Quasi-one-dimensional systems, having tendencies toward density-wave order in competition with superconductive pairing in their ground states, may give rise to unconventional superconductivity, a central theme in condensed matter physics. Partial density-wave gapping of electronic bands at the Fermi surface in such systems can yield superconductivity at very low carrier density that challenges Bardeen-Cooper-Schrieffer (BCS) theory since the pairing energy scale may approach or exceed the Fermi energy and render screening of the Coulomb interaction ineffective. Here we present low-$T$ magnetotransport measurements on the quasi-one-dimensional conductor ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$ showing the metallic state from which superconductivity emerges ($T_c\simeq 2$ K) to possess among the lowest known carrier densities, $\sim {10}^{17}{\mathrm{cm}}^{-3}$, and a ratio of $T_c$ to Fermi temperature within the BCS–Bose-Einstein-condensation crossover regime. A semimetallic state caused by a density-wave-induced Fermi surface reconstruction with highly anisotropic electron and hole pockets is implied. The degree of interpocket nesting appears to determine whether the extreme low-density ground state is superconducting or undergoes additional Fermi surface gapping.

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• Electrical conductivity
• Hall effect
• Superconductivity
• Thermal expansion
• Thermoelectric effects
• Transport phenomena