The fractional quantum Hall states in the second Landau level exhibits exotic physics; some states have even been experimentally found to host non-Abelian quasi-particles, which could be devised as qubits for fault-tolerant topological quantum computation. The Coulomb interaction is the principal interaction in the fractional quantum Hall effect, prompting the development of several theories and models to elucidate these states over the years. However, an unresolved debate persists between theoretical predictions and experimental observations. In contrast to the lowest Landau level, the influence of Landau-level mixing becomes notably pronounced at the second Landau level, which arises in a comparatively lower magnetic field. At a moderate range of Landau level mixing strength, consistent with GaAs-GaAlAs systems, we find a reentrant Anomalous phase (A-phase) that is quantized and exhibits a substantial gap in the thermodynamic limit, being topologically distinct from the phase associated with pure Coulomb interaction. We propose a ground state wave function for the 5/2 state in the second Landau level and generalize it to all experimentally observed states in the second Landau level. These wave functions have remarkably high overlap with the corresponding exact ground states in the A-phase and can support non-Abelian quasiparticle excitation. We believe our proposed wave functions for all the second Landau level states in this A-phase should possibly corroborate with the experimentally observed states.

 

References:

[1] S. Das, S. Das, and S. S. Mandal, Phys. Rev. Lett. 131, 056202 (2023).

[2] S. Das, S. Das, and S. S. Mandal, Phys. Rev. Lett. 132, 029602 (2024).

[3] S. Das, S. Das, and S. S. Mandal, Phys. Rev. Lett. 132, 106501 (2024).

[4] S. Das, S. Das, and S. S. Mandal, Phys. Rev. B 110, L121303 (2024).