# Graphene on incommensurate substrates: Trigonal warping and emerging Dirac cone replicas with halved group velocity

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Jeroen van den Brink, Jul 27, 2015 Available from:### Click to see the full-text of:

Article: Graphene on incommensurate substrates: Trigonal warping and emerging Dirac cone replicas with halved group velocity

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- "Graphene-hBN composite system has also been intensively studied as another example of incommensurate multilayer system, where the two layers share the same hexagonal lattice structure but with slightly-different lattice constants, leading to the long-period modulation even at zero rotation angle [15] [16] [17] [18] [19] [20] [21]. The electronic structure in graphene-hBN system was theoretically studied [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35], and the recent transport measurements revealed remarkable effects such as the formation of mini-Dirac bands and the fractal subband structure in magnetic fields [36] [18] [19] [20]. The previous theoretical works mainly targeted the honeycomb lattice to model twisted bilayer graphene and graphene-hBN system, and also particularly focus on the long-period moiré modulation which arises when the crystal structures of two layers are slightly different. "

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**ABSTRACT:**We present a general theoretical formulation to describe the interlayer interaction in incommensurate bilayer systems with arbitrary crystal structures. By starting from the tight- binding model with the distance-dependent transfer integral, we show that the interlayer coupling, which is highly complex in the real space, can be simply written in terms of generalized Umklapp process in the reciprocal space. The formulation is useful to describe the interaction in the two-dimensional interface of different materials with arbitrary lattice structures and relative orientations. We apply the method to the incommensurate bilayer graphene with a large rotation angle, which cannot be treated as a long-range moir\'{e} superlattice, and obtain the quasi band structure and density of states within the first-order approximation.New Journal of Physics 01/2015; 17(1). DOI:10.1088/1367-2630/17/1/015014 · 3.67 Impact Factor -
- "Fermi velocity is reduced to 0.64 ± 0.03 × 10 6 m/s for the new electrons and 0.78 ± 0.03 × 10 6 m/s for the new holes. The reduction agrees with recent theoretical predictions [15] and our numerical calculations. Evidence for the presence of the superlattice Dirac point can also be seen in the global conductivity as a function of gate voltage (see Supplementary "

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**ABSTRACT:**The Schr\"odinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of band gaps near points of the reciprocal lattice known as Brillouin zone boundaries. However, in the case of massless Dirac fermions, it has been predicted that the chirality of the charge carriers prevents the opening of a band gap and instead new Dirac points appear in the electronic structure of the material. Graphene on hexagonal boron nitride (hBN) exhibits a rotation dependent Moir\'e pattern. In this letter, we show experimentally and theoretically that this Moir\'e 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. The local density of states near these Dirac cones exhibits hexagonal modulations indicating an anisotropic Fermi velocity.Nature Physics 02/2012; 8(5). DOI:10.1038/nphys2272 · 20.60 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Using a first-principles approach we calculate the acoustic electron-phonon couplings in graphene for the transverse (TA) and longitudinal (LA) acoustic phonons. Analytic forms of the coupling matrix elements valid in the long-wavelength limit are found to give an almost quantitative description of the first-principles based matrix elements even at shorter wavelengths. Using the analytic forms of the coupling matrix elements, we study the acoustic phonon-limited carrier mobility for temperatures 0-200 K and high carrier densities of 10^{12}-10^{13} cm^{-2}. We find that the intrinsic effective acoustic deformation potential of graphene is \Xi_eff = 6.8 eV and that the temperature dependence of the mobility \mu ~ T^{-\alpha} increases beyond an \alpha = 4 dependence even in the absence of screening when the full coupling matrix elements are considered. The large disagreement between our calculated deformation potential and those extracted from experimental measurements (18-29 eV) indicates that additional or modified acoustic phonon-scattering mechanisms are at play in experimental situations.Physical review. B, Condensed matter 01/2012; 85(16). DOI:10.1103/PhysRevB.85.165440 · 3.66 Impact Factor