Magnetic Field Dependence of Activation Energies in the Fractional Quantum Hall Effect

Abstract

We have studied the temperature dependence of the fractional quantum Hall effect at Landaulevel filling factors $\nu =\frac{1}{3}, \frac{2}{3}, \frac{4}{3}, \frac{5}{3}, \frac{2}{5}, \mathrm{and} \frac{3}{5}$ in magnetic fields up to 28 T to determine the magnitude of the associated energy gaps. The data suggest a single activation energy for $\nu =\frac{1}{3}, \frac{2}{3}, \frac{4}{3}, \mathrm{and} \frac{3}{5}$. Its magnitude, much smaller than predicted by current theories, vanishes for $B\lesssim 6$ T and saturates at $B\gtrsim 18$ T. The data also suggest a single activation energy for $\nu =\frac{2}{5} \mathrm{and} \frac{3}{5}$ which is smaller than predicted.