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.
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