Observation of localized states in atomically thin $MoS2$ field effect transistor

We present electrical transport and low frequency (1/f) noise measurements on mechanically exfoliated single, bi and trilayer $MoS2$-based FET devices on $Si/SiO2$ substrate. We find that the electronic states in $MoS2$ are localized at low temperatures (T) and conduction happens through variable range hopping (VRH). A steep increase of 1/f noise with decreasing T, typical for localized regime was observed in all of our devices. From gate voltage dependence of noise, we find that the noise power is inversely proportional to square of the number density (∝ 1/n²) for a wide range of T, indicating number density fluctuations to be the dominant source of 1/f noise in these $MoS2$ FETs.