Fermi Surface (FS), i.e. by adding extra FSs in different BZ regions to provide coupling to further phonon branches[@PickettBook]. Since the evolution of the band structure of MoS$_2$ with field-effect doping is analogous to that of other semiconducting TMDs[@BrummePRB2015; @BrummePRB2016; @DasPRB2015; @WuNatCommun2016; @KangNanoLett2017], a similar mechanism is likely associated with the emergence of SC in TMDs in general. Thus, optimization of the FS connectivity can be a viable strategy in the search of new superconductors.

![a) Hall bar FL-MoS$_2$ flake with voltage probes ($V_i$), source (S), drain (D) and liquid-gate (LG) electrodes. A ionic liquid droplet covers the flake and part of the LG electrode. The sample is biased with a source-drain voltage ($V_{SD}$) and dual gate control is enabled by a voltage applied on the liquid gate ($V_{LG}$) and on the solid back gate ($V_{BG}$). b) Optical image of Hall bar with six voltage probes. The LG electrode is on the upper-right corner. c) AFM scan of the MoS$_2$ Hall bar after ionic liquid removal.[]{data-label="figure:device"}](Figure_device_6.eps){width="0.8\columnwidth"}

We study flakes with N=4-10, as Refs. predicted that flakes with N$\geq$4 are representative of the bulk electronic structure, and Ref. experimentally observed that both $T_c$ and the critical magnetic field $H_{c2}$ in 4L 