Absence of floating delocalized states in a two-dimensional hole gas

Abstract

By tracking the delocalized states of the two-dimensional hole gas in a $p$-type ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructure as a function magnetic field, we mapped out a phase diagram in the density--magnetic-field plane. We found that the energy of the delocalized state from the lowest Landau level flattens out as the magnetic field tends toward zero. This finding is different from that for the two-dimensional electron system in an $n$-type ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructure where delocalized states diverge in energy as $B$ goes to zero indicating the presence of only localized states below the Fermi energy. The possible connection of this finding to the recently observed metal-insulator transition at $B=0$ in the two-dimensional hole gas systems is discussed.