Charge transport in graphene field effect transistors with ferroelectric gating

Recent experiments on ferroelectrically gated graphene field effect transistors (GFeFETs) open new opportunities for exploring new graphene physics and functionalities. The non-linear, hysteretic dielectric response of ferroelectrics introduces non-volatility in GFeFETs, which can be utilized for memory and data storage applications. Here, we present a comprehensive way in understanding and controlling ferroelectric gating in GFeFETs. We quantitatively characterize the hysteretic ferroelectric gating using the reference of an independent background doping (n$_{back})$ provided by normal dielectric gating. More importantly, we prove that n$_{back}$ can be used to control the ferroelectric gating by uni-directionally shifting the hysteretic ferroelectric doping in graphene. Utilizing this electrostatic effect, we demonstrate symmetrical bit writing in graphene-ferroelectric FETs with resistance change over 500{\%} and reproducible no-volatile switching over 10$^{5}$ cycles. In the quantum hall regime (2K and 9T), by controlling the polarization magnitude in the ferroelectric dielectric layer, we observe additional integer quantization steps besides the well-known (N+1/2)e$^{2}$/h steps. We also explore the possibility to introduce ultra-high charge carrier doping in graphene by ferroelectric gating.