Coulomb Blockade Doppelgangers in Quantum Hall States

TL;DR

This paper demonstrates that Coulomb blockade experiments are ineffective at reliably distinguishing different topological orders in quantum Hall states, as many states share identical signatures despite having different underlying topological properties.

Contribution

It provides a general expression linking Coulomb blockade peak spacings to edge mode properties and shows that many non-Abelian states have indistinguishable signatures, revealing limitations of current experimental methods.

Findings

Coulomb blockade peak spacings weakly relate to topological order.

Many states at the same filling fraction share identical Coulomb signatures.

Coulomb blockade experiments cannot reliably identify topological order.

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.