Topological Nodal Surface and Quadratic Dirac Semimetal States and van Hove Singularities in ScH(3) and LuH(3) Superconductors

[Image: see text] The coexistence of non-trivial topology and superconductivity in a material may induce a novel physical phenomenon known as topological superconductivity. Topological superconductors have been the subject of intense research, yet there are severe limitations in their application due to a lack of suitable materials. Topological nodal surface semimetals with nearly flat nodal surfaces near the Fermi level can be promising materials to achieve topological superconductivity. Here, we use first-principles calculations to examine the topological electronic characteristics of two new superconductors, ScH(3) and LuH(3), at both ambient and high pressures. Our studies show that both ScH(3) and LuH(3) have van Hove singularities, which confirms their superconductivity. Interestingly, both materials host topological nodal surface states under the protection of time reversal and spatial inversion symmetries in the absence of spin–orbit coupling (SOC). These nodal surfaces are distinguished by a pair of unique drum-head-like surface states not previously observed in nodal surface semimetals. Moreover, the nodal surfaces transform into essential spin–orbit quadratic Dirac points when SOC is included. Our findings demonstrate that ScH(3) and LuH(3) are good candidates to investigate the exotic properties of both nodal surface semimetals (NSSMs) and quadratic Dirac semimetal states and also provide a platform to explore the coexistence of topology and superconductivity in NSSMs with promising applications in high-speed electronics and topological quantum computing.