We use a tight binding approach and density functional theory calculations to study the band structure of graphene/hexagonal boron nitride bilayer system in the most stable configuration. We show that an electric field applied in the direction perpendicular to the layers significantly modifies the electronic structure of the whole system, including shifts, anticrossing and other deformations of bands, which can allow to control the value of the energy gap. It is shown that band structure of biased system may be tailored for specific requirements of nanoelectronics applications. The carriers' mobilities are expected to be higher than in the bilayer graphene devices.

We have performed a density functional study of graphene adsorbed on Au(111) surface using both a local density approximation and a semiempirical van der Waals approach proposed by Grimme, known as the DFT-D2 method. Graphene physisorbed on metal has the linear dispersion preserved in the band-structure, but the Fermi level of the system is shifted with respect to the conical points which results in a doping effect. We show that the type and amount of doping depends not only on the choice of the exchange-correlation functional used in the calculations, but also on the supercell geometry that models the physical system. We analyzed how the factors such as the in-plane cell parameter and interlayer spacing in gold influence the Fermi level shift and we found that even a small variation in these parameters may cause a transition from p-type to n-type doping. We have selected a reasonable set of model parameters and obtained that graphene is either undoped or at most slightly p-type doped on the clean Au(111) surface, which seems to be in line with experimental findings. On the other hand, modifications of the substrate lattice may induce larger doping up to 0.30-0.40 eV depending on the graphene-metal adsorption distance. The sensitivity of the graphene-gold interface to the structural parameters may allow to tune doping across the samples which could lead to possible applications in graphene-based electronic devices. We believe that the present remarks can be also useful for other studies based on the periodic DFT.

Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene [1-3]. The linear energy dispersion and non-trivial Berry phase play the pivotal role in the remarkable electronic, optical, mechanical and chemical properties of 2D Dirac materials [4]. The known 2D Dirac materials are gapless only within certain approximations, for example, in the absence of SOC. Here we report a route to establishing robust Dirac cones in 2D materials with nonsymmorphic crystal lattice. The nonsymmorphic symmetry enforces Dirac-like band dispersions around certain high-symmetry momenta in the presence of SOC [5, 6]. Through µ-ARPES measurements we observe Dirac-like band dispersions in α-bismuthene. The nonsymmorphic lattice symmetry is confirmed by µ-LEED and STM. Our firstprinciples simulations and theoretical topological analysis demonstrate the correspondence between nonsymmorphic symmetry and Dirac states. This mechanism can be straightforwardly generalized to other nonsymmorphic materials. The results open the door for the search of symmetry enforced Dirac fermions in the vast uncharted world of nonsymmorphic 2D materials.

Electronic properties of the graphene layer sandwiched between two hexagonal boron nitride sheets have been studied using the first principles calculations and the minimal tight-binding model. It is shown that for the ABC-stacked structure in the absence of external field the bands are linear in the vicinity of the Dirac points as in the case of single layer graphene. For certain atomic configuration the electric field effect allows opening of a bandgap of over 230 meV. We believe that this mechanism of energy gap tuning could significantly improve the characteristics of graphene-based field effect transistors and pave the way for novel electronic applications.

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