Crossed Andreev reflection in a zigzag graphene nanoribbon-superconductor junction

We investigate the crossed Andreev reflection (CAR) in a zigzag graphene nanoribbon/superconductor/nanoribbon junction. It is shown that when the zigzag chain number of the ribbon is even and only the zero-energy mode is involved in transport either the elastic cotunneling or the local Andreev reflection could be entirely suppressed by using a gate voltage whereas a sizable CAR is achieved. When one of the ribbon leads is magnetized not only is the CAR exclusive, but also the spin state of the CAR transmission is nonlocally controllable. The physical origin is the peculiar valley selection rule in the even zigzag graphene nanoribbon. The ideal Cooper-pair splitting in the proposed device holds for all applied bias in the superconducting energy gap.

Figure 1

(a) An overview of the setting from the top. A normal superconductor lead (shadow $S$) on the top of the ZR is grounded and divides the ZR into three regions: the left, $S$, and right ZR regions; the left and right ZRs are, respectively, applied with voltage $V_L$ and $V_R$. (b) Electron and hole energy dispersions of the edge states in the nonmagnetic even ZR. The hole band “$h$” is obtained as a mirror image of the electron band “$e$” over the Fermi level (horizontal dotted line), “+” and “−” denote, respectively, the even and odd pseudoparities of the edge states. The left and right panels stand for the situations without and with a gate voltage applied on the ribbon. (c) Electron and hole energy dispersion of a magnetized even ZR. The spin-up (down) electron band overlaps with spin-down (up) hole band with opposite pseudoparities, and the spin exchange energy causes to a shift of the Dirac point from the Fermi level.

Figure 2

Plot of the AR, CAR, and EC transmission coefficients versus the bias voltage ${\mathrm{eV}}_L$ applied on the left ZR. The solid, dashed, and dotted lines represent the AR, CAR, and EC processes, respectively. Parameters are ${\mathrm{eV}}_R=0$, $L=40$, $U_S=-10$ meV, $U_L=0$, $U_R=-5$ meV in the upper panel (a), and $U_L=-5$ meV, $U_R=0$ in the lower panel (b).

Figure 3

Plot of the spin-resolved AR, CAR, and EC transmission coefficients versus the bias voltage ${\mathrm{eV}}_L$ applied on the left ZR. Only $T_{\mathrm{CAR}}^{\uparrow }$ and $T_{\mathrm{EC}}^{\uparrow }$ in (a) and $T_{\mathrm{CAR}}^{\downarrow }$ and $T_{\mathrm{EC}}^{\downarrow }$ in (b) are nonzero while all other quantities are vanishing. Parameters are ${\mathrm{eV}}_R=0$, $L=40$, $U_L=U_R=0$, $h=5$ meV, $U_S=-10$ meV in (a), and $U_S=10$ meV in (b).

Figure 4

Spin-dependent (a) CAR and (b) EC transmission coefficients versus the $S$ region length $L$. Parameters are ${\mathrm{eV}}_R=0$, $U_L=U_R=0$, $h=5$ meV, $U_S=-10$ meV, ${\mathrm{eV}}_L=-0.5\Delta$ in (a), and ${\mathrm{eV}}_L=0.5\Delta$ in (b).