Computational design of three-dimensional metallic boron nitride*

Based on comprehensive calculations, we have shown that the 3D BN structures composed of interlocking BN hexagons are metallic and dynamically stable. These newly designed 3D BN structures (T-BxNx, x$=$4n-1, n$=$1, 2, 3...) are hybrid systems with one B and one N atom in sp3 hybridization and (4n-2) sp2-bonded B and N atoms respectively per unit cell. The sp3 bonded B (N) atom binds to its surrounding four sp2 bonded N (B) atoms forming the 3D backbone and is responsible for stability. The sp2 bonded B atoms, on the other hand, play the key role in rendering the conducting network and metallicity. This special geometrical feature results in a unique property: unlike previously reported functionalized c-BN thin film whose metallicity stems from strong inbuilt polarization, the metallicity in 3D T-BxNx is intrinsic and comes from the delocalized electrons distributed around the B sites. The metallicity exhibited in the studied structures opens new door for BN materials with potential applications in electron transport, metal-free catalysis and electronic devices.