Fractionally charged impurity states of a fractional quantum Hall system

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 quasibound states (long-lived resonances). Averaging the spectral weights of the quasi-bound states and extrapolating to the thermodynamic limit, for filling factor ν = 1/3 we find evidence consistent with localized fractionally charged e/3 quasi-particles. For ν = 2/5, the results are slightly more ambiguous, due to finite size effects and possible bunching of Laughlin-quasi-particles.