Coulomb Blockade Doppelgangers in Quantum Hall States

Abstract

In this paper, we ask the question: How well can Coulomb blockade experiments correctly identify and distinguish between different topological orders in quantum Hall states? We definitively find the answer to be: Quite poorly. In particular, we write the general expression for the spacing of resonance peaks in a simple form that explicitly displays its dependence on the conformal scaling dimensions of the systems' edge modes. This form makes transparent the general argument that the Coulomb blockade peak spacings do not provide a strongly indicative signature of the topological order of the system, since it is only weakly related to the braiding statistics. We bolster this general argument with examples for all the most physically relevant non-Abelian candidate states, demonstrating that they have Coulomb blockade doppelgangers -- candidate states at the same filling fraction with identical Coulomb blockade signatures, but dramatically different topological orders and braiding statistics.

12 pages, 1 figure; portions of this paper were formerly included in Appendix C of arXiv:0903.3108; v2: examples added, minor corrections made; v3: discussions of non-uniform filling and of hierarchical counterparts of multi-component states added, minor corrections made

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Cited by in corpus (22)

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• Measurement-Only Topological Quantum Computation via Tunable Interactions
• Interference, Coulomb blockade, and the identification of non-abelian quantum Hall states
• Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Quantum Hall hierarchy from coupled wires
• Partition Functions of Non-Abelian Quantum Hall States
• Identification of 331 quantum Hall states with Mach-Zehnder interferometry
• Topological dephasing in the $\nu =2/3$ fractional Quantum Hall Regime
• One-dimensional itinerant interacting non-Abelian anyons
• Signatures of non-Abelian statistics in non-linear coulomb blockaded transport
• Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers
• Coulomb blockade with neutral modes
• Hierarchical Nature of the Quantum Hall Effects
• Thermoelectric properties of Coulomb-blockaded fractional quantum Hall islands
• Thermopower and thermoelectric power factor of ${\mathbb{Z}}_k$ parafermion quantum dots
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Edge mode velocities in the quantum Hall effect from a dc measurement
• Thermoelectric characteristics of ${\mathbb{Z}}_k$ parafermion Coulomb islands
• Thermopower in the Coulomb blockade regime for Laughlin quantum dots