The fractional quantum hall effect observed in 2D system is one of the remarkable result of topological nature of band. Now one much more awaiting phenomenon is to observation 3D version of 2D fractional Quantum hall effect. For integer quantum hall effect (observed in 2D electron gas under magnetic field) the time reversal protected chiral edge state are in 1D. Now a 3D topological insulator where we have chiral edge states in 2D (as similar Graphene, but in Graphene everything occur from band theory whereas in topological insulator it's the symmetry protected surface topological states ). In this analogy, 3D topological insulator can be thought as a dimensional extension of 2D integar quantum hall effect.
Similarly, one would expect to a 3D (Topological Insulator) version of 2D fractional quantum hall effect !! Waooo that would much more interesting from because the excitation in that system will be just extraordinary !! As in 2D (http://www.tandfonline.com/doi/abs/10.1080/00018739500101566) fractional quantum hall effect electron electron correlation played a crucial role (which not the case for integer quantum hall effect) , on have consider similar interaction in 3D topological insulator.
There is a proposal of this here
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.085422
Similarly, one would expect to a 3D (Topological Insulator) version of 2D fractional quantum hall effect !! Waooo that would much more interesting from because the excitation in that system will be just extraordinary !! As in 2D (http://www.tandfonline.com/doi/abs/10.1080/00018739500101566) fractional quantum hall effect electron electron correlation played a crucial role (which not the case for integer quantum hall effect) , on have consider similar interaction in 3D topological insulator.
There is a proposal of this here
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.085422
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