AC Josephson effect in a capacitively shunted graphene Josephson junction

Recent advances in the search of novel sub-gap modes in Josephson junctions have put forth stringent requirements regarding the control of material properties. Thus it has become a common practice to fabricate bias-gate(s) in close proximity to the junction. However, unexpected shunt capacitance might be introduced and its effect on the behaviour of Josephson junction is less well understood, particularly when the junction is under RF radiation. Here we study the AC Josephson effect on a junction made of graphene encapsulated in boron nitride and contacted by electrodes made of a molybdenum-rhenium alloy. The device comes with a back-gate for chemical potential tuning and two top-gates for boundary tuning. In regions where chemical potential is close to the charge neutrality point and the RF drive current is comparable with critical current, this device demonstrated a bi-stability between the first Shapiro steps, indicating the Josephson junction is in a chaotic regime. This observation casts doubts over arguments that AC Josephson effect in the low RF drive amplitude region would offer the opportunity to observe 4-\pi current phase relation in topological Josephson junctions.