Edge Probes of Topological Order

Abstract

According to the bulk-edge correspondence principle, the physics of the gapless edge in the quantum Hall effect determines topological order in the gapped bulk. As the bulk is less accessible, the last two decades saw the emergence of several experimental techniques that invoke the study of the compressible edge. We review the properties of the edge, and describe several experimental techniques that include shot noise and thermal noise measurements, interferometry, and energy (thermal) transport at the edge. We pay special attention to the filling factor 5/2 in the first excited Landau level (in two-dimensional electron gas in GaAs), where experimental evidence of a non-abelian topological order was found. A brief discussion is devoted to recent interferometry experiments that uncovered unexpected physics in the integer quantum Hall effect. The chapter also addresses the theory of edge states, for systems with abelian and non-abelian topological orders.

arXiv commentThe preprint will be a chapter in the book "New Developments in Fractional Quantum Hall Effects," eds. B. I. Halperin and J. K. Jain, to be published by World Scientific

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Cited by in corpus (22)

• Isolated Ballistic Non-Abelian Interface Channel
• Anyonic interference and braiding phase in a Mach-Zehnder Interferometer
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Fractionalization and anyonic statistics in the integer quantum Hall collider
• Breakdown of Diffusion on the Edge
• Does shot noise always provide the quasiparticle charge?
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• Quasiparticle Andreev scattering in the $\nu =1/3$ fractional quantum Hall regime
• Excitons in the Fractional Quantum Hall Effect
• Thermal interferometry of anyons
• Anyonic Mach-Zehnder interferometer on a single edge of a 2D electron gas
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• Electron Pairing of Interfering Interface-Based Edge Modes
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• Domain Textures in the Fractional Quantum Hall Effect
• Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions
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