Coexistence of nontrivial topological properties and strong ferromagnetic fluctuations in $A_2$Cr${}_3$As${}_3$ ($A$=Na, K, Rb and Cs)

Superconductivity in crystals without inversion symmetry has received extensive attention due to its unconventional pairing and possible nontrivial topological properties. Using first-principles calculations, we systemically study the electronic structure of noncentrosymmetric superconductors $A_2$Cr${}_3$As${}_3$ ($A$=Na, K, Rb and Cs). Topologically protected triply degenerate points connected by one-dimensional arcs appear along the $C_3$ axis, coexisting with strong ferromagnetic (FM) fluctuations in the non-superconducting state. Within random phase approximation, our calculations show that strong enhancements of spin fluctuations are present in K${}_2$Cr${}_3$As${}_3$ and Rb${}_2$Cr${}_3$As${}_3$, and are substantially reduced in Na${}_2$Cr${}_3$As${}_3$ and Cs${}_2$Cr${}_3$As${}_3$. Symmetry analysis of spin-orbit coupling $g_k$ suggests that the arc surface states might remain stable in the superconducting state, giving rise to possible nontrivial topological properties.