Critical current fluctuations in graphene Josephson junctions

We have studied 1/f noise in critical current I$_{c}$ in h-BN encapsulated monolayer graphene contacted by NbTiN electrodes. The sample is close to diffusive limit and the switching supercurrent with hysteresis at Dirac point amounts to ≃5 nA. The low frequency noise in the superconducting state is measured by tracking the variation in magnitude and phase of a reflection carrier signal v$_{rf}$ at 600–650 MHz. We find 1/f critical current fluctuations on the order of δI$_{c}$/I$_{c}$≃10$^{-3}$ per unit band at 1 Hz. The noise power spectrum of critical current fluctuations SI$_{c}$ measured near the Dirac point at large, sub-critical rf-carrier amplitudes obeys the law SI$_{c}$/I$_{c}$$^{2}$=a/f$^{ß}$ where a≃4×10$^{-6}$ and β≃1 at f>0.1 Hz. Our results point towards significant fluctuations in I$^{c}$ originating from variation of the proximity induced gap in the graphene junction.