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
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
t must be long enough!
restoring force field!!
When |q| decreases, the restoring force decreases too.
For 2DES in GaAs/AlGaAs, n2D=3x1011 cm-2, 2p/|q| =10um, fp=100GHz.
The restoring force is enhanced by the magnetic field.
Edge magnetoplasma (EMP) in a finite 2DES
Confinement potential may affect the group velocity of the edge electrons.
Scattering between the bulk 2D and the edge may damp the oscillation.
EMP is in the RF or microwave frequency range.
First Observation of EMP
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
JEPT Lett., 42, 557 (1985)
depend on the details of the confinement potential.
depend on the scattering and interactions.
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.
Landau level spacing
JEPT Lett., 57, 587 (1993)
For wt>>1, L>>W
For wt<<1, L>>W
Edge-magnetoplasmon excitations in GaAs-AlxGa1-xAs QWs
I. Grodnensky, D. Heitmann, K. v. Klitzing, K. Ploog, A. Rudenko, and A. Kamaev
,PRB, 49, 10778-10781 (1994).
Detection by Coplanar Waveguide (CPW) Sensors
The CPW is patterned by
There are about 60 alignment keys along the CPW.
Quantum wire array is patterned by e-beam lithography.
Detection by Phase-Locked Loops (PLL)
f0 =f1+ fs =b1l1+bs(B)ls
Df0 =0=Df1+Dfs(B) =Db1l1+Dbs(B)ls
Sample under detection
B: the parameter (magnetic field) sweeping in the experimentu: phase velocity of the signal in coaxial cable
Pulsed Microwave PLL and Gated Average System
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%).
A homemade PLL-MW system
Comparing with commercial vector meters
Observation of EMP in a QW array
About 7000 QWs (0.7μm×20μm) in the gaps of CPW
2 1 2/3
2 1 2/3
Result for a 2DES
SdH oscillation is screened by EMP!!!
No SdH peaks were detected
in this region.
Polarizability or susceptibility