Tunable supercurrent at the charge neutrality point via strained graphene junctions

We theoretically calculate the charge-supercurrent through a ballistic graphene junction where superconductivity is induced via the proximity-effect. Both monolayer and bilayer graphene are considered, including the possibility of strain in the systems. We demonstrate that the supercurrent at the charge neutrality point can be tuned efficiently by means of mechanical strain. Remarkably, the supercurrent is enhanced or suppressed relative to the nonstrained case, depending on the direction of this strain. We also calculate the Fano factor in the normal state of the system and show how its behavior varies depending on the direction of strain.

Figure 1

Schematic setup of a strained graphene Josephson junction. The two superconducting electrode interfaces are located at $x=0,L$. There is also a controllable gate voltage for tuning the concentration of carriers (not shown). $Z$ and $A$ stand for zigzag and armchair strains, while ${\mathrm{\sigma ⃗}}_i$ represent displacement vectors of the three nearest-neighbor C atoms in the strained graphene. ${\theta }_g$ is the strained angle between C-C junctions, which can be either larger or smaller than the nonstrained value, ${60}^{°}$.

Figure 2

The critical current $I_c$ (left) and its product with the normal-state resistance $I_c{R}_N$ (right) as a function of $\mu L/\hslash v$ for a monolayer system. The solid line pertains to a nonstrained junction. For $Z$ tension, $t_{⊢}=0.56t_0,\hspace{0.5em}t=1.1t_0$, while for $A$ strain, $t_{⊢}=0.95t_0,\hspace{0.5em}t=0.5t_0$. The arrow indicates how the Josephson current may be enhanced by means of the applied direction of tension to the system. Inset: Critical supercurrent as a function of strain.

Figure 3

The critical current $I_c$ (left) and its product with the normal-state resistance $I_c{R}_N$ (right) as a function of $\mu L/\hslash v$ for a strongly coupled bilayer system. The solid line pertains to a nonstrained junction. Here, the same values as for the monolayer system have been used for the tensions, that is, in the case of $Z$ tension, $t_{⊢}=0.56t_0,\hspace{0.5em}t=1.1t_0$, while for $A$ tension, $t_{⊢}=0.95t_0,\hspace{0.5em}t=0.5t_0$ for $s=0.2$.

Figure 4

Fano factor $F$ for both monolayer and bilayer systems with a weakly doped region sandwiched between two heavily doped sides (the normal state of the mentioned $\mathrm{S}|$N$|$S junction) as a function of $\mu L/\hslash v$. In the scenarios with strain, the same parameters as in Figs. 2 and 3 were used.