bars by using polymethyl methacrylate (PMMA) as a mask and removing the unprotected MoS$_2$ with reactive ion etching (RIE) in a $150$mTorr atmosphere of CF$_4$:O$_2$=5:1, as shown in Figs.\[figure:device\]a,b. A droplet of 1-Butyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)imide (BMPPD-TFSI) is used to cover the FL-MoS$_2$ surface and part of the side electrode for liquid gate operation (LG), as sketched in Fig.\[figure:device\]a.

AFM analysis is performed with a Bruker Dimension Icon in tapping mode. The scan in Fig.\[figure:device\]c is done after the low-T experiments and removal of the ionic liquid, and confirms that the FL-MoS$_2$ sample does not show topographic damage after the measurement cycle.

![Representative Raman spectra at 514nm of a 4L-MoS$_2$ flake before (blue) and after (red) device fabrication, deposition of the ionic liquid droplet and low-T transport measurements.[]{data-label="figure:Raman"}](Figure_Raman_1.eps){width="\columnwidth"}

We use Raman spectroscopy to characterize the devices both before and after fabrication and BMPPD-TFSI deposition. Raman measurements are performed with a Horiba LabRAM Evolution at 514nm, with a 1800grooves/mm grating and a spectral resolution$\sim0.45$cm$^{-1}$. The power is kept below 300$\mu$W to avoid any damage. A representative Raman spectrum of 4L-MoS$_2$ is shown in Fig.\[figure:Raman\] (blue curve). The peak at$\sim$455cm$^{-1}$ is due to a second-order longitudinal acoustic mode at the M point[@StacJPCS1985]. The E$_{2g}^1$ 