Coulomb blockade doppelgängers in quantum Hall states

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 doppelgängers–candidate states at the same filling fraction with identical Coulomb blockade signatures but dramatically different topological orders and braiding statistics.

Figure 1

(Color online) A quantum Hall liquid (hatched regions) with two constrictions generated by top gates (gray rectangles) which deplete the Hall liquid underneath them. This forms an isolated puddle with tunnel junctions on both sides, where electrons can tunnel (dashed lines) to and from the puddle, allowing some current to flow through the blockade. Tunneling resonance patterns may be observed in the edge current (arrows) as a result of changing the area of the puddle with a side gate $P$. These resonance patterns will depend on the total topological charge of the quasiparticles (dots) contained in the puddle.