Electro-superlubric springs for continuously tunable resonators and oscillators

Resonators and resonator-based oscillators are used in most electronics systems and they are classified as either mechanical or electrical, with fixed or difficult-to-tune resonant frequencies. Here, we propose an electro-superlubric spring, whose restoring force between two contacting sliding solid surfaces in the structural superlubric state is linearly dependent on the sliding displacement from the balanced position. We use theoretical analysis and finite element methods to study the restoring force and stability. The stiffness of this electro-superlubric spring is proportional to the square of the applied electric bias, facilitating continuous tuning from zero to several megahertz or gigahertz for the microscale or nanoscale resonators, respectively. Furthermore, we propose an electro-superlubric oscillator that is easily operated by varying a pair of harmonic voltages. The resonant frequency, resonant amplitude, quality factor, and maximum resonant speed can be continuously tuned via the applied voltage and bias. These results indicate significant potential in the applications of electro-superlubric resonators and oscillators. Microscale resonators are widely used in modern technology and achieving large tunability of their resonant frequency is highly desirable. Here, a design for electro-superlubric springs, based on a restoring force between sliding solid surfaces, is predicted to have continuously tunable resonant frequencies from zero to several GHz.