Origin of Charge Density Wave in Topological Semimetals SrAl₄ and EuAl₄

Topological semimetals in BaAl₄-type structure have shown many interesting behaviors, such as charge density wave (CDW) in SrAl₄ and EuAl₄, but not the isostructural and isovalent BaAl₄, SrGa₄ and BaGa₄, although they all host Dirac points and nodal line Dirac-like dispersion. Here using Wannier functions based on density functional theory, we have calculated the susceptibility functions with millions of k-points to reach the small q-vector and study the origin and driving force behind the CDW. Our comparative study reveals that the origin of the CDW in SrAl₄ and EuAl₄ is the strong electron-phonon coupling interaction for the transverse acoustic mode at small q-vector along the <!--[if gte msEquation 12]> style='mso-bidi-font-style:normal'>ΓΓ-Z direction besides the maximum of the real part of the susceptibility function from the nested Fermi surfaces of the Dirac-like bands, which explains well the absence of CDW in the other three closely related compounds in a good agreement with experiment.