Two-Dimensional Sigma-Hole Systems in Boron Layers: A First-Principles Study on Mg_{1-x}Na_xB_2 and Mg_{1-x}Al_xB_2

We study two-dimensional sigma-hole systems in boron layers by calculating the electronic structures of Mg_{1-x}Na_xB_2 and Mg_{1-x}Al_xB_2. In Mg_{1-x}Na_xB_2, it is found that the concentration of sigma holes is approximately described by (0.8 + 0.8 x) * 10^{22} cm^{-3} and the largest attainable concentration is about 1.6 * 10^{22} cm^{-3} in NaB_2. In Mg_{1-x}Al_xB_2, on the other hand, it is found that the concentration of sigma holes is approximately described by (0.8 - 1.4 x) * 10^{22} cm^{-3} and sigma holes are disappeared at x of about 0.6. These relations can be used for experimental studies on the sigma-hole systems in these materials.