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High-Frequency Dynamic Magnetotransport Properties of Quantum Wires

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

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  1. 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

  2. OUTLINES • 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

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

  4. 2D plasma 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

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

  6. Edge magnetoplasma (EMP) in a finite 2DES 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

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

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

  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. EF wc Edge Channels Landau level spacing 9

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

  11. For wt>>1, L>>W For wt<<1, L>>W 11

  12. 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). 540nm×4.5mm 12

  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. 13

  14. T =0.3K 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

  15. 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%). 1. 2. (mixers) 15

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

  17. Comparing with commercial vector meters • 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

  18. Observation of EMP in a QW array 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

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

  20. Landau Level 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. 21

  22. adsorption phase 22

  23. Polarizability or susceptibility wj w(f) 23

  24. 24

  25. 25

  26. Sample A 700nm MW B 20mm 26

  27. Sample B B MW 20mm 700nm 27

  28. 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. 28

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