous works about EMP of low-dimensional electron systems (LDES’s).

2. Experimental setup-- Development of high-sensitive microwave vector detection system at an extremely low-power level.

3. EMP excitations in quantum-wire array

4. Conclusions

3140.120.11.120

3D plasma

restoring force field!!

charge flow

m

enp

2

D32dispersion:

2

22

10

31)(

p

Fp

qq

must be long enough!

2

q

4140.120.11.120

2D plasma

~/|q|

qm

enp

2

2D22

When |q| decreases, the restoring force decreases too.

Ej xx

For 2DES in GaAs/AlGaAs, n2D=3x1011 cm-2, 2/|q| =10um, fp=100GHz.

5140.120.11.120

2D magnetoplasma

~/|q|

xxxx Ej

Bxyxy Ej

m

eBq

m

encp

cpmp

22

D22

222

2

The restoring force is enhanced by the magnetic field.

6140.120.11.120

Edge magnetoplasma (EMP) in a finite 2DES

B

EFE

EXB

drift

B

B

PB

EP

f

1

~

BE

Scattering between the bulk 2D and the edge may damp the oscillation.

Confinement potential may affect the group velocity of the edge electrons.

EMP is in the RF or microwave frequency range.

e-

EB

xyxx

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First Observation of EMP

Observation of Bulk and EMP in two dimensional electron fluidD. B. Mast, A. J. Dahm, and A. L. Fetter, PRL 54, 1706-1709 (1985)

A 2DES on the surface ofLiquid Helium placed in aperpendicular B-field.

B ≠ 0

B = 0

BfEMP1

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B

il

pq

B

Oql

B

EMP

xx

xy

xyEMP

/1

Field-B strongIn

.2/

,/2

,/1

)1(2

ln2

),(

0

0

JEPT Lett., 42, 557 (1985)

depend on the details of the confinement potential.

depend on the scattering and interactions.

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Quantum Hall Effect (QHE) provides a very unique platform to study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

EF

Edge Channels

c

Landau level spacing

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JEPT Lett., 57, 587 (1993)

WELE

Ej

fjiji

yx

xy

/,/

0,0

1122

21

0)(

))((22

2221212

WL

f

L

f

Wi xyxxxx

11140.120.11.120

For >>1, L>>W

22

2

2

12

22

22212

0

2/1202,1

4

,)(

)1(

xyxx

xx

xyxx

fW

L

WL

f

i

Lm

ne

Wm

ne

clowcup

2

22//

212

222//

22222

,

/,

For 1, L>>W

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Edge-magnetoplasmon excitations in GaAs-AlxGa1-xAs QWsI. Grodnensky, D. Heitmann, K. v. Klitzing, K. Ploog, A. Rudenko, and A. Kamaev

,PRB, 49, 10778-10781 (1994).

540nm×4.5mm

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Detection by Coplanar Waveguide (CPW) Sensors

The CPW is patterned by photolithography.There are about 60 alignment keys along the CPW.

Quantum wire array is patterned by e-beam lithography.

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T =0.3K

Detection by Phase-Locked Loops (PLL)

Type-II PLL

Sample under detection

phase=1=11PLL system

s=ss

0 =1+ s =11

+s(B)s

0 =0=1+ s(B) =11+s(B)s

B: the parameter (magnetic field) sweeping in the experiment: phase velocity of the signal in coaxial cable

sample

known /1

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Pulsed Microwave PLL and Gated Average System

1.2.

(mixers)

Schematic of a homemade PLL system for microwave signals up to 18 GHz.

The phase resolution is about 0.001 degree even at very low average input power level (~ -100dBm).

A special designed homodyne amplitude detection scheme allows us to detect very small microwave adsorption (smaller than 0.005%).

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A homemade PLL-MW system(50M-21GHz)

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Comparing with commercial vector meters

T=0.3K

1. Better than a commercial VNA at an extremely low-power level !!

2. The resolutions achieved here are better than 0.005% (0.0087dB) for amplitude variation and 0.001

O for phase

with a very low-average power (about -100dBm) into the sample.

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0 2 4 6 8 10 0 2 4 6 8 10

0.2%

256MHz

0.2o

0.4%

548MHz

0.2o

0.1% 598MHz

0.2o

A

0.2% 831MHz

B (Tesla)

-

0.2o

B (Tesla)

Observation of EMP in a QW arrayAbout 7000 QWs (0.7μm×20μm) in the gaps of CPW

2 1 2/32 1 2/3(a) (b)Result for a 2DES

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0.2 0.4 0.6 0.8 1.0

0.5o

B-1 (Tesla-1)

0.2 0.4 0.6 0.8 1.0

0.5%

-1*

A

B-1 (Tesla-1)

1.91GHz

133MHz

Landau levelfilling factor321 4 321 4

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0 0.2 0.4 0.6 0.8 1.0

B-1 (Tesla-1)

f (G

Hz)

The peak-positions1 2 3 4 Landau Level

Filling Factor

No SdH peaks were detected in this region.

T=0.3KSdH oscillation is screened by EMP!!!

21140.120.11.120

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adsorption

phase

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Polarizability or susceptibility

22

2

)(

j

jf

m

eelectronic

2/1

2

2

0

0

2

2

)or (

E

VC

ZN

a

s

(f)j

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0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 5 6 7 8

0.0

0.5

1.0

1.5

2.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

A (%)

Lm3979C62004/04/14

f (G

Hz)

B (Tesla)

-1.6-1.5-1.4-1.3-1.2-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10

A (%)

f (G

Hz)

B-1 (Tesla-1)

-1.6-1.5-1.4-1.3-1.2-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10

22

2

2

12

22

22212

0

2/1202,1

4

,)(

)1(

xyxx

xx

xyxx

fW

L

WL

f

i

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B20m

700nm

-0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4

0.5%1.8G

0.4%3.1G

0.4%6.4G

2%

A

9.9G

0.5%

13.2G

3%14.2G

0.5%

B (Tesla)

17.5G

0.04o

0.2o

0.4o

1o

1o

2o

B (Tesla)

2o

MW

Sample A

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-0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4

0.2%9.05GHz

0.1%12.1GHz

0.1%12.5GHz

0.1%

A

13.5GHz

0.2%14.7GHz

0.1%

16GHz

0.5%

B (Tesla)

18GHz

0.2o

0.1o

0.5o

0.5o

1o

0.5o

B (Tesla)

0.5o

B

20m

700nm

MW

Sample B

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1. We observed EMP excitations in a QW array with a homemade very-high-sensitivity vector detection system.

2. The low-frequency part of the data can be explained by Mikhailov’s theory, while the high-frequency part exhibits a 2DES-like behavior. We mapped out the transition in between, which is not included in the simple theory.

3. We measured the polarizability of a QW array.