Tunneling spectroscopy of gate-induced superconductivity in MoS$_2$

The ability to gate-induce superconductivity by electrostatic charge accumulation is a recent breakthrough in physics and nano-electronics. With the exception of LaAlO$_3$/SrTiO$_3$ interfaces, experiments on gate-induced superconductors have been largely confined to resistance measurements, which provide very limited information about the superconducting state. Here, we explore gate-induced superconductivity in MoS$_2$ by performing tunneling spectroscopy to determine the energy-dependent density of states (DOS) for different levels of electron density $\textit{n}$. In the superconducting state, the DOS is strongly suppressed at energy smaller than the gap, \Delta, which is maximum (\Delta ~ 2 meV) for $\textit{n}$ of ~ 10$^{14}$ cm$^{-2}$ and decreases monotonously for larger $\textit{n}$. A perpendicular magnetic field $\textit{B}$ generates states at $E<\Delta$ that fill the gap, but a 20% DOS suppression of superconducting origin unexpectedly persists much above the transport critical field. Conversely, an in-plane field up to 10 T leaves the DOS entirely unchanged. Our measurements exclude that the superconducting state in MoS$_2$ is fully gapped and reveal the presence of a DOS that vanishes linearly with energy, the explanation of which requires going beyond a conventional, purely phonon-driven Bardeen-Cooper-Schrieffer mechanism.