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 map ping a FQHE system to the corresponding integer system with gauge inte raction. We investigate in detail the effects of Coulomb interaction a nd gauge interaction on the collective excitation and energy gap. Cons istent with the experimental result, the energy gaps are found to be r oughly linear with DELTAB, the deviation of the magnetic field from ha lf filling. This linear dependence is attributed to the intimate conne ction between the ground state at nu = p/(2p + 1) and the wave functio n of p-filled Landau levels.