Gate Tunable Magneto-resistance of ultra-thin WTe$_{\mathrm{2}}$ devices*

We have carried out magneto-transport experiment on ultra-thin WTe$_{\mathrm{2}}$ field effect transistors that are far away from charge neutrality (in the heavily electron-doped regime). We found that the magnetoresistance (MR) of the samples is tunable by gate voltage, and the two-fluid model captured most of the physics in this regime phenomenogically. By tuning the 2D electron-hole imbalance from 8.2 × 10$^{\mathrm{17}}$m-2 to 3.3 × 10$^{\mathrm{17}}$m$^{\mathrm{-2}}$, we were able to change the MR of the devices by 850{\%}. The change of MR could be as large as 400,000{\%} if the sample is tuned to neutrality when preserving the mobility observed in bulk samples. We also found that the change of MR of the ultra-thin WTe$_{\mathrm{2}}$ is determined largely by a single parameter, namely, the difference between the number of electrons and holes. Our findings show the potential of ultra-thin WTe$_{\mathrm{2}}$ as a variable magnetoresistance material in future applications such as magnetic field sensors, information storage and extraction, and galvanic isolators.