Figure 1: Gated Josephson junctions and spatial distribution of supercurrents.

(a) Electron micrograph of our typical device (in false colour). Nb leads (green) are connected to bilayer graphene (its edges are indicated by red dashes). The top gate is shown in yellow. (b) Schematics of such junctions. (c) Illustration of uniform and edge-dominant current flow through Josephson junctions (top and bottom panels, respectively). (d) The corresponding behaviour of the critical current I_c as a function of B. I_c(B) is related to J_s(x) by the equation shown in d. For a uniform current flow, I_c should exhibit a Fraunhofer-like pattern (top panel) such that the supercurrent goes to zero each time an integer number N of magnetic flux quanta Φ₀ thread through the junction. Maxima in I_c between zeros also become smaller with increasing N. For the flow along edges (bottom panel), I_c is minimal for half-integer flux values Φ=(N+1/2)Φ₀, and maxima in I_c are independent of B. The spatial distribution J_s(x) can be found^24,25 from I_c(B) using the inverse FFT. Due to a finite interval of Φ over which the interference pattern is usually observed experimentally, J_s(x) obtained from the FFT analysis are usually smeared over the x axis as shown schematically in c.