Quantitative experimental test for the theoretical gap energies in the fractional quantum Hall effect

Abstract

The energy gap for quasiparticle excitations in the $\frac{p}{3}$ states of the fractional quantum Hall effect (FQHE) has been determined in an ultrahigh-mobility ($\mu =5\mathrm{}\times {10}^6$ ${\mathrm{cm}}^2$/V sec), quasi-two-dimensional electron system in GaAs-(Al,Ga)As, for which the finite thickness of the carrier system is accurately known. Recent few-particle numerical calculations incorporating such a finite thickness and mixing with higher Landau levels account for the high-magnetic-field data to within ∼20%. This provides the first quantitative test for theories on the FQHE.