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
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
D plasma restoring force field!! charge flow dispersion: must be long enough!
D 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.
D magnetoplasma ~ /|q| B The restoring force is enhanced by the magnetic field.
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
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, (1985) A 2DES on the surface of Liquid Helium placed in a perpendicular B-field. B ≠ 0 B = 0
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. EFEF Edge Channels cc Landau level spacing
JEPT Lett., 57, 587 (1993)
For >>1, L>>W For 1, L>>W
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, (1994). 540nm×4.5mm
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.
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 = s (B) s 0 =0 = 1 + s (B) = s (B) s B: the parameter (magnetic field) sweeping in the experiment : phase velocity of the signal in coaxial cable sample known
Pulsed Microwave PLL and Gated Average System (mixers) Schematic of a homemade PLL system for microwave signals up to 18 GHz. The phase resolution is about 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 (50M-21GHz)
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 O for phase with a very low-average power (about -100dBm) into the sample.
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
GHz 133MHz Landau level filling factor
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!!!
adsorption phase
Polarizability or susceptibility (f)(f) jj
B 20 m 700nm MW Sample A
B 20 m 700nm MW Sample B
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.