Sensing the binding and unbinding of anyons at impurities

Anyons are quasiparticles with fractional charge and statistics that arise in strongly correlated two-dimensional systems such as the fractional quantum Hall effect and fractional Chern insulators. Interactions between anyons can lead to emergent phenomena, such as anyon superconductivity as well as anyon condensation that allows for a hierarchical construction of quantum Hall states. In this work, we study how quasihole anyons in a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>ν</a:mi> <a:mo>=</a:mo> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>3</a:mn> </a:mrow> </a:math> 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>MoTe</b:mi> <b:mn>2</b:mn> </b:msub> </b:math> offer a platform that may realize the strong-impurity regime.