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.