High-Frequency Dynamic Magnetotransport Properties of Quantum Wires
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High-Frequency Dynamic Magnetotransport Properties of Quantum Wires. 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

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High-Frequency Dynamic Magnetotransport Properties of Quantum Wires

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) , aB. C. Lee (李秉奇),cand 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

1


OUTLINES Quantum Wires

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

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

  • EMP excitations in quantum-wire array

  • Conclusions

2


3D plasma Quantum Wires

charge flow

t must be long enough!

restoring force field!!

dispersion:

3


2D plasma Quantum Wires

l

~p/|q|

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

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

4


2D magnetoplasma Quantum Wires

~p/|q|

B

The restoring force is enhanced by the magnetic field.

5


Edge magnetoplasma (EMP) in a finite 2DES Quantum Wires

sxx

sxy

B

EXB drift

EF

E

B

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

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

e-

B

E

EMP is in the RF or microwave frequency range.

6


First Observation of EMP Quantum Wires

Observation of Bulk and EMP in two dimensional electron fluid

D. B. Mast, A. J. Dahm, and A. L. Fetter, PRL 54, 1706-1709 (1985)

B = 0

B ≠ 0

A 2DES on the surface of

Liquid Helium placed in a

perpendicular B-field.

7


JEPT Lett., Quantum Wires42, 557 (1985)

depend on the details of the confinement potential.

depend on the scattering and interactions.

8


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

wc

Edge Channels

Landau level spacing

9


JEPT Lett., study EMPs. EMP is also a very unique tool for studying the edge states of QHEs. 57, 587 (1993)

10


For study EMPs. EMP is also a very unique tool for studying the edge states of QHEs. wt>>1, L>>W

For wt<<1, L>>W

11


Edge-magnetoplasmon excitations in GaAs-Al study EMPs. EMP is also a very unique tool for studying the edge states of QHEs. xGa1-xAs QWs

I. Grodnensky, D. Heitmann, K. v. Klitzing, K. Ploog, A. Rudenko, and A. Kamaev

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

540nm×4.5mm

12


Detection by Coplanar Waveguide (CPW) Sensors study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

The CPW is patterned by

photolithography.

There are about 60 alignment keys along the CPW.

Quantum wire array is patterned by e-beam lithography.

13


T =0.3K study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

Detection by Phase-Locked Loops (PLL)

f0 =f1+ fs =b1l1+bs(B)ls

Df0 =0=Df1+Dfs(B) =Db1l1+Dbs(B)ls

fs=bsls

PLL system

phase=f1=b1l1

sample

known

Sample under detection

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

Type-II PLL

14


Pulsed Microwave PLL and Gated Average System study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

Schematicof 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%).

1.

2.

(mixers)

15


A homemade PLL-MW system study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

(50M-21GHz)

16


Comparing with commercial vector meters study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

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

  • The resolutions achieved here are better than 0.005% (0.0087dB) for amplitude variation and 0.001O for phase with a very low-average power (about -100dBm) into the sample.

T=0.3K

17


Observation of EMP in a QW array study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

About 7000 QWs (0.7μm×20μm) in the gaps of CPW

2 1 2/3

(a)

2 1 2/3

(b)

Result for a 2DES

18


Landau level study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

filling factor

2

1

3

4

4

2

1

3

1.91GHz

133MHz

19


Landau Level study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

Filling Factor

1

2

3

4

The peak-positions

T=0.3K

SdH oscillation is screened by EMP!!!

No SdH peaks were detected

in this region.

20


21 study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.


adsorption study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

phase

22


Polarizability or susceptibility study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

wj

w(f)

23


24 study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.


25 study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.


Sample A study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

700nm

MW

B

20mm

26


Sample B study EMPs. EMP is also a very unique tool for studying the edge states of QHEs.

B

MW

20mm

700nm

27


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

  • 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.

  • We measured the polarizability of a QW array.

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