We report density-functional-theory calculations of the electronic band structures and optical absorption spectra of two-dimensional crystals of Ga 2 X 2 (X = S, Se, and Te). Our calculations show that all three two-dimensional materials are dynamically stable indirect-band-gap semiconductors with a sombrero dispersion of holes near the top of the valence band. We predict the existence of Lifshitz transitions-changes in the Fermi-surface topology of hole-doped Ga 2 X 2 -at hole concentrations n S = 7.96 × 10 13 cm −2 , n Se = 6.13 × 10 13 cm −2 , and n T e = 3.54 × 10 13 cm −2 .