Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect.pdf

Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect Sudhansu S. Mandal and J.K. Jain Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802 (February 1, 2008) 1 0 Motivated by the discovery of extremely low energy collective modes in the fractional quantum Hall 0 effect (Kang, Pinczuk et al.), with energies below the Zeeman energy, we study theoretically the 2 spin reversed excitations for fractional quantum Hall states at ν = 2/5 and 3/7 and find qualita- tively different behavior than for ν = 1/3. We find that a low-energy, charge-neutral “spin roton,” r a associated with spin reversed excitations that involve a change in the composite-fermion Landau M level index, has energy in reasonable agreement with experiment. 2 Inelastic light scattering has proved to be an extremely plest approximation, neglecting excitations involving the 2 useful tool for investigating the neutral excitations of the third CF-LL, there are three possible low-energy excita- 1 fractional quantum Hall effect (FQHE) . The initial fo- tions: (i) 1↑ → 0↓, (ii) 1↑ → 1↓, and (iii) 0↑ → 0↓. The ] l cus was at at ν = 1/3, where three modes have been last two conserve the CF-LL index, whereas the compos- l a observed: the long wavelength collective mode, the ro- ite fermion lowers its LL index in the first. One combina- h ton mode, and the spin wave mode. The last has an tion of these mus