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We use density functional theory to calculate the electronic band structures, cohesive energies, phonon dispersions, and optical absorption spectra of two-dimensional In2X2 crystals, where X is S, Se, or Te. We identify two crystalline phases (α and β) of monolayers of hexagonal In2X2, and show that they are characterized by different sets of Raman-active phonon modes. We find that these materials are indirect-band-gap semiconductors with a sombrero-shaped dispersion of holes near the valence-band edge. The latter feature results in a Lifshitz transition (a change in the Fermi-surface topology of hole-doped In2X2) at hole concentrations nS=6.86×1013 cm-2, nSe=6.20×1013 cm-2, and nTe=2.86×1013 cm-2 for X=S, Se, and Te, respectively, for α-In2X2 and nS=8.32×1013 cm-2, nSe=6.00×1013 cm-2, and nTe=8.14×1013 cm-2 for β-In2X2.</p
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