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Topological semimetals in BaAl4-type structure have shown many interestingbehaviors, such as charge density wave (CDW) in SrAl4 and EuAl4, but not theisostructural and isovalent BaAl4, SrGa4 and BaGa4, although they all hostDirac points and nodal line Dirac-like dispersion. Here using Wannier functionsbased on density functional theory, we have calculated the susceptibilityfunctions with millions of k-points to reach the small q-vector and study theorigin and driving force behind the CDW. Our comparative study reveals that theorigin of the CDW in SrAl4 and EuAl4 is the strong electron-phonon couplinginteraction for the transverse acoustic mode at small q-vector along the{\Gamma}-Z direction besides the maximum of the real part of the susceptibilityfunction from the nested Fermi surfaces of the Dirac-like bands, which explainswell the absence of CDW in the other three closely related compounds in a goodagreement with experiment.

Origin of Charge Density Wave in Topological Semimetals SrAl4 and EuAl4