Topological states in the noncentrosymmetric superconductors LaPtSi and LaPtGe

The interaction between bulk Dirac points and $s$-wave bulk superconductivity can sustain an exotic quasiparticle excitation, namely, a gapless one-dimensional helical Majorana mode. Herein, based on first-principles calculations, we predict that noncentrosymmetric superconductors LaPtSi and LaPtGe are Dirac superconducting semimetal candidates. Without spin-orbit coupling (SOC), LaPtSi and LaPtGe show three-dimensional metallic behavior with a normal band order. SOC induces energy level splitting and reordering, resulting in two pairs of bulk Dirac points with type-II and type-III characteristics and a topological insulator state in the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}Z$ direction. The obtained nonzero topological ${\mathbb{Z}}₂$ invariants and multiple nontrivial surface states on the (001) surface directly demonstrate the nontrivial topological features of LaPtSi and LaPtGe. Thus, these predicted compounds provide realistic platforms for the interplay of bulk Dirac points and superconductivity.