Differential graphene resonator as a mass detector

We consider a fundamentally new scheme of graphene resonator, namely, a differential resonator, which provides a significantly increased sensitivity to the mass deposited on it. The differential resonator consists of two parallel graphene sheets located one over the other, the upper (basic) sheet and the lower (supplementary) sheet. The layers are fixed in supporting insulators, and the supplementary layer is located over the conducting surface. The power link between the layers is implemented by the electrostatic field in the space between the layers. Several equilibria are possible in such a mechanical system. The free vibration near the stable equilibrium are considered. The electric field strength in the space between the layers is chosen so that the mechanical system of two graphene layers has two close natural frequencies. The free vibrations of such a system exhibit beating. The characteristic frequency of the envelope, which is further called the beating frequency and is equal to half the difference of natural frequencies of the system, is much lower than the partial natural frequency of each layer. If a particle is deposited on the upper layer, then the partial natural frequency of this layer decreases. In this case, the characteristic frequency of the envelope changes, and a small variation in the partial natural frequency can lead to a significant change in the characteristic frequency of the envelope. This ensures that the differential resonator is more sensitive to the detected particle mass than single-layer resonators. The influence of various parameters of the differential resonator on the measurement accuracy is studied.