【作者】 赵勇杰；

【导师】 郭光灿； 郭国平；

【作者基本信息】 中国科学技术大学 ， 光学， 2009， 博士

【摘要】 从GaAs/A1GaAs半导体量子阱中二维电子气在极低温强磁场下量子输运的实验出发,通过调节磁场大小、倾斜角度、电子气浓度、样品温度和射频场等外加参数,测量霍尔样品的纵向电阻和霍尔电阻,研究了量予霍尔系统中存在的各种量子相以及量子相变的问题。研究量子霍尔系统中这些相与相变的问题,不仅有助于我们理解这些现象背后的相互作用,而且更给我们提供了控制它们的技术手段。考虑到其中的某些态可以用来做量子信息处理,我相信我们的工作将会给未来实现基于二维电子气系统的量子计算机提供线索。本论文的主要内容:1.介绍了二维电子气系统在磁场下存在的经典的与量子的输运现象。基于不可压缩的量子态以及无序的存在,给出了量子霍尔效应的一个理论解释。2.介绍了量子霍尔系统中局域态-扩展态相变的标度理论,同时实验上研究了GaAs/GaAIAs量子阱单子带二维电子系统中的量子霍尔效应以及其平台间的相变问题。3.研究了GaAs/AlGaAs量子阱双子带二维电子气系统中的拓扑相图,并且发现了因面内磁场导致的赝自旋量子霍尔铁磁态所发生的相变。4.在双子带量子霍尔系统中,研究了朗道能级简并处的局域态与扩展态间的相变的性质。5.介绍了电阻探测核磁共振基本的原理和方法,研究了填充因子v=4附近各个赝自旋态的核磁共振信号的响应以及核自旋弛豫时间T₁。6.对于博士期间工作的总结,以及对于进一步进行实验的展望,介绍了基于量子霍尔系统的量子信息处理的最新进展。本论文的主要创新点:1.对于理论预言的标度函数进行了实验验证,指出临界相变的不同区域满足不同形式的标度函数。2.在双子带二维电子气系统填充v=4处,首次发现了一个由于面内磁场导致的具有SU（2）对称性的赝自旋量子霍尔铁磁态到具有SU（4）对称性的一个未知态的相变。3.在双子带系统中朗道能级交叉混合处进行了标度行为的研究,指出对于特定无序分布的样品,朗道能级的混合不会改变系统的标度行为。4.对于赝自旋量子霍尔铁磁态进行了电阻探测核磁共振的研究,发现了仅有easy-axis型的量子霍尔铁磁态对于NMR的探测是敏感的,存在低能自旋激发的迹象。同时发现了核磁共振信号的不对称分布。更多还原

【Abstract】 Starting from the quantum transport experiments of two-dimensional electron gas （2DEG） in GaAs/AlGaAs semiconductor quantum well system under condition of low temperature and high magnetic field,by varying the parameters such as the magnetic field,tilted angle,electron density,temperature and radio frequency,the longitudinal and Hall resistance of the Hall bar samples were measured and we studied the quantum phases and quantum phase transitions which exist in quantum Hall system.To study the phases and phase transitions in quantum Hall system,not only helps us understand the nature of the interaction beneath the phenomena,but also gives us the techniques to control them.Considering that some of these states can be utilized as the candidate for the quantum information process,I think our works will give us clues to realize the quantum computer based on two-dimensional electron gas system in future.The main content and characteristics of this dissertation are listed as follows:1.Described the classical and quantum transport phenomena of 2DEG in magnetic field.Based on incompressible quantum states and disorder,we gave an explanation to quantum Hall effect.2.Introduced the scaling theory for plateau transition in quantum Hall system.In GaAs/AlGaAs quantum well with single subband 2DEG system,we studied the quantum Hall effect and the plateau transition.3.Studied the topological phase diagram of GaAs/AlGaAs quantum well with twosubband 2DEG system.Found a phase transition of pseudo-spin quantum Hall ferromagnetic state which is induced by in-plane magnetic field.4.Studied the phase transition between localized and extended state in the region of Landau level mixing in two-subband quantum Hall system.5.Described the principle of Resistively Detected Nuclear Magnetic Resonance （RD-NMR）,and studied the NMR signal and nuclear spin relaxation time T₁ in the filling factorν=4 where the pseudo-spin quantum Hall ferromagnetic states are well developed.6.Provided the summary of the works during the PhD research,and gave a perspective about the future research works.And the recent progress in the quantum information process based on quantum Hall system were introduced.The main innovations of this dissertation are summarized as follows:1.Gave an experimental support for theoretical proposed scaling functions,and proved that different scaling functions applied in different range of the critical region.2.Firstly found a phase transition at filling factorν=4,which is induced by inplane magnetic field and during the phase transition the pseudo-spin quantum Hall ferromagnetic state with SU（2） symmetry changes into an unknown state with SU（4） symmetry.3.Studied the scaling behavior in the region of Landau levels crossing in twosubband system.And gave a conclusion that the mixing of Landau levels doesn’t change the scaling behavior of system for a given disorder profile.4.Used the RD-NMR to detect the pseudo-spin quantum Hall ferromagnetic state, and found that only easy-axis pseudospin quantum Hall state is sensitive to the RD-NMR measurement and there is signature of low energy spin excitation.And at the same time the distribution of NMR signal is asymmetry.更多还原