Stabilizing benzene-like planar N₆ rings to form a single atomic honeycomb BeN₃ sheet with high carrier mobility

It is a longstanding quest to use the planar N₆ ring as a structural unit to build stable atomic sheets. However, unlike C₆H₆, the neutral N₆ ring is unstable due to the strong repulsion of the lone-pair of electrons. Using first-principles calculations and the global structure search method, we show that the N₆ unit can be stabilized by the linkage of Be atoms, forming a h-BeN₃ honeycomb monolayer, in which the geometry and the π-molecular orbitals of the N₆ rings are well kept. This sheet is not only energetically, dynamically and thermally stable, but also can withstand high temperatures up to 1000 K. Band structure calculation combined with a group theory analysis and a tight-binding model uncover that h-BeN₃ has a π-band dominated band structure with an indirect band gap of 1.67 eV. While it possesses a direct band gap of 2.07 eV at the Γ point lying in the photon energy region of visual light, its interband dipole transition is symmetrically allowed so that electrons can be excited by photons free of phonons. Based on deformation potential theory, a systematic study of the transport properties reveals that the h-BeN₃ sheet possesses a high carrier mobility of ∼10³ cm² V^-1 s^-1, superior to the extensively studied transition metal dichalcogenide monolayers. We further demonstrate that this sheet can be rolled up into either zigzag or armchair nanotubes. These nanotubes are also dynamically stable, and are all direct band gap semiconductors with carrier mobility comparable to that of their 2D counterparts, regardless of their chirality and diameter. The robust stability and novel electronic and transport properties of the h-BeN₃ sheet and its tubular derivatives endow them with great potential for applications in nanoelectronic devices.