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.

The 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

References in corpus (33)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Quantum limit of heat flow across a single electronic channel
• Observation of neutral modes in the fractional quantum Hall regime
• Dephasing in the electronic Mach-Zehnder interferometer at filling factor 2
• Finite bias visibility of the electronic Mach-Zehnder interferometer
• Aharonov-Bohm interference of fractional quantum Hall edge modes
• Edge Channel Interference Controlled by Landau Level Filling
• Two-electron bunching in transport through a QD induced by Kondo correlations
• Detecting non-Abelian Statistics with Electronic Mach-Zehnder Interferometer
• Shot Noise in Anyonic Mach-Zehnder Interferometer
• Experimental probe of topological orders and edge excitations in the second Landau level
• Noise dephasing in the edge states of the Integer Quantum Hall regime
• Melting of interference in the fractional quantum Hall effect: Appearance of neutral modes
• Hanbury-Brown and Twiss interference of anyons
• Extracting net current from an upstream neutral mode in the fractional quantum Hall regime
• Competing ν= 5/2 fractional quantum Hall states in confined geometry
• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Mach-Zehnder interferometer in the Fractional Quantum Hall regime
• Electron interferometry in quantum Hall regime: Aharonov-Bohm effect of interacting electrons
• Charge-statistics separation and probing non-Abelian states
• Why a noninteracting model works for shot noise in fractional charge experiments
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Probing the neutral edge modes in transport across a point contact via thermal effects in the Read-Rezayi non-abelian quantum Hall states
• Long tunneling contact as a probe of fractional quantum Hall neutral edge modes
• Chirality, causality, and fluctuation-dissipation theorems in non-equilibrium steady states
• Identification of 331 quantum Hall states with Mach-Zehnder interferometry
• Low-temperature illumination and annealing of ultra-high quality quantum wells
• Transmission of heat modes across a potential barrier
• Probing the $\nu =\frac{5}{2}$ quantum Hall state with electronic Mach-Zehnder interferometry
• Solution of a model for the two-channel electronic Mach-Zehnder interferometer

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?
• Thermal equilibration on the edges of topological liquids
• 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
• PH-Pfaffian order in a translationally and rotationally invariant system
• Electron Pairing of Interfering Interface-Based Edge Modes
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Localization and conductance in fractional quantum Hall edges
• Different fractional charges from auto- and cross-correlation noise in quantum Hall states without upstream modes
• Transport Signatures of Fractional Quantum Hall Binding Transitions
• Domain Textures in the Fractional Quantum Hall Effect
• Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions
• Signature of anyonic statistics in the integer quantum Hall regime
• Extracting the scaling dimension of quantum Hall quasiparticles from current correlations
• Elevated Hall Responses as Indicators of Edge Reconstruction