Electrons and phonons in single layers of hexagonal indium chalcogenides fromab initiocalculations

We use density functional theory to calculate the electronic band structures, cohesive energies, phonon dispersions, and optical absorption spectra of two-dimensional In${}_{2}$${X}_{2}$ crystals, where X is S, Se, or Te. We identify two crystalline phases ($\ensuremath{\alpha}$ and $\ensuremath{\beta}$) of monolayers of hexagonal In${}_{2}$${X}_{2}$, and show that they are characterized by different sets of Raman-active phonon modes. We find that these materials are indirect-band-gap semiconductors with a sombrero-shaped dispersion of holes near the valence-band edge. The latter feature results in a Lifshitz transition (a change in the Fermi-surface topology of hole-doped In${}_{2}$${X}_{2}$) at hole concentrations ${n}_{\mathrm{S}}=6.86\ifmmode\times\else\texttimes\fi{}{10}^{13}$ cm${}^{\ensuremath{-}2}$, ${n}_{\mathrm{Se}}=6.20\ifmmode\times\else\texttimes\fi{}{10}^{13}$ cm${}^{\ensuremath{-}2}$, and ${n}_{\mathrm{Te}}=2.86\ifmmode\times\else\texttimes\fi{}{10}^{13}$ cm${}^{\ensuremath{-}2}$ for X=S, Se, and Te, respectively, for $\ensuremath{\alpha}$-In${}_{2}$${X}_{2}$ and ${n}_{\mathrm{S}}=8.32\ifmmode\times\else\texttimes\fi{}{10}^{13}$ cm${}^{\ensuremath{-}2}$, ${n}_{\mathrm{Se}}=6.00\ifmmode\times\else\texttimes\fi{}{10}^{13}$ cm${}^{\ensuremath{-}2}$, and ${n}_{\mathrm{Te}}=8.14\ifmmode\times\else\texttimes\fi{}{10}^{13}$ cm${}^{\ensuremath{-}2}$ for $\ensuremath{\beta}$-In${}_{2}$${X}_{2}$.