  Recently, a number of new two-dimensional (2D) materials based on puckered
phosphorene and arsenene have been predicted with moderate band gaps, good
absorption properties and carrier mobilities superior to transition metal
dichalcogenides. For heterojunction applications, it is important to know the
relative band alignment of these new 2D materials. We report the band alignment
of puckered CaP$_3$, CaAs$_3$ and BaAs$_3$ monolayers at the quasiparticle
level of theory (G$_0$W$_0$), calculating band offsets for isolated monolayers
according to the electron affinity rule. Our calculations suggest that
monolayer CaP$_3$, CaAs$_3$ and BaAs$_3$ all form type-II (staggered)
heterojunctions. Their quasiparticle gaps are 2.1 (direct), 1.8 (direct) and
1.5 eV (indirect), respectively. We also examine trends in the electronic
structure in the light of chemical bonding analysis. We show that the indirect
band gap in monolayer BaAs$_3$ is caused by relatively strong As $3p$ - Ba $5d$
bonding interactions that stabilize the conduction band away from the $\Gamma$
point between $\Gamma$ and $S$.
