Superconductivity in the regime of attractive interactions in the Tomonaga-Luttinger liquid.

While the vast majority of known physical realizations of the Tomonaga-Luttinger liquid (TLL) have repulsive interactions defined with the dimensionless interaction parameter $K_{\rm c}<1$, we here report that Rb$_2$Mo$_3$As$_3$ is in the opposite TLL regime of attractive interactions. This is concluded from a TLL-characteristic power-law temperature dependence of the {\red $^{87}$Rb} spin-lattice relaxation rates over broad temperature range yielding the TLL interaction parameter for charge collective modes $K_{\rm c}=1.4$. The TLL of the one-dimensional band can be traced down to $T_{\rm c} = 8 $~K (in 9.39~T), where unusual bulk superconducting state is stabilized by the presence of a 3D band and characterized by the temperature independent Knight shift, the absence of Hebel-Slichter coherence peak in the relaxation rates, and the small, possibly nodal, superconducting gap. The uniqueness of this superconducting state stems from the attractive interactions defining the precursor TLL and the weak disorder effects associated with the Rb positional disorder.