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Inspired by the great development of graphene, more and more works have been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition metal oxides (VO2)n/(TiO2)m and (CrO2)n/(TiO2)m, organic and organometallic crystals, so-MoS2, and artificial lattices (electron gases and ultracold atoms). Their structural and electronic properties are summarized. We also investigate how Dirac points emerge, move, and merge in these systems. The von Neumann-Wigner theorem is used to explain the scarcity of Dirac cones in 2D systems, which leads to rigorous requirements on the symmetry, parameters, Fermi level, and band overlap of materials to achieve Dirac cones. Connections between existence of Dirac cones and the structural features are also discussed., Comment: Review paper, 31 pages, 10 figures

We present a first-principles study of the migration and recombination of edge defects (carbon adatom and/or vacancy) and their influence on electrical conductance in zigzag graphene nanoribbons (ZGNRs). It is found that at room temperature, the adatom is quite mobile while the vacancy is almost immobile along the edge of ZGNRs. The recombination of an adatom-vacancy pair leads to a pentagon-heptagon ring defect structure having a lower energy than the perfect edge, implying that such an edge-defect can be formed spontaneously. This edge defect can suppresses the conductance of ZGNRs drastically, which provides some useful hints for understanding the observed semiconducting behavior of the fabricated narrow GNRs., Comment: 6 pages, 4 figures, to appear in PRB

We investigate the dissociation of O2 on Pb(111) surface using first-principles calculations. It is found that in a practical high-vacuum environment, the adsorption of molecular O2 takes place on clean Pb surfaces only at low temperatures such as 100 K, but the O2 easily desorbs at (elevated) room temperatures. It is further found that the Pb adatoms enhance the molecular adsorption and activate the adsorbed O2 to dissociate during subsequent room-temperature annealing. Our theory explains the observation of a two-step oxidation process on the Pb surfaces by the unique role of Pb adatoms.

First-principles calculations reveal half metallicity in zigzag boron nitride (BN) nanoribbons (ZBNNRs). When the B edge, but not the N edge, of the ZBNNR is passivated, despite being a pure $sp$-electron system, the ribbon shows a giant spin splitting. The electrons at the Fermi level are 100% spin polarized with a half-metal gap of 0.38 eV and its conductivity is dominated by metallic single-spin states. The two states across at the Dirac point have different molecular origins, which signals a switch of carrier velocity. The ZBNNR should be a good potential candidate for widegap spintronics., Comment: 10 pages, 3 figures

We have studied the adsorption of gas molecules (CO, NO, NO2, O2, N2, CO2, and NH3) on graphene nanoribbons (GNRs) using first principles methods. The adsorption geometries, adsorption energies, charge transfer, and electronic band structures are obtained. We find that the electronic and transport properties of the GNR with armchair-shaped edges are sensitive to the adsorption of NH3 and the system exhibits n type semiconducting behavior after NH3 adsorption. Other gas molecules have little effect on modifying the conductance of GNRs. Quantum transport calculations further indicate that NH3 molecules can be detected out of these gas molecules by GNR based sensor., Comment: 13 pages and 5 figures

Using a first-principles-based approach, we determine the ferroelectric pattern in PbZr$_{0.5}$Ti$_{0.5}$O$_3$ ultrathin film. It is found that vortex stripes are formed in the system and they are responsible for the 180$^\circ$ domains observed. When a local external field is exerted, the vortex stripe transforms into the vortex loop structure, which leads to the formation of a smaller domain with the polarization antiparallel to the field in the center of the field region. This may provide a convenient way to manipulate nanodomains in thin films., Comment: 5 pages, 3 figures

The ferroelectric properties of disorder Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$ thin films are investigated with Monte Carlo simulations on the basis of a first-principles-derived Hamitonian. It is found that there exists a critical thickness of about three unit cells ($\sim$12 \AA) below which the ferroelectricity disappears under the condition that the in-plane polarizations are suppressed by sufficient clamping effect. Above the critical thickness, periodic $180^{\circ}$ stripe domains with out-of-plane polarizations are formed in the systems in order to minimize the energy of the depolarizaing field. The stripe period increases with increasing film thickness. The microscopic mechanism responsible for these phenomena is discussed., Comment: 5 pages, 5 figures

Monte Carlo simulations based on a first-principles-derived Hamiltonian are conducted to study the properties of PZT alloys compositionally modulated along the [100] pseudocubic direction near the morphotropic phase boundary (MPB). It is shown that compositional modulation causes the polarization to continuously rotate away from the modulation direction, resulting in the unusual triclinic and C-type monoclinic ground states and huge enhancement of electromechanical responses (the peak of piezoelectric coefficient is as high as 30000 pC/N). The orientation dependence of dipole-dipole interaction in modulated structure is revealed as the microscopic mechanism to be responsible for these anomalies., Comment: 5 pages, 4 figures