Anisotropic fully-gapped superconductivity in quasi-one-dimensional Li$_{0.9}$Mo$_6$O$_{17}$

Superconductivity in quasi-one-dimensional Li$_{0.9}$Mo$_6$O$_{17}$ emerges from an exotic, non-metallic normal state that exhibits signatures of Tomonaga-Luttinger liquid behavior, emergent symmetry and excitonic order. The high upper critical field, $H_{c2}$, in Li$_{0.9}$Mo$_6$O$_{17}$ suggests that that the favored pairing state is spin-triplet in nature. Here, we report measurements of the magnetic penetration depth down to $0.08\,\mathrm{K}$ ($T/T_c \lesssim 0.04$) and the specific heat down to $0.4\,\mathrm{K}$ ($T/T_c \lesssim 0.2$), and show that they are consistent with a moderately-coupled, fully-gapped superconducting state with marked gap anisotropy and a minimum ($\Delta_{\rm min} \simeq 0.4\,k_{\mathrm{B}}T_c$) occurring over a very narrow region in $k$-space. Combined with knowledge of $H_{c2}$, these measurements support the presence of a nodeless and possibly odd-parity spin-triplet superconducting order parameter in Li$_{0.9}$Mo$_6$O$_{17}$.