# Anomalous optical and electronic properties of dense sodium 

Dafang Li, 1 Hanyu Liu, 1, 2 Bao-Tian Wang, 1, 3 Hongliang Shi, 1, 4 Shao-Ping Zhu, 1 Jun Yan, 1, 5 and Ping Zhang 1, 5, ∗ 

$^{1}$LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China 

$^{2}$National Laboratory of Superhard Materials, Jilin University, Changchun 130012, People’s Republic of China 

$^{3}$Institute of Theoretical Physics and Department of Physics, Shanxi University, Taiyuan 030006, People’s Republic of China 

$^{4}$SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, P. O. Box 912, Beijing 100083, People’s Republic of China 

$^{5}$Center for Applied Physics and Technology, Peking University, Beijing 100871, People’s Republic of China 

## Abstract 

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 et al. , Nature 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. 

PACS numbers: 71.20.-b, 71.20.Dg, 78.20.Ci, 78.20.-e 

## I. INTRODUCTION 

The electronic structure and property of alkali met- als under pressure have drawn extensive attentions re- cently. At low pressures they all possess simple body- centered-cubic (bcc) or face-centered-cubic (fcc) struc- ture, for which the tightly bound core electrons remain largely unaltered with respect to those in the free atoms 1 . However, the application of pressure may cause the core states to come into play and thus results in unexpected varieties of complex phenomena. Sodium (Na) is unique among alkali metals due to the occupied electronic states. Under pressure, Na is apt to adopting low-symmetry structures 2,3 and even incommensurate phase 4 . The high pressure transition sequence of Na has been recognized as follows: Na in bcc structure transforms to fcc structure at 65 GPa 6 and then to a more complex cI16 structure (16- atom bcc) at 105 GPa 5,7 ; The orthorhombic oP8 phase is observed between 118 to 125 GPa 3 ; At 125 GPa, oP8 transforms to an incommensurate phase tI19 3 . Though the darkening of Na at the transition to tI19 was ob- served, the phase is still notably metalic 4 . Until recently, Ma et al . reported a new phase of Na transparent to visible light at pressure about 200 GPa 8 , which suggests that the metal has become an insulator or at least semi- conductor. First-principles evolutionary methodology for crystal structure prediction identified the new phase as wide bandgap dielectric with a six-coordinated, highly distorted double-hexagonal close-packed structure, de- noting as hp4 8 . This finding may stimulate the study of transition mechanisms from metal to nonmetal un- der high pressures and promote the development of high pressure theory as well. It is encouraged to study the electronic properties of the insulating phase Na-hp4. 

Optical measurement is a powerful tool for studying the electronic structures of semiconductor and metal. The optical absorption and reflective spectra of Na have been studied extensively both experimentally and theoretically 4,9–11 . In particular, Lazicki et al . have recently studied the optical properties of Na in bcc, fcc, cI16, oP8 and tI19 phases comparatively using synchrotron infrared spectroscopy and first-principles method within DFT 12 . It was found that Na gradu- ally loses its Drude-like luster under compression, and tends towards less metallic behavior. As for the insulat- ing phase Na-hp4, though spectroscopic data have been obtained, the main optical spectra are still scarce except experimentally measured absorption spectra in a small energy range. It is indispensable to study the optical properties of Na-hp4 systematically both for interpreta- tion of the mechanism of metal transition to insulator and for further insight into the electronic structure of Na-hp4. As dielectric material, exploration of dielectric constants of Na-hp4 may be useful from the viewpoint of technological applications. Besides, it is also expected that the calculated results can be as useful reference for future experimental studies. 

In the present study, the electronic structure and opti- cal properties of Na-hp4 are calculated based on ab initio DFT using generalized gradient approximation (GGA). These calculations demonstrate that Na-hp4 is transpar- ent to visible light anisotropically. The $_{p}$-$_{d}$ hybridization of valence electrons and strong interstitial charge concen- trations are the main character of Na-hp4. Through DOS and Bader analysis of Na-hp4, we conclude that electrons transfer between the two inequivalent atoms in the unit cell and ionicity exists between them. And also the ion- icity becomes stronger with increasing pressure. The rest 

