Frequency as a Clock: Synchronization and Intrinsic Recovery in Graphene Transistor Dynamics

Hysteresis and memory effects in graphene field-effect transistors (GFETs) offer unique opportunities for neuromorphic computing, sensing, and memory applications, yet their physical origins remain debated due to competing volatile and nonvolatile interpretations. Here, we present a unified dynamic model that captures the essential physics of the GFET response under periodic gate modulation, accounting for both intrinsic relaxation processes and externally driven charge transfer. By modeling nonequilibrium carrier dynamics as a competition between injection and reabsorption rates, we uncover two distinct regimes: one governed by intrinsic, frequency-independent relaxation and another exhibiting frequency-locked behavior where the response is tied to the external drive. This distinction resolves apparent nonvolatile effects and explains loop invariance in floating-gate structures via displacement-current-driven charge injection. Our framework predicts the evolution of the hysteresis loop shape, amplitude, and direction across a wide range of driving conditions, offering a versatile tool for interpreting experimental results and guiding the design of next-generation graphene-based electronic systems.