Fractionally charged impurity states of a fractional quantum Hall system

TL;DR

This paper investigates how impurities affect fractional quantum Hall states, revealing that electron interactions create multiple quasi-bound states and evidence for localized fractionally charged quasiparticles at certain filling factors.

Contribution

It demonstrates that electron-electron interactions significantly modify impurity potentials, leading to multiple quasi-bound states and provides evidence for localized fractional charges in quantum Hall systems.

Findings

Multiple quasi-bound states form due to interactions.

Evidence of localized $e/3$ quasiparticles at $ u=1/3$.

Ambiguous results at $ u=2/5$ due to finite size effects.

Abstract

The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In contrast to the noninteracting case, where only a single bound state below the lowest Landau level forms, electron-electron interactions strongly renormalize the impurity potential, effectively giving it a finite range, which can support many quasi-bound states (long-lived resonances). Averaging the spectral weights of the quasi-bound states and extrapolating to the thermodynamic limit, for filling factor $\nu=1/3$ we find evidence consistent with localized fractionally charged $e/3$ quasiparticles. For $\nu=2/5$, the results are slightly more ambiguous, due to finite size effects and possible bunching of Laughlin-quasiparticles.