Molecular anyons in fractional quantum Hall effect

TL;DR

This paper reveals that fractional quantum Hall anyons can form stable clusters called molecular anyons, explaining experimental puzzles and predicting new phenomena in quantum Hall systems.

Contribution

It introduces the concept of molecular anyons formed by binding of elementary anyons, supported by high-precision microscopic calculations, a novel insight into FQH physics.

Findings

Anyons often bind into stable clusters called molecular anyons.

The size and binding energy of clusters depend on the FQH state and electron interactions.

Charge-$1/4$ non-Abelian anyons can form charge-$1/2$ Abelian clusters.

Abstract

One of the profound consequences of the fractional quantum Hall (FQH) effect is the notion of fractionally charged anyons. In spite of extensive experimental study, puzzles remain, however. For example, both shot-noise and Aharonov-Bohm interference measurements sometimes report a charge that is a multiple of the elementary charge. We report here high-precision microscopic calculations that reveal the surprising result that the FQH anyons often bind together into stable clusters, which we term molecular anyons. This is counterintuitive, given that the elementary anyons carry the same charge and are therefore expected to repel one another. The number of anyons in a cluster, its binding energy and its size depend sensitively on the parent FQH state and the interaction between electrons (which is experimentally tunable, e.g., by varying the quantum well width). Our calculations further suggest that the charge-$1/4$ non-Abelian anyons of the $5/2$ FQH state may also bind to form charge-$1/2$ Abelian clusters. The existence of molecular anyons not only can provide a natural explanation for the observed charges, but also leads to a host of new predictions for future experiments and invites a re-analysis of many past ones.