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

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,$$g \mu _B B$$gμBB, 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$$\nu$$νfor the$$R_{xx}$$Rxxminimum, e.g., from$$\nu = 11/7$$ν=11/7to$$\nu = 8/5$$ν=8/5, and a corresponding change in the$$R_{xy}$$Rxy, e.g., from$$R_{xy}/R_{K} = (11/7)^{-1}$$Rxy/RK=(11/7)-1to$$R_{xy}/R_{K} = (8/5)^{-1}$$Rxy/RK=(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=4/3and$$\nu = 7/5$$ν=7/5resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of$$R_{xy}$$Rxyat the$$R_{xx}$$Rxxminima- the latter occurring for$$\nu = 4/3, 7/5$$ν=4/3,7/5and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same$$\nu$$νand$$R_{xy}$$Rxy, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.

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Nature Publishing Group
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Scientific Reports
Medium: X
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National Science Foundation
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