Density dependence of the nu=5/2 energy gap: Experiment and theory

A density-tunable GaAs-AlGaAs heterostructure is used to study the density dependence of the filling factor nu=5/2 and other fractional and reentrant integer quantum-Hall states in the second Landau level. The activation energy at nu=5/2 can be determined for densities between 1.3 and 2.7 X 10(11)/cm(2) and reaches up to 310 mK. The 5/2 energy gap is calculated numerically, including finite width and Landau-level-mixing corrections, both as a function of electron density. The discrepancy between theory and experiment increases moderately with density and reaches about 1.5 K at the highest density. We argue that the activation energy is strongly influenced by disorder from ionized donors and attribute this to the surprisingly large size of the 5/2 quasiparticles. We find that the quasiparticles have a diameter of at least 12 times the magnetic length or 150 nm at a magnetic field of 4 T. Implications for heterostructure design are discussed.