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Electronic Properties of Graphene Heterostructures with Hexagonal Crystals pp 19–32Cite as

Monolayer Graphene on a hBN Underlay

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Abstract

This chapter provides a general phenomenological description electrons in graphene placed on substrates with the hexagonal Bravais lattice (such as hexagonal boron nitride). In particular, we identify conditions at which the first moiré miniband is separated from the rest of the spectrum by either one or a group of three isolated secondary Dirac points, and is not obscured by dispersion surfaces coming from other minibands. In such cases, the Hall coefficient exhibits two distinct alternations of its sign as a function of charge carrier density. This phenomenological analysis is complemented by microscopic calculations.

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Notes

  1. 1.

    The Hamiltonian in the vicinity of other two inequivalent points on the sBZ edge, \(\varvec{\mu }'=\hat{R}_{2\pi /3}\varvec{\mu }\), \(\varvec{\mu }''=\hat{R}_{4\pi /3}\varvec{\mu }\), can be obtained using \(H_{\varvec{\mu }+\varvec{q}}=H_{\varvec{\mu }'+\hat{R}_{2\pi /3}\varvec{q}}=H_{\varvec{\mu }''+\hat{R}_{4\pi /3}\varvec{q}}\).

  2. 2.

    Note that the spectra derived from \(\hat{H}_{\zeta (\varvec{\kappa }+\varvec{q})}\) obey the three-fold rotational symmetry.

  3. 3.

    In Eqs. (2.5) and (2.6) this transformation is equivalent to a gauge transform and therefore leaves the bandstructure unaltered.

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Authors and Affiliations

  1. Department of Physics, Lancaster University, Lancaster, UK

    John R. Wallbank

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  1. John R. Wallbank
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Correspondence to John R. Wallbank .

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Wallbank, J.R. (2014). Monolayer Graphene on a hBN Underlay. In: Electronic Properties of Graphene Heterostructures with Hexagonal Crystals. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-07722-2_2

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