Anomalous optical and electronic properties of dense sodium

Based on ab initio density-functional-theory using generalized gradient approximation, we systematically study the optical and electronic properties of the insulating dense sodium phase (Na-hp4) reported recently [Ma \textit{et al.}, Nature \textbf{458}, 182 (2009)]. The structure is found optically anisotropic and transparent to visible light, which can be well interpreted using its electronic band structure and angular moment decomposed density of states. Through the bader analysis of Na-hp4 at different pressures, we conclude that ionicity exists in the structure and becomes stronger with increasing pressure. In addition, the absorption spectra in the energy range from 1.4 to 2.4 eV are compared with recent experimental results and found good agreement. It is found that the deep-lying valence electrons participate in the interband transition.