in 1L-MoS$_2$[@ChakrabortyPRB2012], while the opposite is observed in gated 1L[@DasNatureNanotech2008] and two-layer (2L)[@DasPRB2009] graphene. Ref. reported a gate-induced superconducting state at the surface of liquid-gated MoS$_2$ flakes with N$\gtrsim$25[@YeScience2012], while Ref. detected this down to N=1.

Most of these results have been interpreted in terms of the population of the conduction band minima at K/K’[@YeScience2012; @LuScience2015; @SaitoNatPhys2016; @ChenPRL2017], which are global minima in both 1L-MoS$_2$[@MakPRL2010; @GePRB2013] and electrostatically-doped FL-MoS$_2$[@YeScience2012; @LuScience2015; @SaitoNatPhys2016; @BrummePRB2015], Fig.\[figure:bands\]b. Theoretical investigations however suggested that the population of the high-energy minima at Q/Q’ may have an important role in determining the properties of gated MoS$_2$ flakes, by providing contributions both to EPC[@GePRB2013; @BrummePRB2015] and SOC[@KadantsevSSC2012; @WuNatCommun2016]. Ref. predicted that when the Q/Q’ valleys of 1L-MoS$_2$ are populated (Fig.\[figure:bands\]c,d), EPC strongly increases (from$\sim0.1$ to$\sim18$), leading to a superconducting transition temperature $T_c\sim20$K for a doping level $x=0.18$ electrons(e$^-$)/unit cell (corresponding to $E_F=0.18\pm0.02$eV at K/K’ and $0.08\pm0.02$eV at Q/Q’)[@BrummePRB2015]). However, Ref. measured $T_c\sim2$K for $x\sim0.09\div0.17$ e$^-$/unit cell in e$^-$-doped 1L-MoS$_2$. This mismatch may be associated with the contribution of e$^-$–e$^-$ interactions, whose role in the determination of $T_c$ is still under debate[@RoldanPRB2013; @DasPRB2015]. Overall, the agreement between the model of Ref. and the trend of $T_c$ with e$^-$ doping in 