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Aspects of the Fractional Quantum Hall Effect in Graphene

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Physics of Graphene

Part of the book series: NanoScience and Technology ((NANO))

Abstract

We present a brief overview of the nature of the fractional quantum Hall effect (FQHE) in monolayer and bilayer graphene. After a short introduction on the effect and the pseudopotential description of interacting electrons in the quantum Hall regime, we discuss in detail the magnetic field effects on electrons in monolayer graphene. We also briefly discuss the experimental signatures of the effect reported in the literature. In bilayer graphene, the effect manifests itself in a very different manner and we discuss in detail the various novel effects one expects there due to electron-electron interactions. The nature of the collective excitations of Dirac fermions in trilayer graphene is also briefly discussed. Existence of some exotic states in bilayer graphene, such as the Pfaffian state is also highlighted. Finally, we have touched upon the properties of the FQHE states of Dirac fermions on the surface of a topological insulator.

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Notes

  1. 1.

    In this brief introduction to the FQHE, we limit ourselves only to the description of the filling factor \(\nu=\frac{1}{q}\). Interested readers could consult other sources for a more detailed account [7, 8, 10].

  2. 2.

    If not otherwise stated, in what follows, we consider the positive values of n.

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Acknowledgements

This work has been supported by the Canada Research Chairs program of the Government of Canada. We would like to thank Peter Maksym for carefully reading the manuscript and offering valuable comments to improve the article.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2

    Tapash Chakraborty

  2. Department of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA

    Vadim Apalkov

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Correspondence to Tapash Chakraborty .

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  1. Faculty of Science Department of Physics, University of Tokyo, Tokyo, Japan

    Hideo Aoki

  2. Physics and Electrical Eng. Dept., Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Mildred S. Dresselhaus

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Chakraborty, T., Apalkov, V. (2014). Aspects of the Fractional Quantum Hall Effect in Graphene. In: Aoki, H., S. Dresselhaus, M. (eds) Physics of Graphene. NanoScience and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02633-6_8

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