Controllable $0\mathrm{\text{−}}\pi$ Transition in a Superconducting Graphene-Nanoribbon Junction

The supercurrent in a Josephson junction composed of the zigzag edged graphene nanoribbon (ZGNR) lying between two superconducting leads [superconductor-graphene-superconductor (SGS) junction] has been studied by the Green’s function method. It is found that a small transverse electric field applied on the ZGNR can reverse the supercurrent direction, leading to a so-called $0\mathrm{\text{−}}\pi$ phase transition. The $0\mathrm{\text{−}}\pi$ phase transition can happen periodically with a change in the ZGNR’s length, and, more importantly, can be easily and electrically controllable by a gate voltage, which is absent in the conventional superconducting $\pi$ junction and would make the SGS junction very promising for future application in superconducting electronics, as well as quauntum information and computation.

Figure 1

(a) Left: Geometrical structure of an 8-ZGNR, where $W$ and $L$ denote its width and length, respectively, and the 8 is the number of carbon chains along the width’s direction. $a_0=2.46\AA$ is the graphene’s lattice constant. Two leads are illustrated by the blue rectangles, and the red arrow denotes the $E_T$’s direction. Right: the distribution of the spin density $S_i=⟨n_{i,\uparrow }-n_{i,\downarrow }⟩$. (b) Splitting of the spin-dependent energy bands nearest to the neutrality point by an $E_T$, taken as 0.001. (c) An enlargment of the detailed $E_T$ influence on the bottom of the conduction band. The dashed (blue) and solid (red) lines denote, respectively, the up-shifted spin-up band and the down-shifted spin-down one.

Figure 2

Supercurrent dependence of a SGS $\pi$ junction with its 8-ZGNR length $L=220a_0$ at a gate voltage $V_g=0.15$: (a) on the phase difference $\Delta \varphi$ between two superconducting leads for different $E_T$ values, and (b) on the $E_T$ values for three $\Delta \varphi =0.25$, 0.5, and $0.75\pi$. Here, $I^0=\frac{4et}{h}$.

Figure 3

Supercurrent dependence of a SGS $\pi$ junction at a fixed $\Delta \varphi =0.5\pi$: (a) on the ZGNR length at a fixed $V_g=0.15$ for different $E_T$ values, and (b) on the gate-voltage at a fixed $E_T=0.002$ and a ZGNR length of $400a_0$.