We investigate the possibility of realizing quantum anomalous Hall effect in graphene. We show that a bulk energy gap can be opened in the presence of both Rashba spin-orbit coupling and an exchange field. We calculate the Berry curvature distribution and find a non-zero Chern number for the valence bands and demonstrate the existence of gapless edge states. Inspired by this finding, we also study, by first principles method, a concrete example of graphene with Fe atoms adsorbed on top, obtaining the same result.

Experimental electrical double-layer capacitances of porous carbon electrodes fall below ideal values, thus limiting the practical energy densities of carbon-based electrical double-layer capacitors. Here we investigate the origin of this behaviour by measuring the electrical double-layer capacitance in one to five-layer graphene. We find that the capacitances are suppressed near neutrality, and are anomalously enhanced for thicknesses below a few layers. We attribute the first effect to quantum capacitance effects near the point of zero charge, and the second to correlations between electrons in the graphene sheet and ions in the electrolyte. The large capacitance values imply gravimetric energy storage densities in the single-layer graphene limit that are comparable to those of batteries. We anticipate that these results shed light on developing new theoretical models in understanding the electrical double-layer capacitance of carbon electrodes, and on opening up new strategies for improving the energy density of carbon-based capacitors.

Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on the recent progress in the engineering of topologically nontrivial phases (such as Z2 topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc.) in two-dimensional material systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.

We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of BiFeO3. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tuned experimentally by applying external pressure.

When atomically thin two-dimensional (2D) materials are layered they often form incommensurate noncrystalline structures that exhibit long-period moiré patterns when examined by scanning probes. In this paper we present an approach which uses information obtained from ab initio calculations performed on short-period crystalline structures to derive effective Hamiltonians that are able to efficiently describe the influence of the moiré pattern superlattices on electronic properties. We apply our approach to the cases of graphene on graphene (G/G) and graphene on hexagonal boron nitride (G/BN), deriving explicit effective Hamiltonians that have the periodicity of the moiré pattern and can be used to calculate electronic properties of interest for arbitrary twist angles and lattice constants.

The existence of inequivalent valleys K and K′ in the momentum space of two-dimensional hexagonal lattices provides a new electronic degree of freedom, the manipulation of which can potentially lead to new types of electronics, in analogy to the role played by electron spin 1-3 . In materials with broken inversion symmetry, such as an electrically gated bilayer graphene 4,5 , the momentum-space Berry curvature  carries opposite sign in the K and K′ valleys. A sign reversal of  along an internal boundary of the sheet gives rise to counterpropagating one-dimensional conducting modes encoded with opposite valley indices. These metallic states are topologically protected against backscattering in the absence of valley-mixing scattering, and thus can carry current ballistically 1,6-11 . In bilayer graphene, the reversal of  can occur at the domain wall of AB and BA stacked domains 12-14 , or at the line junction of two oppositely gated regions 6 . The latter approach can provide a scalable platform to implement valleytronic operations such as valves and waveguides 9,15 , but is technically challenging to realize. Here we fabricate a dual-split-gate structure in bilayer graphene and demonstrate transport evidence of the predicted metallic states. They possess a mean free path of up to a few hundred nanometers in the absence of a magnet field. The application of perpendicular magnetic field suppresses backscattering significantly and enables a 400-nanometer-long junction to exhibit conductance close to the ballistic limit of 4 e 2 /h at 8 Tesla. Our experiment paves the path to the realization of gate-controlled ballistic valley transport and the development of valleytronic applications in atomically thin materials.Exploiting the valley degree of freedom in hexagonal lattices may offer an alternative pathway to achieving low-power-consumption electronics. Experiments have shown that a net valley polarization in the material can be induced by the use of circularly polarized light 2,16,17 or a net bulk current [18][19][20] . However the use of light is not always desirable in electronics and device proposals using bulk valley polarization often put stringent requirements on the size and edge orientation of the active area 3 . Alternatively, electrically created, valley-polarized topological conducting channels in high-mobility bilayer graphene may offer a robust, scalable platform to realize valleytronic operations 1,6,[8][9][10][11][12][13][14][15] . Figure 1a illustrates the dual-split-gating scheme proposed by Martin et al 6 , where an AB-stacked bilayer graphene (BLG) sheet is controlled by two pairs of top and bottom gates separated by a line junction. The device operates in the regime where both the left and the right regions of the BLG sheet are insulating due to a bulk band gap induced by the independently applied displacement fields DL and DR. In the "odd" field configuration, where DLDR < 0, theory predicts the existence of eight conducting modes (referred to as the "kink" states) propagating along the line ...

We systematically investigate the magnetic and electronic properties of graphene adsorbed with diluted 3d-transition and noble metal atoms using first principles calculation methods. We find that most transition metal atoms (i.e. Sc, Ti, V, Mn, Fe) favor the hollow adsorption site, and the interaction between magnetic adatoms and π-orbital of graphene induces sizable exchange field and Rashba spin-orbit coupling, which together open a nontrivial bulk gap near the Dirac K/K ′ (Γ) points in the 4 × 4 (3 × 3) supercell of graphene leading to the quantum-anomalous Hall effect. We also find that the noble metal atoms (i.e. Cu, Ag, Au) prefer the top adsorption site, and the dominant inequality of the AB sublattice potential opens another kind of nontrivial bulk gap exhibiting the quantum-valley Hall effect in the 4 × 4 supercell of graphene.

Bilayer graphene with an interlayer potential difference has an energy gap and, when the potential difference varies spatially, topologically protected one-dimensional states localized along the difference's zero lines. When disorder is absent, electronic travel directions along zero-line trajectories are fixed by valley Hall properties. Using the Landauer-Büttiker formula and the nonequilibrium Green's function technique, we demonstrate numerically that collisions between electrons traveling in opposite directions, due to either disorder or changes in path direction, are strongly suppressed. We find that extremely long mean free paths of the order of hundreds of micrometers can be expected in relatively clean samples. This finding suggests the possibility of designing low power nanoscale electronic devices in which transport paths are controlled by gates which alter the interlayer potential landscape.