Strong-coupling electron-phonon superconductivity in noncentrosymmetric quasi-one-dimensional K$_2$Cr$_3$As$_3$

I study the lattice dynamics and electron-phonon coupling in non-centrosymmetric quasi-one-dimensional K$_2$Cr$_3$As$_3$ using density functional theory based first principles calculations. The phonon dispersions show stable phonons without any soft-mode behavior. They also exhibit features that point to a strong interaction of K atoms with the lattice. I find that the calculated Eliashberg spectral function shows a large enhancement around 50 cm$^{-1}$. The phonon modes that show large coupling involve in-plane motions of all three species of atoms. The $\mathbf{q}$ dependent electron-phonon coupling decreases strongly away from the $q_z = 0$ plane. The total electron-phonon coupling is large with a value of $\lambda_{\textrm{ep}} = 3.0$, which readily explains the experimentally observed large mass enhancement.