梁啟德臺灣大學：物理研究所陳則銘Chen, Tse-MingTse-MingChen2007-11-262018-06-282007-11-262018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/54627This thesis focus on electron and composite fermion transport properties in GaAs two-dimensional electron systems. The experiments fall into two sets. 1. Transport and Quantum Lifetime Dependence on Electron Density in Gated GaAs/AlGaAs Heterostructures We present a study of the transport and quantum lifetime dependence on electron density in two completely di erent kinds of two-dimensional electron gas systems. We observed that both the two scattering times increase with increasing the electron density. But for the GaAs heterostructure with InAs self-assembled quantum dots, the two lifetimes and the ratio of them are much smaller than those of the conventional GaAs heterostructures. We concluded that the short-range scattering dominates the two-dimensional electron gas as a consequence of the InAs quantum dots. Furthermore, for another GaAs heterostructure with ultra high mobility, we showed that the dominated scattering mechanism is the long-range scattering associated with the ionized donors. Besides, a substantial increase of the quantum lifetime with carrier density, which do not conform to the conventional theory, were observed and we speculate that the screening e ects need to be considered in order to explain our experimental results. The theoretical calculations were also made to investigate our experimental results. 2. Evolution of the Second Lowest Extended State as a Function of Effective Magnetic Field in the Fractional Quantum Hall Regime It has been shown that at a Landau level filling factor is equal to 1/2, a two-dimensional electron system can be mathematically transformed into a composite fermion system interacting with a Chern-Simons gange field. Besides, since it is believed that all state should be localized in a 2D system at B = 0, a profound question concerning the fate of the extended states as B approach to 0 arose soon after the discovery of the quantum Hall effect. Integrating these two ideas, we present the first study of the evolution of the second lowest extended state of the composite fermions in a vanishing effective magnetic field in the fractional quantum Hall regime.Acknowledgements i Abstract iii Publications vii 1 Introduction 1 1.1 Low-dimensional Physics . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Two-dimensional Electron Systems . . . . . . . . . . . . . . . . . 2 1.2.1 Fabrication of two-dimensional electron systems . . . . . . 2 1.2.2 Modulation-doped heterostructure . . . . . . . . . . . . . . 4 1.2.3 Varying the electron density . . . . . . . . . . . . . . . . . 5 2 Electron Transport in Two-dimensional Electron Systems at Low Temperatures 7 2.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Drude model . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Ground-state properties of an electron gas . . . . . . . . . 9 2.2 Landau Levels and Shubnikov-de Haas Oscillations . . . . . . . . 10 2.3 The Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 The Integer Quantum Hall Effect . . . . . . . . . . . . . . . . . . 15 2.5 The Fractional Quantum Hall Effect . . . . . . . . . . . . . . . . 18 3 Device Fabrication and Cryogenics 23 3.1 Device Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1.1 Molecular beam epitaxy . . . . . . . . . . . . . . . . . . . 23 3.1.2 Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Cryogenic Experimental Set-up . . . . . . . . . . . . . . . . . . . 26 3.2.1 3He refrigerators . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.2 Four-terminal resistance measurements . . . . . . . . . . . 28 4 Transport and Quantum Lifetimes in Two-Dimensional Electron Gases 31 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . 32 4.2.1 Transport and quantum lifetime . . . . . . . . . . . . . . . 32 4.2.2 Lifetime dependence on carrier density . . . . . . . . . . . 35 4.3 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.1 Small-angle scattering in 2D electron gas . . . . . . . . . . 36 4.3.2 Theoretical correlation correction . . . . . . . . . . . . . . 38 4.4 Measurements on Transport and Quantum Lifetime Dependence on Carrier Density . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.4.2 Sample structure . . . . . . . . . . . . . . . . . . . . . . . 39 4.4.3 Experimental procedure . . . . . . . . . . . . . . . . . . . 41 4.5 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . 45 4.6 Theoretical Calculation . . . . . . . . . . . . . . . . . . . . . . . . 50 4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5 Evolution of the Extended State in the Fractional Quantum Hall Regime 55 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.2 Fate of the Extended States in a Vanishing Magnetic Field . . . . 56 5.2.1 Levitation of extended-state bands in a strong magnetic field on theoretical grounds . . . . . . . . . . . . . . . . . 56 5.2.2 Previous experimental works . . . . . . . . . . . . . . . . . 58 5.3 Composite Fermion . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.4 Studies of the Extended State Evolution in the Fractional QuantumHallRegime . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.4.1 Motivation and experimental procedure . . . . . . . . . . . 61 5.4.2 Sample structure . . . . . . . . . . . . . . . . . . . . . . . 63 5.5 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . 64 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6 Conclusions 71 Bibliography 731297901 bytesapplication/pdfen-US複合費米子砷化鎵GaAscomposite fermionquantum lifetimestwo-dimensionalthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54627/1/ntu-93-R91222044-1.pdf