Coulomb Blockade Doppelgangers in Quantum Hall States

Understand

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.