Finite-thickness effect of the fractional quantum Hall states in the second Landau level*

Given the finite thickness of the samples in experiments, the in-plane magnetic field will squeeze the single-particle electron wave function in the direction perpendicular to the plane, effectively decrease the quantum well (QW) width and modify the electron interaction. However, this effect has only been reported in the non-Abelian candidate, 5/2 fractional quantum Hall (FQH) state, while other FQH states in the second Landau level (SLL), including the particle-hole conjugate of 5/2 FQH state, i.e. 7/2 FQH state, remain uninvestigated. We will present our energy gap measurements of the FQH states (7/3, 5/2, 8/3 and 7/2) in the SLL under tilted magnetic fields. A universal critical in-plane magnetic field of around 1.0 T is observed at different fillings, which corresponds to an in-plane magnetic length of around 26 nm. This critical value is comparable with the QW width of 28 nm in our sample, indicating the finite-thickness effect in the SLL. At higher in-plane magnetic fields, we found that the FQH states deviated from its strengthening tendency with in-plane field, further demonstrating the finite-thickness effect.