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At half filling, the electronic structure of graphene can be modelled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field, an everywhere-real Kekule…

Graphene's original promise to succeed silicon faltered due to pervasive edge disorder in lithographically patterned deposited graphene and the lack of a new electronics paradigm. Here we demonstrate that the annealed edges in…

Using ab initio methods we have investigated the fluorination of graphene and find that different stoichiometric phases can be formed without a nucleation barrier, with the complete "2D-Teflon" CF phase being thermodynamically most stable.…

Four fundamental dimer manipulations can be used to produce a variety of localized and extended defect structures in graphene. Two-dimensional templates result in graphene allotropes, here viewed as extended defects, which can exhibit…

The electronic properties of a graphene sheet with attached hydrogen atoms is studied using a modified Falicov-Kimball model on the honeycomb lattice. It is shown that in the ground state this system separates into two phases: fully…

Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, we form a versatile…

Void defect is a possible origin of ferromagnetic like feature of pure carbon material. Applying density functional theory to void defect induced graphene nano ribbon (GNR), a detailed relationship between multiple spin state and structure…

Lattice defects are inevitably present in two-dimensional materials, with direct implications on their physical and chemical properties. We show that the formation energy of a lattice defect in buckled two-dimensional crystals is not…

The chapter combines analytical (statistical-thermodynamic and kinetic) with numerical (Kubo-Greenwood-formalism-based) approaches used to ascertain an influence of the configurations of point (impurities, vacancies) and line (grain…

Due to Klein tunneling, electrostatic confinement of electrons in graphene is not possible. This hinders the use of graphene for quantum dot applications. Only through quasi-bound states with finite lifetime has one achieved to confine…

Graphene was the first material predicted to be a time-reversal-invariant topological insulator; however, the insulating gap is immeasurably small owing to the weakness of spin-orbit interactions in graphene. A recent experiment [1]…

Theory predicts that double layer systems realize "two-component composite fermions," which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid and crystal…

Electronic properties of two-dimensional graphene superlattice made with partial hydrogenation were thoroughly studied via Density Functional Tight Binding approach (DFTB) which incorporates the tight-binding method into the density…

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED$_{4,3}$ with $N$ four component…

Since the ground-breaking discovery of the quantum Hall effect, half-quantized quantum Hall plateaus have been some of the most studied and sought-after states. Their importance stems not only from the fact that they transcend the composite…

Magnetic properties of a single vacancy in graphene is a relevant and still much discussed problem. The experimental results point to a clearly detectable magnetic defect state at the Fermi energy, while calculations based on density…

The unique electronic properties of graphene offer the possibility that it could replace silicon when microelectronics evolves to nanoelectronics. Graphene grown epitaxially on silicon carbide is particularly attractive in this regard…

Graphene is considered one of the most promising materials for future electronic. However, in its pristine form graphene is a gapless material, which imposes limitations to its use in some electronic applications. In order to solve this…

We report the electronic properties of two-dimensional systems made of graphene nanoribbons which are patterned with ad-atoms in two separated regions. Due to the extra electronic confinement induced by the presence of the impurities, we…

The study of vacancies in graphene is a topic of growing interest. A single vacancy induces a localized stable charge of order unity interacting with other charges of the conductor through an unscreened Coulomb potential. It also breaks the…