Superconducting current and proximity effect in ABA and ABC multilayer graphene Josephson junctions

Using a numerical tight-binding approach based on the Chebyshev–Bogoliubov–de Gennes method we describe Josephson junctions made of multilayer graphene contacted by top superconducting gates. Both Bernal (ABA) and rhombohedral (ABC) stacking are considered and we find that the type of stacking has a strong effect on the proximity effect and the supercurrent flow. For both cases the pair amplitude shows a polarization between dimer and nondimer atoms, being more pronounced for rhombohedral stacking. Even though the proximity effect in nondimer sites is enhanced when compared to single-layer graphene, we find that the supercurrent is suppressed. The spatial distribution of the supercurrent shows that for Bernal stacking the current flows only in the topmost layers while for rhombohedral stacking the current flows throughout the whole structure.

Figure 1

Schematic layout of a multilayer graphene JJ showing the superconducting (SC) leads which are separated by a distance $L$. $W$ corresponds to the width of the junction. On the right-hand side the layer arrangements in multilayer graphene show the two different stacking configurations: ABC (rhombohedral) and ABA (Bernal).

Figure 2

Absolute value of the pair correlation along the line $(x,y,z)=(W/2,y,1)$ in a single-layer graphene JJ and in the topmost layer in (a) ABC and (b) ABA multilayer graphene JJs with $N=2$, 3, and 10 layers. $a_0=3a/2$ where $a$ is the intralayer C-C distance. Pair correlation function at the middle point of the junction along the $\widehat{z}$ vertical axis, $(x,y,z)=(W/2,L/2,z)$, for (c) ABC and (d) ABA multilayer graphene JJs with $N=10$ layers. The integer index $z/c$, where $c$ corresponds to the distance between adjacent layers, labels the different layers where $z/c=1$ corresponds to the topmost layer and open (closed) circles correspond to A (B) sublattice (see Fig. 1). Dotted lines in (c) correspond to the results obtained for small doping $\mu =0.0014t$. The insets in (c) and (d) show the vertical profile of the pair correlation at the middle point right underneath the superconducting contacts.

Figure 3

(a), (b) LDOS around the Dirac point for both sublattices A (dashed) and B (solid) in $(x,y,z)=(W/2,L/2,z)$ along the $z$ direction for a trilayer graphene (TLG) JJ with ABC and ABA stacking configuration. (c), (d) Profile of the amplitude of the pair correlation along the line $(x,y,z)=(W/2,y,z)$ in the different layers of an ABC and ABA TLG JJ, respectively.

Figure 4

Amplitude of the pair correlation at the middle point $(x,y,z)=(W/2,L/2,1)$ as a function of the junction length $L$ for different values of the doping ${\mu }_N$ for the A sublattice in the topmost layer of the ABC and ABA (inset) multilayer graphene JJ containing $N=10$ layers.

Figure 5

(a) Josephson current as a function of the total number of layers, $N$. (b) Current density-phase relation for single ($N=1$), bilayer ($N=2$), trilayer ($N=3$), and multilayer ($N=10$) graphene JJs. Both stackings are considered. (c) Critical current density as a function of the junction length $L$ for $T=0$ K (solid lines) and $T=10$ K (dashed lines). Note that the current densities in panels (b) and (c) are normalized by the maximum Josephson current obtained for single-layer graphene, as shown in panel (a).

Figure 6

In-plane current-phase relation for the different layers in (a) ABC and (b) ABA stacked trilayer ($N=3$) graphene JJ. (c) $z$-resolved in-plane critical current through the different graphene layers for ABC and ABA multilayer graphene JJs with $N=10$. Note that the current densities in panels (a)–(c) are normalized by the maximum Josephson current obtained for single-layer graphene, as shown in Fig. 5a.