Fractional quantum Hall effect atν=23and43in strained Si quantum wells

Abstract

We report transport measurements on the $\ensuremath{\nu}=\frac{2}{3}$ and $\frac{4}{3}$ fractional quantum Hall effect states in the two-dimensional electron system (2 DES) in a ${\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}}_{0.75}{\mathrm{Ge}}_{0.25}$ heterostructure (density $n\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{11}{\mathrm{cm}}^{\ensuremath{-}2}$ and mobility $\ensuremath{\mu}\ensuremath{\sim}9\ifmmode\times\else\texttimes\fi{}{10}^{4}{\mathrm{cm}}^{2}/\mathrm{V}\mathrm{}\mathrm{s})$ at temperatures down to 40 mK and in magnetic fields (B) up to 42 T. An energy gap $\ensuremath{\Delta}\ensuremath{\sim}0.6\mathrm{K}$ was deduced at $\ensuremath{\nu}=\frac{2}{3},$ which is small compared to the theoretically expected value (\ensuremath{\sim}30 K) and to that measured in the ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures with similar electron scattering rate. This large discrepancy cannot be accounted for by finite thickness and Landau level mixing corrections, and suggests that the valley degeneracy inherent in Si may play a role. Tilting B-field experiments were performed to study the spin polarization of these two states and ${\ensuremath{\rho}}_{\mathrm{xx}}$ and ${\ensuremath{\rho}}_{\mathrm{xy}}$ were seen to maintain their strength up to the highest tilt angle of 48\ifmmode^\circ\else\textdegree\fi{}. From this observation we conclude that the $\ensuremath{\nu}=\frac{2}{3}$ and $\frac{4}{3}$ states are spin polarized.