Quantitative Analysis of the Disorder Broadening and the Intrinsic Gap for the $ u=5/2$ Fractional Quantum Hall State

We report a reliable method to estimate the disorder broadening parameter from the scaling of the gaps of the even and major odd denominator fractional quantum Hall states of the second Landau level. We apply this technique to several samples of vastly different densities and grown in different MBE chambers. Excellent agreement is found between the estimated intrinsic and numerically obtained energy gaps for the $ u=5/2$ fractional quantum Hall state. Futhermore, we quantify, for the first time, the dependence of the intrinsic gap at $ u=5/2$ on Landau level mixing.

Particle-hole Asymmetry of Fractional Quantum Hall States in the Second Landau Level of a Two-dimensional Hole System

We report the first unambiguous observation of a fractional quantum Hall state in the Landau level of a two-dimensional hole sample at the filling factor $ u=8/3$. We identified this state by a quantized Hall resistance and an activated temperature dependence of the longitudinal resistance and found an energy gap of 40 mK. To our surprise the particle-hole conjugate state at filling factor $ u=7/3$ in our sample does not develop down to 6.9 mK. This observation is contrary to that in electron samples in which the 7/3 state is typically more stable than the 8/3 state. We present evidence that the asymmetry between the 7/3 and 8/3 states in our hole sample is due to Landau level mixing.