Gated Tuned Superconductivity and Phonon Softening in Mono- and Bilayer MoS$_2$

Superconductors at the atomic two-dimensional (2D) limit are the focus of an enduring fascination in the condensed matter community. This is because, with reduced dimensions, the effects of disorders, fluctuations, and correlations in superconductors become particularly prominent at the atomic 2D limit; thus such superconductors provide opportunities to tackle tough theoretical and experimental challenges. Here, based on the observation of ultrathin 2D superconductivity in mono- and bilayer molybdenum disulfide (MoS$_2$) with electric-double-layer (EDL) gating, we found that the critical sheet carrier density required to achieve superconductivity in a monolayer MoS$_2$ flake can be as low as 0.55*10$^{14}$cm$^{-2}$, which is much lower than those values in the bilayer and thicker cases in previous report and also our own observations. Further comparison of the phonon dispersion obtained by ab initio calculations indicated that the phonon softening of the acoustic modes around the M point plays a key role in the gate-induced superconductivity within the Bardeen-Cooper Schrieffer (BCS) theory framework. This result might help enrich the understanding of 2D superconductivity with EDL gating.