Frequency (MHz) Gate Voltage (V) -40 -20 0 20 40 -40 -20 0 20 40 32 29 32 29 -40 -20 0 20 40 Gate Voltage (V) Amplitude (a.u.)$^{i)}$ -3.5 -1.5 0.5 2.5 Log (Current (nA)) Frequency (MHz) Gate Voltage (V) 100mV 200mV 400mV 300mV -40 -20 0 20 40 -40 -20 0 20 40 32 29 32 29 a) d) b) c) e) f) h) g) FIG. 5: (color online) a), b), c), and d) Color logscale plots of mixing current from device-1 as a function of V DC g and ω in non-linear regime with increasing amplitude of driving force starting from 100 mV to 400 mV respectively. e), f), g), and h) Colorscale plots of calculated amplitude of a resonator in the non-linear regime using Duffing equation with increasing amplitude of driving force from Fig.5e to Fig.5h. i) Shows the amplitude for the two directions of V DC g which indicates hysteresis at constant frequency 31 MHz (red and blue arrows show corresponding gate sweep direction). 16