First-principles study of mechanism of high birefringence in alkali metal vanadates <i>A</i>V<sub>3</sub>O<sub>8</sub> (<i>A</i> = Li, Na, K, Rb)

Birefringence, as a fundamental parameter of optical crystals, plays a vital role in numerous optical applications such as phase modulation, light splitting, and polarization, thereby making them key materials in laser science and technology. The significant birefringence of vanadate polyhedra provides a new approach for developing birefringent materials. In this study, first-principles calculations are used to investigate the band structures, density of states (DOS), electron localization functions (ELFs), and birefringence behaviors of four alkali metal vanadate crystals <i>A</i>V<sub>3</sub>O<sub>8</sub> (<i>A</i> = Li, Na, K, Rb). The computational results show that all <i>A</i>V<sub>3</sub>O<sub>8</sub> crystals have indirect band gaps, whose values are 1.695, 1.898, 1.965, and 1.984 eV for LiV<sub>3</sub>O<sub>8</sub>, NaV<sub>3</sub>O<sub>8</sub>, KV<sub>3</sub>O<sub>8</sub>, and RbV<sub>3</sub>O<sub>8</sub>, respectively. The DOS analysis reveals that near the Fermi level, the conduction band minima (CBM) in these vanadates are predominantly occupied by the outermost orbitals of V atoms, while the valence band maxima (VBM) are primarily contributed by O-2p orbitals. The O-2p orbitals also exhibit strong localization near the Fermi level. Combined with highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) analysis and population analysis, the bonding interactions in all four crystals mainly arise from the hybridization between V-3p and O-2p orbitals, indicating strong covalent bonding in V—O bonds. Through the analysis of structure-property relationships, the large birefringence is primarily attributed to the pronounced structural anisotropy, high anisotropy index of responsive electron distribution, unique arrangement of anionic groups, and d-p orbital hybridization between V-3d and O-2p orbitals. The calculated birefringence values at a wavelength of 1064 nm for LiV<sub>3</sub>O<sub>8</sub>, NaV<sub>3</sub>O<sub>8</sub>, KV<sub>3</sub>O<sub>8</sub>, and RbV<sub>3</sub>O<sub>8</sub> are 0.28, 0.30, 0.28, and 0.27, respectively.