Spin-orbit interaction enhanced fractional quantum Hall states in the second Landau level

We study the fractional quantum Hall effect at ν = 7/3 and 5/2 in the presence of the spin-orbit interaction, using the exact diagonalization method and density matrix renormalization group (DMRG) method in a spherical geometry. Trial wave functions at these fillings are the Laughlin state and Moore-Reed-Pfaffian state. The ground-state excitation energy gaps and pair-correlation functions at fractional filling factors ν = 7/3 and 5/2 in the second Landau level are calculated. We find that the spin-orbit interaction stabilizes the fractional quantum Hall states.