Emergence of superlattice Dirac points in graphene on hexagonal boron nitride

Abstract

The Schrödinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of bandgaps near points of the reciprocal lattice known as Brillouin zone boundaries 1 . However, in the case of massless Dirac fermions, it has been predicted that the chirality of the charge carriers prevents the opening of a bandgap and instead new Dirac points appear in the electronic structure of the material 2,3 . Graphene on hexagonal boron nitride exhibits a rotation-dependent moiré pattern 4,5 . Here, we show experimentally and theoretically that this moiré pattern acts as a weak periodic potential and thereby leads to the emergence of a new set of Dirac points at an energy determined by its wavelength. The new massless Dirac fermions generated at these superlattice Dirac points are characterized by a significantly reduced Fermi velocity. Furthermore, the local density of states near these Dirac cones exhibits hexagonal modulation due to the influence of the periodic potential.Owing to its hexagonal lattice structure with a diatomic unit cell, graphene has low-energy electronic properties that are governed by the massless Dirac equation 6 . This has a number of consequences, among them Klein tunnelling [7][8][9][10] , which prevents electrostatic confinement of charge carriers and inhibits the fabrication of standard semiconductor devices. This has motivated a number of recent theoretical investigations of graphene in periodic potentials 2,3,[11][12][13][14][15] , which explored ways of controlling the propagation of charge carriers by means of various superlattice potentials. On the analytical side, one-dimensional potentials render particle propagation anisotropic 2,3,11,14 and generate new Dirac points, where the electron and hole bands meet, at energies ±hv F |G|/2 given by the reciprocal superlattice vectors G (refs 2,3), where v F is the Fermi velocity. Numerical approaches have extended several of these results to the case of two-dimensional potentials 2,3,14,15 . Unlike for Schrödinger fermions, the periodic potentials generally induce new Dirac points but do not open bandgaps in graphene, owing to the chiral nature of the Dirac fermions.Recent scanning tunnelling microscope (STM) topography experiments have reported well-developed moiré patterns in graphene on crystalline substrates, which suggests that the latter generate effective periodic potentials 4,5,16,17 . Of particular interest is hexagonal boron nitride (hBN), because it is an insulator which only couples weakly to graphene. Furthermore, graphene on hBN exhibits the highest mobility ever reported for graphene on any substrate 18 , and has strongly suppressed charge inhomogeneities 4,5 . Hexagonal boron nitride is a layered material whose planes have the same atomic structure as graphene, with a 1.8% longer lattice constant. The influence of the weak graphene-substrate interlayer coupling on the electronic transport and spectroscopic properties of graphene is not well understood. In particular, there ...

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