Subharmonic gap structure in short ballistic graphene junctions

We present a theoretical analysis of the current-voltage characteristics of a ballistic superconductor-normal-superconductor (SNS) junction, in which a strip of graphene is coupled to two superconducting electrodes. We focus in the short-junction regime, where the length of the strip is much smaller than superconducting coherence length. We show that the differential conductance exhibits a very rich subharmonic gap structure which can be modulated by means of a gate voltage. On approaching the Dirac point the conductance normalized by the normal-state conductance is identical to that of a short diffusive SNS junction.

Figure 1

(Color online) Upper panel: schematic of a strip of graphene of width $W$, contacted by two superconducting electrodes (black rectangles) at a distance $L$. A voltage source drives a current through the strip. A separate gate electrode (not shown) allows the carrier concentration in the strip to be tuned around the neutrality point. Lower panel: normal transmission of the conduction channels of the graphene junction as a function of the transversal momentum in the limit $W∕L⪢1$. The different curves correspond to different values of the dimensionless gate voltage $\kappa =e\mid V_{\text{gate}}\mid L∕\hslash v$.

Figure 2

(Color online) (a) Zero-temperature current-voltage characteristics of a superconducting ballistic graphene junction (length $L$ short compared to the width $W$ and the superconducting coherence length $\xi$) for different values of the gate voltage in the normal region $(\kappa =e\mid V_{\text{gate}}\mid L∕\hslash v)$. (b) The same as in panel (a), but the current is normalized by the resistance of the junction in the normal state $R_{\mathrm{N}}$.

Figure 3

(Color online) (a) Differential conductance corresponding to the $I\text{−}V$ curves of Fig. 2. In panel (b) the conductance is normalized by the normal-state conductance $G_{\mathrm{N}}$. As a guide for the eyes, the dotted vertical lines indicate the position of the voltages $2\Delta ∕ne$ $(n=1,2,\dots ,7)$.

Figure 4

(a) Zero-temperature excess current as function of the gate voltage for a short ballistic graphene SNS junction. (b) The same as in panel (a), but normalized by the resistance of the junction in the normal state, $R_{\mathrm{N}}$.