Sensing the binding and unbinding of anyons at impurities

TL;DR

This paper investigates how impurities can bind anyons in fractional quantum Hall states, proposing experimental methods and highlighting the potential of fractional Chern insulators in twisted MoTe$_2$ for observing these phenomena.

Contribution

It introduces a study of anyon binding to impurities in FQH states, emphasizing the role of impurity strength and proposing experimental detection techniques.

Findings

Impurities can bind quasiholes in FQH states under strong attractive potentials.

Tuning chemical potential affects the number of bound quasiholes.

Fractional Chern insulators in twisted MoTe$_2$ are promising platforms for observing anyon binding.

Abstract

Anyons are quasiparticles with fractional charge and statistics that arise in strongly correlated two-dimensional systems such as the fractional quantum Hall (FQH) effect and fractional Chern insulators (FCI). Interactions between anyons can lead to emergent phenomena, such as anyon superconductivity as well as anyon condensation which allows for a hierarchical construction of quantum Hall states. In this work, we study how quasihole anyons in a $\nu=1/3$ Laughlin fractional quantum Hall state can be bound together by a sufficiently strong attractive impurity potential. The competition between the repulsive interaction between the quasiholes themselves and the attractive interaction between the quasiholes and the impurity leads to states with different numbers of quasiholes bound to the impurity. Tuning the chemical potential via gating while remaining within a quantum Hall plateau changes the number of quasiholes bound to the impurity. We propose methods for studying these states experimentally, for example using scanning tunneling microscopy and exciton spectroscopy. While the impurities in traditional platforms such as GaAs heterostructures are typically too weak to observe the binding of anyons, the recently discovered zero-field fractional Chern insulators in twisted MoTe$_2$ offer a platform which may realize the strong-impurity regime.