Anyon molecules in fractional quantum Hall states

TL;DR

This study uses advanced numerical methods to analyze how screening influences the formation of anyon molecules in various fractional quantum Hall states, revealing state-dependent binding behaviors.

Contribution

It demonstrates that screening can bind like-charged anyons into molecules across different quantum Hall states, with dependencies on filling factor, gate distance, and fusion channels.

Findings

Stable $ extstyle rac{2e}{3}$ molecules in Laughlin state over a broad gate-distance range.

Jain state exhibits molecular binding throughout the considered range.

Strong binding of charge-$e/2$ molecules in anti-Pfaffian state on the hole side.

Abstract

We use segment DMRG on the infinite cylinder to compute energies of charged excitations in gate-screened fractional quantum Hall states. For the $\nu=1/3$ Laughlin, $\nu=2/5$ Jain, and $\nu=5/2$ anti-Pfaffian states, we find screening can bind like-charged anyons into molecules, with a strong dependence on filling-factor, gate distance, and fusion channel. In the Laughlin state, stable $\pm 2e/3$ molecules and larger clusters appear over a broad gate-distance window. The Jain state is molecular throughout the range we consider. In the anti-Pfaffian, binding is strongest on the hole side, where the charge-$e/2$ molecule is fused into the $\psi$ channel over a broad window of gate distances. In all three cases, screening suppresses long-range repulsion and exposes an intermediate-range attraction encoded in the oscillatory density tail of the fundamental anyon. We discuss consequences for addition spectra, interferometry, Wigner crystallization, anyon superconductivity, and entropy measurements.