Competition Between Fractional Quantum Hall Liquid, Bubble and Wigner Crystal Phases in the Third Landau Level

Magnetotransport measurements were performed in a ultra-high mobility GaAs/AlGaAs quantum well of density $\sim 3.0\times {10}^{11}$ $c{m}^{-2}$. The temperature dependence of the magnetoresistance $R_{xx}$ was studied in detail in the vicinity of $\nu =9\mathrm{/}2$. In particular, we discovered new minima in $R_{xx}$ at filling factor $\nu \simeq 41\mathrm{/}5$ and $44\mathrm{/}5$, but only at intermediate temperatures $80\lesssim T\lesssim 120$ mK. We interpret these as evidence for a fractional quantum Hall liquid forming in the N=2 Landau level and competing with bubble and Wigner crystal phases favored at lower temperatures. Our data suggest that a magnetically driven insulator-insulator quantum phase transition occurs between the bubble and Wigner crystal phases at T=0.