Van der Waals heterostructures of graphene and hexagonal boron nitride feature a moire superlattice for graphenes Dirac electrons. Here, we review the effects generated by this superlattice, including a specific miniband structure featuring gaps and
secondary Dirac points, and a fractal spectrum of magnetic minibands known as Hofstadters butterfly.
We present a phenomenological theory of the low energy moire minibands of Dirac electrons in graphene placed on an almost commensurate hexagonal underlay with a unit cell pproximately three times larger than that of graphene.A slight incommensurabili
ty results in a periodically modulated intervalley scattering for electrons in graphene. In contrast to the perfectly commensurate Kekule distortion of graphene, such supperlattice perturbation leaves the zero energy Dirac cones intact, but is able to open a band gap at the edge of the first moire subbband, asymmetrically in the conduction and valence bands.
We study the superlattice minibands produced by the interplay between moire pattern induced by hexagonal BN substrate on graphene layer and the interlayer coupling in bilayer graphene with Bernal stacking (BLG). We compare moire miniband features in
BLG, where they are affected by the interlayer asymmetry of BLG-hBN heterostructure and trigonal warping characteristic for electrons in Bernal-stacked bilayers with those found in monolayer graphene.
Using a general symmetry-based approach, we provide a classification of generic miniband structures for electrons in graphene placed on substrates with the hexagonal Bravais symmetry. In particular, we identify conditions at which the first moire min
iband is separated from the rest of the spectrum by either one or a group of three isolated mini 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.
Combining the tight-binding approximation and linear elasticity theory for a planar membrane, we investigate stretching of a graphene flake assuming that two opposite edges of the sample are clamped by the contacts. We show that, depending on the asp
ect ratio of the flake and its orientation, gapped states may form in the membrane in the vicinity of the contacts. This gap in the pre-contact region should be biggest for the armchair orientation of the flake and width to length ratio of around 1.
We present a self-consistent calculation of the interlayer asymmetry in bilayer graphene caused by an applied electric field in magnetic fields. We show how this asymmetry influences the Landau level spectrum in bilayer graphene and the observable in
ter-Landau level transitions when they are studied as a function of high magnetic field at fixed filling factor as measured experimentally by E.A. Henriksen et al., Phys. Rev. Lett. 100 (2008), 087403. We also analyze the magneto-optical spectra of bilayer flakes in the photon-energy range corresponding to transitions between degenerate and split bands of bilayers.
We show theoretically how constant-energy maps of the angle-resolved photoemission intensity can be used to test wave function symmetry in graphene. For monolayer graphene, we demonstrate that the observed anisotropy of ARPES spectra is a manifestati
on of what has been recently branded as electronic chirality. For bilayer graphene, we show that the anisotropy of the constant-energy maps may be used to extract information about the magnitude and sign of interlayer coupling parameters and about symmetry breaking inflicted on a bilayer by the underlying substrate.
