Quasiparticle band alignment and stacking-independent exciton in MA${}_2$Z${}_4$ (M = Mo, W, Ti; A= Si, Ge; Z = N, P, As)

Motivated by the recently synthesized two-dimensional semiconducting MoSi${}_2$N${}_4$, we systematically investigate the quasiparticle band alignment and exciton in monolayer MA${}_2$Z${}_4$ (M = Mo, W, Ti; A= Si, Ge; Z = N, P, As) using ab initio GW and Bethe-Salpeter equation calculations. Compared with the results from density functional theory (DFT), our GW calculations reveal substantially more significant band gaps and different absolute quasiparticle energy but predict the same types of band alignments.