Anomalous Phase Dynamics of Driven Graphene Josephson Junctions

Josephson junctions with weak-links of exotic materials allow the elucidation of the Josephson effect in previously unexplored regimes. In this work, we report on DC and AC Josephson effect of high-mobility, hexagonal boron nitride encapsulated graphene Josephson junctions. We measure phase-locked Shapiro steps on the application of RF radiation. The shape of resistive transitions between the steps is anomalous in the form of extended nodes. Moreover, an unexpected bistability between ±1 steps is observed with switching times on the order of seconds. A critical scaling of a bistable state with DC current and RF power is measured directly from the switching time, allowing for a comparison to numerical simulations. We show such intermittent chaotic behavior is a consequence of the nonlinear dynamics of underdamped junctions and has a sensitive dependence on the current-phase relation. We numerically investigate the switching time scaling as a consequence of the interplay between noise level and basin structure of the solutions. This work draws connections between nonlinear phenomena in dynamical systems and their implications for ongoing condensed matter experiments exploring topology and exotic physics.