Structural and electronic properties of a single layered $\alpha $-tetragonal B$_{\mathrm{50}}$ sheet.

Ultrathin single-crystalline boron nanosheets with $\alpha $-tetragonal B$_{\mathrm{50}}$ symmetry ($\alpha $-t-B$_{\mathrm{50}})$ have recently been synthesized [1]. In this presentation, the relaxed structure of this new type of boron sheet is determined using a robust self-consistent and environment-dependent semi-empirical Hamiltonian developed within the LCAO framework that includes MD and power quenching schemes. Upon relaxation, the sheet symmetry is broken and the icosahedral B$_{\mathrm{12}}$ units in the sheet are found to be distorted. This stability of the sheet was investigated through a calculation of the vibrational frequencies. The sheet electronic density of states exhibits no energy gap at the Fermi level, suggesting a metallic character similar to that of the bulk $\alpha $-t-B$_{\mathrm{50}}$. Finally, the cohesive energy of the $\alpha $-t-B$_{\mathrm{50}}$ sheet is found to be higher than that of the recently reported icosahedral B$_{\mathrm{12}}$-$\delta_{\mathrm{6\thinspace }}$sheet [2]. [1] Adv. Sci. 2, 1500023 (2015) [2] Nanotechnology 26, 405701 (2015)