1. 140.120.11.120 1 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 b Department of Physics, National Chung Hsing University, Taichung, Taiwan, R.O.C. a Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, R.O.C. c Department of Electronics Engineering, National Chiao Tung University, Sinchu, Taiwan, R.O.C High-Frequency Dynamic Magnetotransport Properties of Quantum Wires

2. 140.120.11.120 2 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

3. 140.120.11.120 3 3D plasma restoring force field!! charge flow dispersion:  must be long enough!

4. 140.120.11.120 4 2D plasma ~  /|q| When |q| decreases, the restoring force decreases too. For 2DES in GaAs/AlGaAs, n 2D =3x10 11 cm -2, 2  /|q| =10um, f p =100GHz.

5. 140.120.11.120 5 2D magnetoplasma ~  /|q| B The restoring force is enhanced by the magnetic field.

6. 140.120.11.120 6 Edge magnetoplasma (EMP) in a finite 2DES B EFEF E EXB drift B 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-e- E B  xy  xx

7. 140.120.11.120 7 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) A 2DES on the surface of Liquid Helium placed in a perpendicular B-field. B ≠ 0 B = 0

8. 140.120.11.120 8 JEPT Lett., 42, 557 (1985) depend on the details of the confinement potential. depend on the scattering and interactions.

9. 140.120.11.120 9 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. EFEF Edge Channels cc Landau level spacing

10. 140.120.11.120 10 JEPT Lett., 57, 587 (1993)

11. 140.120.11.120 11 For  >>1, L>>W For  1, L>>W

12. 140.120.11.120 12 Edge-magnetoplasmon excitations in GaAs-Al x Ga 1-x As QWs I. Grodnensky, D. Heitmann, K. v. Klitzing, K. Ploog, A. Rudenko, and A. Kamaev,PRB, 49, 10778-10781 (1994). 540nm×4.5mm

13. 140.120.11.120 13 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.

14. 140.120.11.120 14 T =0.3K Detection by Phase-Locked Loops (PLL) Type-II PLL Sample under detection phase=  1 =  1 1 PLL system  s =  s s  0 =  1 +  s =  1 1 +  s (B) s  0 =0 =  1 +   s (B) =  1 1 +  s (B) s B: the parameter (magnetic field) sweeping in the experiment  : phase velocity of the signal in coaxial cable sample known

15. 140.120.11.120 15 Pulsed Microwave PLL and Gated Average System 1.1. 2.2. (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%).

16. 140.120.11.120 16 A homemade PLL-MW system (50M-21GHz)

17. 140.120.11.120 17 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.

18. 140.120.11.120 18 Observation of EMP in a QW array About 7000 QWs (0.7μm×20μm) in the gaps of CPW 2 1 2/3 (a)(a) (b)(b) Result for a 2DES

19. 140.120.11.120 19 1.91GHz 133MHz Landau level filling factor 3 2 1 4 3 2 1 4

20. 140.120.11.120 20 The peak-positions 1234 Landau Level Filling Factor No SdH peaks were detected in this region. T=0.3K SdH oscillation is screened by EMP!!!

21. 140.120.11.120 21

22. 140.120.11.120 22 adsorption phase

23. 140.120.11.120 23 Polarizability or susceptibility (f)(f) jj

24. 140.120.11.120 24

25. 140.120.11.120 25

26. 140.120.11.120 26 B 20  m 700nm MW Sample A

27. 140.120.11.120 27 B 20  m 700nm MW Sample B

28. 140.120.11.120 28 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.