Coexistence of topological electronic bands and flat non-contractible phonon nodal lines in Cmce LuS₂

Superconductors featuring topological electronic and phonon states have garnered considerable attention due to their potential to facilitate novel physics and phenomena. In this study, we systematically investigate the high-pressure phase diagram of the LuS₂ system using first-principles calculations and crystal structure predictions. Our results reveal two stable phases of LuS₂ under pressure: P2₁/c (from 5 to 58.8 GPa) and Cmce (from 58.8 to 126 GPa). For the Cmce phase, the band inversion between Lu-d and S-p dominated bands leads to the formation of a nodal crown. Once including SOC, this nodal crown is fully gapped, leading to the topological metal with strong topological insulator nature. Furthermore, based on the effective phonon Hamiltonian in the bases of {Lu,S}⊗{p_x, p_y, p_z}, we identify four non-contractible phonon nodal lines traversing the BZ. Interestingly, these non-contractible phonon nodal lines are nearly dispersionless (∼0.004 THz), which gives four flat Dirac nodal phonon bands. In addition, the phonon modes leading to these four non-contractible nodal lines also host visible contribution to the electron-phonon coupling, which could benefit to theoretical and experimental research on the interplay of topological electronic states, flat nodal phonon states and superconductivity.