Phase coherence and its control of quantum Hall electron systems

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[Resistance fluctuation] GaAs/AlGaAs heterostructure devices, in which two small scattering regions are connected with a quantum Hall electron system, has been studied. The longitudinal resistance is found to exhibit fluctuations in transition regions between successive integer quantum Hall (IQH) states at temperatures below 100mK.The analysis shows that (i) the electron system is coherent over the entire region of the devices, and (ii) the resistance fluctuation arises from the fact that the electron system in transition regions splits into isolated incompressible regions fringed by a network of compressible strips.[Inelastic scattering process] Source-drain voltage dependence of the transition width between IQH states, studied on GaAs/AlGaAs haterostructure devices, revealed that (i) the eigen-states of the electron system are the scattering-wave-states incident from the source and the drain electrodes, and that (ii) the inelastic scattering process between the respective scattering-wave-states is strongly suppressed in the transition regions. This provided the basis for explaining the much longer inelastic scattering lengths found in strong magnetic fields.[Inter-edge-state scattering : Spin polarization] In odd IQH states and in fractional QH states (2/3 and 1/3), remarkable hysteresis behavior was found in the inter-edge-state scattering process. The effects are interpreted by assuming that nuclear spin is induced by the flip of electron spin and the induced nuclear spin significantly increases an effective magnetic field for the electron spin through the hyperfine interaction. In the case of the fractional QH states, this particularly implies that (i) fractional edge states exist and (ii) the fractional edge states have respective spin polarizations.[Breakdown phenomena of IQH states] The mechanism of the current-induced breakdown of IQH states was clarified in terms of a heat instability of IQH electron systems.