Anomalous density dependence of the activation gap of $\nu =$5/2 fractional quantum Hall state at extremely large Landau level mixing

We have conducted a study of the density dependence of $\nu =$5/2 fractional quantum Hall state (FQHS) in the regime of extremely low densities, down to n$=$4.9x10\textasciicircum 10 cm\textasciicircum -2. In the density range accessed in our sample, the Landau level mixing parameter $\kappa $ spans the so far unexplored range 2.52\textless $\kappa $ \textless 2.82. Here we observe an anomalous dependence of the activation gap of $\nu =$5/2 FQHS on the carrier density. We discuss the possible origins of this unexpected behavior. N.S. and G.C. were supported by the NSF grant DMR-0907172 and DMR-1207375. K. West and L. Pfeiffer acknowledge the support of the Princeton NSF-MRSEC and the Moore Foundation.