Electron-phonon coupling superconductivity and tunable topological state in carbon-rich selenide monolayers

The coexistence of Dirac cones and Van Hove singularities (VHSs), as the notable feature on prominent electronic band structure in recently hot-topic Lieb lattice and twisted graphene superlattice materials, has recently drawn tremendous attention since it offers an ideal platform for realizing correlation-driven electronic states (e.g., superconductivity and topological state). Here, we have identified two two-dimensional (2D) crystals, namely ${\mathrm{C}}_{4}\mathrm{Se}$ and ${\mathrm{C}}_{5}\mathrm{Se}$, which exhibit the coexistence of Dirac cones and VHSs. Based on ab initio calculations and the Bardeen-Cooper-Schrieffer theory, we investigated the electron-phonon coupling and possible superconductivity in both structures. The results indicate that ${\mathrm{C}}_{4}\mathrm{Se}$ possesses intrinsic superconducting states, whereas ${\mathrm{C}}_{5}\mathrm{Se}$ exhibits tunable superconductivity when doped. Their superconducting critical temperature (${T}_{c}$) can reach up to 11.6 and 11.2 K, respectively, surpassing the majority of 2D superconductors. Besides, we uncovered an approximate Dirac cone in ${\mathrm{C}}_{6}\mathrm{Se}$ with a small band gap of 0.17 eV. Via the application of a biaxial compressive strain, remarkably, the ${\mathrm{C}}_{6}\mathrm{Se}$ can be transformed into a topological insulator. These findings highlight the potential of carbon-rich C-Se 2D crystals as a promising platform for investigating fascinating band structures and physical states, thus advancing our comprehension of 2D crystals.