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 miniband 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.
We model the optical visibility of monolayer and bilayer graphene deposited on a silicon/silicon oxide substrate or thermally annealed on the surface of silicon carbide. We consider reflection and transmission setups, and find that visibility is strongest in reflection reaching the optimum conditions when the bare substrate transmits light resonantly. In the optical range of frequencies a bilayer is approximately twice as visible as a monolayer thereby making the two types of graphene distinguishable from each other.
We investigate the adsorption of graphene sheets on h-BN substrates by means of first-principles calculations in the framework of adiabatic connection fluctuation-dissipation theory in the random phase approximation. We obtain adhesion energies for different crystallographic stacking configurations and show that the interlayer bonding is due to long-range van der Waals forces. The interplay of elastic and adhesion energies is shown to lead to stacking disorder and moire structures. Band structure calculations reveal substrate induced mass terms in graphene which change their sign with the stacking configuration. The dispersion, absolute band gaps and the real space shape of the low energy electronic states in the moire structures are discussed. We find that the absolute band gaps in the moire structures are at least an order of magnitude smaller than the maximum local values of the mass term. Our results are in agreement with recent STM experiments.
We performed calculations of electronic, optical and transport properties of graphene on hBN with realistic moire patterns. The latter are produced by structural relaxation using a fully atomistic model. This relaxation turns out to be crucially important for electronic properties. We describe experimentally observed features such as additional Dirac points and the Hofstadter butterfly structure of energy levels in a magnetic field. We find that the electronic structure is sensitive to many-body renormalization of the local energy gap.
Graphene on a dielectric substrate exhibits spatial doping inhomogeneities, forming electron-hole puddles. Understanding and controlling the latter is of crucial importance for unraveling many of graphenes fundamental properties at the Dirac point. Here we show the coexistence and correlation of charge puddles and topographic ripples in graphene decoupled from the metallic substrate it was grown on. The analysis of interferences of Dirac fermion-like electrons yields a linear dispersion relation, indicating that graphene on a metal can recover its intrinsic electronic properties.
We investigate the many-body properties of graphene on top of a piezoelectric substrate, focusing on the interaction between the graphene electrons and the piezoelectric acoustic phonons. We calculate the electron and phonon self-energies as well as the electron mobility limited by the substrate phonons. We emphasize the importance of the proper screening of the electron-phonon vertex and discuss the various limiting behaviors as a function of electron energy, temperature, and doping level. The effect on the graphene electrons of the piezoelectric acoustic phonons is compared with that of the intrinsic deformation acoustic phonons of graphene. Substrate phonons tend to dominate over intrinsic ones for low doping levels at high and low temperatures.