Fig. 1. The geometric structures of tetragonal group III monochalcogenide MX: (a) and (b) Top-view and side-view of the structure; (c) considered systems with various choice of compositions; (d) the first Brillouin zone of structure with letters designating special points and the lines for band-structure calculation.

Fig. 2. Top view and side view of the total charge density isosorfaces of tetragonal MX: (a) AlTe; (b) GaSe; (c) GaTe; (d) InSe; (e) InTe. Isosurface value is 0.05 electrons/ų.

Fig. 3. Vibrational phonon spectra of group III monochalocogenide haeckelites monolayers along the high symmetry directions in the 2D Brillouin zone: (a) AlS; (b) AlSe; (c) AlTe; (d) GaS; (e) GaSe; (f) GaTe; (g) InS; (h) InSe; (i) InTe.

Fig. 4. The PBE and HSE band structures for tetragonal MX monolayers. All the compounds are indirect band gap semiconductors.

Fig. 5. The electronic band gaps for tetragonal MX as a function of the in-layer strain from –0.10 to 0.10.

Fig. 6. Electronic band structure of 2D tetragonal GaSe under different strains. The Fermi level is set to zero.