Superhard three-dimensional B3N4 with two-dimensional metallicity

As the stable compound in boron nitrides, stoichiometric BN is a well-known insulator, irrespective of its structure and dimensionality. The exploration of novel B-N compounds with various stoichiometric ratios can lead to the discovery of unexpected electrical and mechanical properties. To the best of our knowledge, previously reported graphite-like or diamond-like B-N compounds obtained from experimental synthesis and theoretical prediction are mostly insulators or semiconductors. In this paper, a sp(2)-sp(3) hybridised tetragonal phase of B3N4 (t-B3N4) possessing unique two-dimensional (2D) metallicity in a 3D ultra-strong framework has been predicted through an unbiased swarm structure search. The structure of t-B3N4 can be considered as sp(3)-hybridised cubic BN blocks interlinked by sp(2) N-N bonds. Noticeably, t-B3N4 is metastable at ambient pressure, but becomes stable under high pressure. The transition pressure from layered B3N4 to t-B3N4 is 14.7 GPa, and the calculated formation enthalpies of t-B3N4 with respect to h-BN and N-2 become negative at pressures above 20 GPa, indicating its viability under pressure. Its structure stability has been confirmed by the criteria of both elastic constants and phonon frequency dispersions. The analyses of the band structure, density of states, and electron orbitals show that the metallic behaviour of t-B3N4 mainly originates from the N 2p electrons, and that the conduction is interrupted by the insulated boron sheets stacked along the c axis, giving rise to the 2D metallicity of the material. The theoretical Vickers hardness of t-B3N4 is estimated to reach 42.5 GPa, which is the highest among all proposed B3N4 polymorphs. Furthermore, t-B3N4 exhibits ultra-high axial incompressibility even beyond that of diamond, due to the existence of strong short N-N bonds.