Short Ballistic Josephson Coupling in Planar Graphene Junctions with Inhomogeneous Carrier Doping

We report on short ballistic (SB) Josephson coupling in junctions embedded in a planar heterostructure of graphene. Ballistic Josephson coupling is confirmed by the Fabry-Perot-type interference of the junction critical current $I_c$. The product of $I_c$ and the normal-state junction resistance $R_N$, normalized by the zero-temperature gap energy ${\mathrm{\Delta }}_0$ of the superconducting electrodes, turns out to be exceptionally large close to 2, an indication of strong Josephson coupling in the SB junction limit. However, $I_c$ shows a temperature dependence that is inconsistent with the conventional short-junction-like behavior based on the standard Kulik-Omel’yanchuk prediction. We argue that this feature stems from the effects of inhomogeneous carrier doping in graphene near the superconducting contacts, although the junction is in fact in the short-junction limit.

Figure 1

(a) (Upper panel) Schematic diagram of our planar graphene Josephson junctions (pGJJs) with boron nitride (BN)-encapsulated graphene contacted by Al electrodes. (Lower panel) False-colored scanning electron microscopy (SEM) image of two pGJJs: SBJJ40-1 (channel length: $\sim 120\mathrm{nm}$) and SBJJ40-2 (channel length: $\sim 220\mathrm{nm}$). (b) Current-voltage characteristic curves of SBJJ40-2 for different gate voltages $V_G$. Bias current was swept from negative to positive. (c) Differential resistance map as a function of magnetic field and bias current: the Fraunhofer pattern. (d) Bias spectroscopy with dips in the differential resistance of the junction arising from multiple Andreev reflection.

Figure 2

(a) Normal-state junction resistance $R_N$ of SBJJ40-1 and SBJJ40-2 measured at 4.2 K for varying $V_G$. The dashed line corresponds to the ballistic limit with perfect transmission ($\tau =1$). (b) Differential resistance map of SBJJ40-2 as a function of $I$ and $V_G$. (c) In-phase Fabry-Perot oscillation of the junction critical current $I_c$ and the normal-state conductance ${(R_N)}^{-1}$ of SBJJ40-2, which indicates ballistic pair transport. The vertical guide lines show the in-phase oscillation between the two curves. (d) The $I_c{R}_N$ product normalized by ${\mathrm{\Delta }}_0/e$ of SBJJ40-1 and SBJJ40-2 for varying $V_G$. The dotted line is the theoretical limit, $\sim 2.4$, for a short ballistic (SB) pGJJ. (e) $I_c(T)$ of SBJJ40-2 for various $V_G$.

Figure 3

(a) (upper) Schematic diagram of the spatial distribution of the electrochemical potential in a pGJJ and (lower) the simplified electrochemical potential distribution used in the calculation. The arrow indicates the undoped electrochemical potential in graphene. (b) $U/\mu$ dependence of $I_c(T)$ for $r=100$. (c) $I_c(T)$ for different values of $r$ between 0.1 and infinity for $U/\mu =5$, which corresponds to $V_G\sim 10\mathrm{V}$ in our experiment.

Figure 4

$I_c(T)$ for three pGJJs; SBJJ40-2, SBJJ40-1, and SBJJ33. Void circles represent data. Fits with the Takane-Imura (TI) and Kulik-Omel’yanchuk (KO) models are shown in blue and gray, respectively. Here, the KO curves are generated for the transmission probabilities of 0.75, 0.72, and 0.64 for the three devices, respectively.