Experimental Studies of the Edge-State Sheath on Quantum Hall Multilayers

该项目研究了一种新型的二维（2D）系统，即半导体多层量子霍尔体系中出现的边缘态鞘。在GaAs/AlGaAs多层中，调制掺杂GaAs量子阱边缘态的耦合形成了边缘态鞘层。理论预测，边缘态鞘层上的高度各向异性输运（层平面周围的手性流动，加上垂直于层的扩散）应该使无序和相互作用的相互作用与传统的全扩散二维系统有质的不同。在不同尺寸、形状和层间耦合强度的多层样品中，对电输运的低温、高磁场测量将测试这些预测，其中包括边缘状态鞘层性质随样品几何形状的独特变化。对一类新的二维系统的研究可以促进对凝聚态物理中一个核心问题的理解：无序、低维和各向异性材料中的电输运，如贝加德盐和碳纳米管的手性相。从事这些实验的研究生和本科生将接受低温、低噪声电子测量和现代半导体加工等最先进实验技术的培训。这个知识基础将为他们在学术界、工业界和政府的科学和工程事业做好准备。在传统的二维（2D）导电片中，电子在两个方向上随机运动。这个项目研究了一种新型的二维系统，其中电子在一个方向上随机运动，但在另一个方向上只以一个方向匀速运动。这种“边缘态护套”是在量子霍尔效应下，围绕多层GaAs/AlGaAs半导体结构的侧面运行的二维皮肤。理论预测，电子在边缘态鞘层上的各向异性流动应该会产生缺陷的影响，以及电子之间的相互作用，与传统的二维材料在质量上不同。对不同尺寸和形状的GaAs/AlGaAs样品上电流如何流经边缘态鞘层的低温、高磁场测量，将测试对独特的几何依赖效应的预测。研究这种各向异性诱导的现象是很重要的，因为在高温超导体和碳纳米管等新兴技术重要性的各向异性低维材料中，缺陷和相互作用具有巨大而复杂的影响。从事这些实验的研究生和本科生将接受低温、低噪声电子测量和现代半导体加工等最先进实验技术的培训。这个知识基础将为他们在学术界、工业界和政府的科学和工程事业做好准备。

This project investigates a new type of two-dimensional (2D) system, the sheath of edge-states that emerges in the quantum Hall regime of semiconductor multilayers. The edge-state sheath forms from coupling of the edge states at the perimeters of modulation-doped GaAs quantum wells in GaAs/AlGaAs multilayers. Theory predicts that the highly anisotropic transport on the edge-state sheath (chiral flow around the layer planes, coupled with diffusion perpendicular to the layers) should make the interplay of disorder and interactions qualitatively different than in conventional, all-diffusive 2D systems. Low-temperature, high-magnetic-field measurements of electrical transport in multilayer samples of different sizes, shapes, and interlayer coupling strengths will test these predictions, which include distinctive changes in edge-state sheath properties with sample geometry. These studies of a new class of two-dimensional system can advance understanding of a central problem in condensed matter physics: electrical transport in disordered, low-dimensional and anisotropic materials, such as Bechgaard salts and chiral phases of carbon nanotubes. The graduate and undergraduate students who work on these experiments will be trained in state-of-the-art experimental techniques in cryogenics, low-noise electronic measurements, and modern semiconductor processing. This knowledge base will prepare them for science and engineering careers in academia, industry, and government. %%%In conventional two-dimensional (2D) conducting sheets, electrons move randomly in both directions. This project investigates a new type of 2D system, in which electrons move randomly in one direction, but travel only one way, with uniform velocity, in the other direction. This "edge-state sheath" is a 2D skin that runs around the sides of multi-layered GaAs/AlGaAs semiconductor structures, in the regime of the quantum Hall effect. Theory predicts that the anisotropic flow of electrons on the edge-state sheath should make effects of imperfections, and of interactions between electrons, qualitatively different than in conventional 2D materials. Low-temperature, high-magnetic-field measurements of how electricity flows through edge-state sheaths on GaAs/AlGaAs samples of different sizes and shapes will test predictions for distinctive, geometry-dependent effects. It is important to study such anisotropy-induced phenomena, because imperfections and interactions have large, complex effects in anisotropic, low-dimensional materials of emerging technological importance, such as high temperature superconductors and carbon nanotubes. The graduate and undergraduate students who work on these experiments will be trained in state-of-the-art experimental techniques in cryogenics, low-noise electronic measurements, and modern semiconductor processing. This knowledge base will prepare them for science and engineering careers in academia, industry, and government.