Universality and phase diagram around half-filled Landau levels

Abstract

Gated $\mathrm{GaAs}/{\mathrm{Al}}_{x}\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}x}$ heterostructures were used to determine the low-temperature behavior of the two-dimensional electron gas near filling factor $\ensuremath{\nu}=\frac{1}{2}$ in the disorder-magnetic-field plane. We identify a line on which ${\ensuremath{\sigma}}_{\mathrm{xy}}$ is temperature independent, has value ${\ensuremath{\sigma}}_{\mathrm{xy}}=0.5\ifmmode\pm\else\textpm\fi{}0.02(\frac{{e}^{2}}{h})$, and a distinct line on which ${\ensuremath{\rho}}_{\mathrm{xy}}=2\ifmmode\pm\else\textpm\fi{}0.04(\frac{h}{{e}^{2}})$. The phase boundaries between the Hall insulator and the principal quantum Hall liquids at $\ensuremath{\nu}=1 \mathrm{and} \frac{1}{3}$ show levitation of the delocalized states of the first Landau levels for electrons and composite fermions. Finally, the data suggest that there is no true metallic phase around $\ensuremath{\nu}=\frac{1}{2}$.