Andreev reflection in ballistic normal metal/graphene/superconductor junctions

We report the study of ballistic transport in normal metal/graphene/superconductor junctions in edge-contact geometry. While in the normal state, we have observed Fabry-Pérot resonances suggesting that charge carriers travel ballistically, the superconducting state shows that the Andreev reflection at the graphene/superconductor interface is affected by these interferences. Our experimental results in the superconducting state have been analyzed and explained with a modified Octavio-Tinkham-Blonder-Klapwijk model taking into account the magnetic pair-breaking effects and the two different interface transparencies, i.e., between the normal metal and graphene, and between graphene and the superconductor. We show that the transparency of the normal metal/graphene interface strongly varies with doping at large scale, while it undergoes weaker changes at the graphene/superconductor interface. When a cavity is formed by the charge transfer occurring in the vicinity of the contacts, we see that the transmission probabilities follow the normal state conductance highlighting the interplay between the Andreev processes and the electronic interferometer.

Figure 1

(a) Schematic of the device geometry. (b) Cross section schematic of the studied devices across the dashed line in (a). (c) False color atomic force micrograph of the two devices with normal (N) and superconducting (S) contacts. Scale bar is 5 $\mu \mathrm{m}$.

Figure 2

Resistance $R$ and conductance $G$ versus charge carrier density ($n$) and gate voltage ($V_{\mathrm{g}}$).

Figure 3

Energy dependence and magnetic field dispersion of the FP interference in the hole-doped region: (a) $G_{\mathrm{osc}}$ versus applied bias voltage $V_{\mathrm{bias}}$ and gate voltage $V_{\mathrm{g}}$ showing asymmetric pattern of the FP resonances at temperature $T=100$ mK and magnetic field $B=50$ mT. (b) $G_{\mathrm{osc}}$ versus magnetic field $B$ and gate voltage $V_{\mathrm{g}}$.

Figure 4

Schematic view of the model for an NGS junction (see text).

Figure 5

Differential conductance $dI/dV$ measured as a function of the applied bias voltage $V_{\mathrm{bias}}$ for: (a) normalized by the normal state conductance $G_{\mathrm{N}}$ (from the measurement at 4.2 K) for applied gate voltage $V_{\mathrm{g}}$ at $T\sim 20$ mK corresponding to electron-doped region (circle), hole-doped region (diamond), and close to the charge neutrality point (triangle). (b) Under various values of perpendicular magnetic field $B$ at $T\sim 20$ mK and $V_{\mathrm{g}}=-9.2$ V corresponding to the hole-doped region. (c) For different temperatures at $V_{\mathrm{g}}=-9$ V, i.e., in the the hole-doped region. In all panels, the symbols represent experimental data and the solid curves represent the best fit of the data with our model.

Figure 6

(a) Transmission probabilities ${\tau }_{\mathrm{N}}$ and ${\tau }_{\mathrm{S}}$ of the normal metal/graphene and graphene/superconducting interface, respectively for device A and B. (b) Normal state conductance $G_{\mathrm{N}}$ as a function of gate voltage $V_{\mathrm{g}}$ covering a large scale of charge carrier density in device B. All the ${\tau }_{\mathrm{N}}, {\tau }_{\mathrm{S}}$, and $G_{\mathrm{N}}$ are obtained from the best fitting values of differential conductance data measured at a base temperature of 20 mK and $B=0$ T using our modified OTBK model.

Figure 7

(a) Oscillations in the normal conductance $G_{\mathrm{N}}$ observed at a base temperature of 20 mK and $B=0$ T as a function of gate voltage $V_{\mathrm{g}}$ in the hole-doped region (circles), and best fitting value for the conductance obtained from the OTBK fits of the experimental data (diamonds). (b) Transmission probability $\tau$ obtained from the OTBK fits of the experimental data.