Electronic band structure and exciton properties of $Pna2_1$ CaSnN$_2$

The electronic band structure of CaSnN$_2$ in the wurtzite-based $Pna2_1$ structure is calculated using the Quasiparticle Self-consistent (QS)GW$^{BSE}$ method, including ladder diagrams in the screened Coulomb interaction W$^{BSE}$ and is found to have a direct gap of 2.59 eV at {\Gamma}, which corresponds to blue light wavelength of 478 nm and makes it an attractive candidate for sustainable blue light-emitting diodes (LEDs), avoiding Ga and In. The valence band splitting is analyzed in terms of symmetry labeling, and the effective mass tensor is calculated for several bands at {\Gamma}. The valence band maximum has a1 symmetry and gives allowed transitions to the conduction band minimum for light polarized along the {\bf c}-direction. While this is unfavorable for light emission with transverse electric (TE) or s-polarization from the basal plane, this would not be an impediment if another surface other than the basal plane is used. Furthermore, the crystal field splitting between the $a_1$ and $b_1$ states, corresponding to polarizations along {\bf c} and {\bf a} respectively, reverses under an applied uniaxial tensile strain of 3.7% along the {\bf c} direction, which might occur under biaxial compressive strain in the basal plane. The optical dielectric function, including electron-hole interaction effects is also reported, and the excitons are analyzed, including several dark excitons.