Electrons and phonons in single layers of hexagonal indium chalcogenides from<i>ab initio</i>calculations

Abstract

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}$.