NaPN2: Deep-ultraviolet nonlinear optical material with unprecedented strong second-harmonic generation coefficient

The electronic band structures and second harmonic generations (SHGs) of phosphorus nitrides ${\mathrm{LiPN}}_{2}, {\mathrm{NaPN}}_{2}$, and ${\mathrm{CuPN}}_{2}$ are studied by first-principles calculations. ${\mathrm{NaPN}}_{2}$ has a band gap of $\ensuremath{\sim}6.2$ eV (200 nm) and the strongest SHG coefficient among phosphorus-based deep-ultraviolet nonlinear optical (NLO) materials, i.e., ${d}_{36}=2.35$ pm/V at static limit and ${d}_{36}=3.77$ pm/V under external optic field with wavelength 1064 nm. Compared with the SHG coefficients of borate NLO materials working in the region of deep ultraviolet, ${\mathrm{NaPN}}_{2}$ presents an unprecedented high SHG coefficient, which is the manifestation of its enhanced orbital hybridization owing to the shorter bond lengths from high pressure facilitated synthesis.