THEORETICAL-STUDY OF ENERGY GAPS AND COLLECTIVE EXCITATIONS IN THE FRACTIONAL QUANTUM HALL-EFFECT

Following a recent experiment by Du et al., we study theoretically the energy gaps and collective excitations of the most prominent sequence of the fractional quantum Hall effect (FQHE) at filling factor nu = p/(2p + 1) around nu = 1/2. Our theoretical study is carried out by mapping a FQHE system to the corresponding integer system with gauge interaction. We investigate in detail the effects of Coulomb interaction and gauge interaction on the collective excitation and energy gap. Consistent with the experimental result, the energy gaps are found to be roughly linear with DELTAB, the deviation of the magnetic field from half filling. This linear dependence is attributed to the intimate connection between the ground state at nu = p/(2p + 1) and the wave function of p-filled Landau levels.