Fractional quantum Hall effect at ν=2/3 and 3/5 in tilted magnetic fields

Abstract

We report on measurements of electron transport for the fractional quantum Hall effect (FQHE) at filling factors \ensuremath{\nu}=2/3 and 3/5, in magnetic fields ${\mathbf{B}}_{\mathit{t}}$ tilted by angles \ensuremath{\theta} with respect to the normal to the sample plane. Our device was prepared at an electron density of only 2.4\ifmmode\times\else\texttimes\fi{}${10}^{10}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, but still exhibited a well-developed FQHE at \ensuremath{\nu}=2/3 and 3/5. This exceptionally low density allowed us to access very low total fields, where the spin is less likely to be completely polarized. For many tilt angles, we obtained gap energies \ensuremath{\Delta} from the temperature dependence of the diagonal conductivity on the FQHE minima. For both 2/3 and 3/5, plots of \ensuremath{\Delta} versus ${\mathit{B}}_{\mathit{t}}$ exhibit minima that are accompanied in transport by splitting of the FQHE. For 2/3 the minimum in \ensuremath{\Delta}(${\mathit{B}}_{\mathit{t}}$) is sharp and deep, with \ensuremath{\Delta} reduced by 70%. With ${\mathit{B}}_{\mathit{t}}$ well above its value at the minimum, \ensuremath{\Delta}(${\mathit{B}}_{\mathit{t}}$) for \ensuremath{\nu}=2/3 is linear, with slope \ensuremath{\approxeq}g${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ for GaAs, indicating an increase in the two-dimensional electron-system Zeeman energy on excitation. We present a detailed survey of the evolution of the splitting of the FQHE with angle, and find that local ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$ minima that are shifted up to 6% upfield of \ensuremath{\nu}=2/3 at \ensuremath{\theta}\ensuremath{\approxeq}23\ifmmode^\circ\else\textdegree\fi{} evolve continuously into an unsplit FQHE at \ensuremath{\nu}=2/3 at \ensuremath{\theta}\ensuremath{\approxeq}0\ifmmode^\circ\else\textdegree\fi{}. The split and shifted FQHE's that we observe are interpreted as effects of phase separation associated with ground-state spin transitions.