Using a structural search method in combination with first-principles calculations, we found lots of low energy 2D carbon allotropes and examined all possible Dirac points around their Fermi levels. Three amazing 2D Dirac carbon allotropes have been discovered, named as S-graphene, D-graphene and E-graphene. By analyzing the topology correlations among S-, T, net W graphene and graphene, we found that a general rule is valuable for constructing 2D carbon allotropes that are keen to possess Dirac cones in their electronic structures. Based on this rule, we have successfully designed many new 2D carbon allotropes possessing Dirac cones. Their energy order can be well described by an Ising-like model, and some allotropes are energetically more stable than those recently reported. The related electronic structures of these Dirac allotropes are anisotropy distinguished from those of graphene. Moreover, the fact that D- and E-graphene present Dirac cones suggests that sp hybridization or sp³ hybridization could not suppress the emerging of Dirac features. Our results demonstrate that the Dirac cone and carrier linear dispersion is a very common feature in 2D carbon allotropes and can exist beyond the limitations of fundamental structure features of graphene.

The recent synthesis of monolayer borophene (triangular boron monolayer) on a substrate has opened the era of boron nanosheets (Science, 2015, 350, 1513), but the structural instability and a need to explore the novel physical properties are still open issues. Here we demonstrated that borophene can be stabilized by full surface hydrogenation (borophane), from first-principles calculations. Most interestingly, our calculations show that borophane has direction-dependent Dirac cones, which are mainly caused by the in-plane p_x and p_y orbitals of boron atoms. The Dirac fermions possess an ultrahigh Fermi velocity of up to 3.5 × 10⁶ m s⁻¹ under the HSE06 level, which is 4 times higher than that of graphene. The Young's moduli are calculated to be 190 and 120 GPa nm along two different directions, which are comparable to those of steel. The ultrahigh Fermi velocity and good mechanical features render borophane ideal for nanoelectronic applications.

S-functionalized V₂C (V₂CS₂) was designed and the properties of it act as anchoring material for Li–S batteries' cathode were investigated by first-principles calculations. Compared with bare V₂C and V₂CO₂, V₂CS₂ is more suitable as anchoring material.

The lack of high-performance anode materials has become a major obstacle to the development of Li- and Na-ion batteries. Recently, 2D transition metal borides (e.g. MBenes) have attracted much attention due to their excellent stability and electrical conductivity. Unfortunately, most of the reported MBene phases typically have an intrinsic metal-rich structure with metal atoms exposed on the surface, which harmfully affect the adsorption of Li/Na atoms. Here, through crystal structure prediction combined with the first-principles density functional theory, a novel TiB₃ MBene has been determined by altering the proportion of non-metallic element boron to wrap metal atoms and weaken nearest-neighbor electrostatic repulsion. Electrostatic potential analysis visually shows a surface with low potential on the TiB₃ monolayer implying high adsorption capacity, and also can be used to quickly screen out the Li/Na adsorption sites. Accurate half-cell battery simulation confirmably shows that the TiB₃ monolayer possesses a theoretical specific capacity of 1335.04 and 667.52 mA h g⁻¹ for Li and Na, respectively. The TiB₃ monolayer can remain metallic after adsorbing Li/Na atoms, which ensures good conductivity during battery cycling. The ultra-low barrier energy (only 38 meV for Li) and suitable open-circuit voltage indicate excellent charging and discharging capabilities. These results suggest that the TiB₃ monolayer could be a promising anode material for Li- and Na-ion batteries, and provide a simple design principle for exposing non-metallic atoms on the surface.