Ref. suggests that the mechanism of Ref. for EPC enhancement when the Q/Q’ valleys are crossed may also hold for FL-MoS$_2$.

Inversion symmetry can be broken in MoS$_2$ either by going to the 1L limit[@GePRB2013], or by applying a transverse electric field[@KormanyosPRB2013; @YuanPRL2014]. This leads to a finite SOC[@KormanyosPRB2013; @YuanPRL2014], which lifts the spin degeneracy in the conduction band and gives rise to two spin-orbit-split sub-bands in each valley[@KormanyosPRB2013; @BrummePRB2015], as shown in Fig.\[figure:bands\]b-d for FL-MoS$_2$. When the system is field-effect doped, the inversion symmetry breaking increases with increasing transverse electric field [@LuScience2015; @ChenPRL2017], due to the fact that induced e$^-$ tend to become more localized within the first layer [@LuScience2015; @ChenPRL2017; @RoldanPRB2013]. Hence, the SOC and the spin-orbit splitting between the bands increase as well, as was calculated in Ref..

When combined to the gate-induced SC state[@YuanPRL2014], this can give rise to interesting physics, such as spin-valley locking of the Cooper pairs[@SaitoNatPhys2016] and 2d Ising superconductivity (SC)[@LuScience2015] with a non-BCS-like energy gap[@CostanzoNatNano2018], suggested to host topologically non-trivial SC states[@RoldanPRB2013; @HsuNatComms2017; @NakamuraPRB2017]. Refs. predicted SOC and spin-orbit splitting between sub-bands to be significantly stronger for the Q/Q’ valleys than for K/K’, thus supporting spin-valley locking at Q/Q’ as well[@WuNatCommun2016]. A 