Bulk and edge quasihole tunneling amplitudes in the Laughlin state

TL;DR

This paper derives a universal analytical formula for quasihole tunneling amplitudes in the Laughlin state, revealing differences between bulk and edge excitations and confirming the topological stability of fractional quantum Hall liquids.

Contribution

It introduces a universal formula for tunneling amplitudes using Jack polynomials, applicable to both bulk and edge quasiholes, and discusses effects of realistic interactions.

Findings

Universal tunneling amplitude formula derived

Crossover behavior between bulk and edge states identified

Topological stability confirmed under realistic conditions

Abstract

The tunneling between the Laughlin state and its quasihole excitations are studied by using the Jack polynomial. We find a universal analytical formula for the tunneling amplitude, which can describe both bulk and edge quasihole excitations. The asymptotic behavior of the tunneling amplitude reveals the difference and the crossover between bulk and edge states. The effects of the realistic coulomb interaction with a background-charge confinement potential and disorder are also discussed. The stability of the tunneling amplitude manifests the topological nature of fractional quantum Hall liquids.