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

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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.