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, 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 for the R_{xx} minimum, e.g., from nu = 11/7 to nu = 8/5, and a corresponding change in the R_{xy}, e.g., from R_{xy}/R_{K} = (11/7)^{-1} to 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 and nu = 7/5 resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of R_{xy} at the R_{xx} minima- the latter occurring for nu = 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 and R_{xy}, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.