Robust 4$\pi$ periodicity in ballistic graphene Josephson junctions

We present direct current magnetic interference measurements on ballistic graphene Josephson junctions. The observed Fabry-Perot cavity is studied by applying a small magnetic field up to 5 mT to modulate the phase of the Josephson junction. Unlike the monotonic behavior at highly doped regions, irregular interference patterns are observed near the Dirac point. For highly doped regions, the uniform distribution of supercurrent can be seen. In the Fabry-Perot cavity region, the supercurrent distribution shows an edge-bulk type alternating feature. This can be understood as cavity quantization off or on resonance. However, an unexpected periodicity doubling is also observed that results in a single electron SQUID interference pattern. Instead of regular h/2e periodicity, a single electron supercurrent state can result in h/e periodicity, which may be observed as 4$\pi$ periodicity in magnetic interference measurements. This 4$\pi$ periodicity is seen in several different samples at many back gate locations. Moreover, it is robust against temperature changes.