Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

Abstract

Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting, $$g \mu _B B$$ g μ B B , comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in $$\nu$$ ν for the $$R_{xx}$$ R xx minimum, e.g., from $$\nu = 11/7$$ ν = 11 / 7 to $$\nu = 8/5$$ ν = 8 / 5 , and a corresponding change in the $$R_{xy}$$ R xy , e.g., from $$R_{xy}/R_{K} = (11/7)^{-1}$$ R xy / R K = ( 11 / 7 ) - 1 to $$R_{xy}/R_{K} = (8/5)^{-1}$$ R xy / R K = ( 8 / 5 ) - 1 , with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the $$\nu = 4/3$$ ν = 4 / 3 and $$\nu = 7/5$$ ν = 7 / 5 resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of $$R_{xy}$$ R xy at the $$R_{xx}$$ R xx minima- the latter occurring for $$\nu = 4/3, 7/5$$ ν = 4 / 3 , 7 / 5 and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same $$\nu$$ ν and $$R_{xy}$$ R xy , but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.