Quasi-Particle Properties from Tunneling in the v = 5/2 Fractional Quantum Hall State

Quasi-particles with fractional charge and statistics, as well as modified Coulomb interactions, exist in a two-dimensional electron system in the fractional quantum Hall (FQH) regime. Theoretical models of the FQH state at filling fraction [fleqn,10pt,legalpaper]{article} {amssymb} {amsfonts} {amsmath} {empty} {document} \(v={⁵}/{₂}\) {document} make the further prediction that the wave function can encode the interchange of two quasi-particles, making this state relevant for topological quantum computing. We show that bias-dependent tunneling across a narrow constriction at [fleqn,10pt,legalpaper]{article} {amssymb} {amsfonts} {amsmath} {empty} {document} \(v={⁵}/{₂}\) {document} exhibits temperature scaling and, from fits to the theoretical scaling form, extract values for the effective charge and the interaction parameter of the quasi-particles. Ranges of values obtained are consistent with those predicted by certain models of the [fleqn,10pt,legalpaper]{article} {amssymb} {amsfonts} {amsmath} {empty} {document} \({⁵}/{₂}\) {document} state.