It has been widely accepted that planar boron structures, composed of triangular and hexagonal motifs are the most stable two-dimensional (2D) phases and likely precursors for boron nanostructures. Here we predict, based on an ab initio evolutionary structure search, a novel 2D boron structure with nonzero thickness, which is considerably, by $50\mathrm{meV}/\mathrm{atom}$, lower in energy than the recently proposed $\alpha$-sheet structure and its analogues. In particular, this phase is identified for the first time to have a distorted Dirac cone, after graphene and silicene the third elemental material with massless Dirac fermions. The buckling and coupling between the two sublattices not only enhance the energetic stability, but also are the key factors for the emergence of the distorted Dirac cone.

We describe a convenient approach for generating arbitrary vector beams in a $4\text{-}f$ system with a spatial light modulator (SLM) and a common path interferometric arrangement. A computer-generated hologram is introduced onto SLM for performing the beam conversion. Optical realization of a variety of polarization configurations confirms the reliability and flexibility of our method.

We present a detailed investigation on optical properties of high-pressure phase ZnO in $B1$ (NaCl) and $B2$ (CsCl) structures, including dielectric function, refractive index, absorption, and electron energy-loss spectrum. Theoretical calculations are performed using the ab initio pseudopotential density functional method, in which we employ the Perdew-Burke-Eruzerhof form of the generalized gradient approximation available in the CASTEP code together with plane wave basis sets for expanding the periodic electron density. Both structures are optimized under the respective structural phase transition pressures; for the $B1$ structure it is $9\mathrm{GPa}$, which has been verified to be in agreement with theory [Jaffe et al., Phys. Rev. B 62, 1660 (2000)] and experiment [Desgreniers, Phys. Rev. B 58, 14102 (1998)], while for the $B2$ structure a transition pressure of $256\mathrm{GPa}$ is predicted in theory [Jaffe et al., Phys. Rev. B 62, 1660 (2000)]. We find that their electronic structures and optical properties under high pressure are quite different from those under ambient pressure.

Helium is generally understood to be chemically inert and this is due to its extremely stable closed-shell electronic configuration, zero electron affinity and an unsurpassed ionization potential. It is not known to form thermodynamically stable compounds, except a few inclusion compounds. Here, using the ab initio evolutionary algorithm USPEX and subsequent high-pressure synthesis in a diamond anvil cell, we report the discovery of a thermodynamically stable compound of helium and sodium, Na₂He, which has a fluorite-type structure and is stable at pressures >113 GPa. We show that the presence of He atoms causes strong electron localization and makes this material insulating. This phase is an electride, with electron pairs localized in interstices, forming eight-centre two-electron bonds within empty Na₈ cubes. We also predict the existence of Na₂HeO with a similar structure at pressures above 15 GPa.

We propose an ultra-thin metamaterial constructed by an ensemble of the same type of anisotropic aperture antennas with phase discontinuity for wave front manipulation across the metamaterial. A circularly polarized light is completely converted to the cross-polarized light which can either be bent or focused tightly near the diffraction limit. It depends on a precise control of the optical-axis profile of the antennas on a subwavelength scale, in which the rotation angle of the optical axis has a simple linear relationship to the phase discontinuity. Such an approach enables effective wave front engineering within a subwavelength scale.

A novel carbon allotrope of C-centered orthorhombic C8 (Cco-C8) is predicted by using a recently developed particle-swarm optimization method on structural search. Cco-C8 adopts a sp3 three-dimensional bonding network that can be viewed as interconnected (2,2) carbon nanotubes through 4- and 6-member rings and is energetically more favorable than earlier proposed carbon polymorphs (e.g., M carbon, bct-C4, W carbon, and chiral C6) over a wide range of pressures studied (0\char21{}100~GPa). The simulated x-ray diffraction pattern, density, and bulk modulus of Cco-C8 are in good accordance with the experimental data on structurally undetermined superhard carbon recovered from cold compression of carbon nanotube bundles. The simulated hardness of Cco-C8 can reach a remarkably high value of 95.1~GPa, such that it is capable of cracking diamond.