Triplet p$_z$-wave pairing in quasi-one-dimensional A$_2$Cr$_3$As$_3$ superconductors (A = K,Rb,Cs)

We construct minimum effective models to investigate the pairing symmetry in the newly discovered quasione-dimensional superconductor K$_2$Cr$_3$As$_3$. We show that a minimum three-band model based on the d$_{z^2}$ , d$_{xy}$ ,and d$_{x^2-y^2}$ orbitals of one Cr sublattice can capture the band structures near Fermi surfaces. In both weak and strong coupling limits, the standard random phase approximation and mean-field solutions consistently yield the triplet pz-wave pairing as the leading pairing symmetry for physically realistic parameters. The triplet pairing is driven by the ferromagnetic fluctuations within the sublattice. The gap function of the pairing state possesses line gap nodes on the k$_z$ = 0 plane on the Fermi surfaces.Experimental consequences of the triplet p$_z$-wave pairing are also discussed, including the NMR, superfluid density and phase-sensitive dc SQUID experiments.