Origin of charge density wave in topological semimetals SrAl4 and EuAl4

Topological semimetals in BaAl 4 -type structure show many interesting behaviors, such as charge density wave (CDW) in SrAl 4 and EuAl 4 , but not the isostructural and isovalent BaAl 4 , SrGa 4 , and BaGa 4 . Here using Wannier functions based on density functional theory, we calculate 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 SrAl 4 and EuAl 4 is the strong electron-phonon coupling interaction for the transverse acoustic mode at small q -vector along the Γ-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 closely related compounds in a good agreement with experiment. We also connect the different CDW behaviors in the Al compounds to the macroscopic elastic properties.