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. Further, such devices offer a direct probe of novel material properties, for example, in the search for Majorana fermions. In this paper, we report on dc and ac Josephson effect of high-mobility, hexagonal boron nitride encapsulated graphene Josephson junctions. On the application of rf radiation, we measure phase-locked Shapiro steps. An unexpected bistability between +/- 1 steps is observed with switching times on the order of seconds. A critical scaling of the bistable state is measured directly from the switching time, allowing for direct comparison to numerical simulations. We show such intermittent chaotic behavior is a consequence of the nonlinear dynamics of the junction and has a sensitive dependence on the current-phase relation. This paper draws connections between nonlinear phenomena in dynamical systems and their implications for ongoing condensed matter experiments exploring topology and exotic physics.