Dirac supercurrent in an asymmetric graphene-based SG<inf>1</inf>/F<inf>B</inf>/SG<inf>2</inf>junction

Abstract

The Josephson current in an asymmetric graphene-based SG1/FB/SG2junction where SG1,2are graphene layers which have been induced into two superconducting states having order parameters Δ1and Δ2(Δ1≠ Δ2) on the left and right sides of a ferromagnetic barrier FBof thickness d, respectively is studied. The presence of the exchange energy Eexand the gate potential VGin the barrier FBare taken into account. For the case of k///0, we find that the Josephson current depends on the exchange energy but is independent of the gate voltage. We find that increasing Δ2can induce the junction to become a π-junction. This does not occur in the case of similar junctions having conventional superconductors in them. The critical current at zero temperature for Δ2→ ∞ has the form IC(Δ2→ ∞) = 2 e Δ1/ ℏ = 2 IC(Δ2= Δ1). This behavior of the Josephson current in a graphene junction is quite different from that of the supercurrent in conventional asymmetric junctions. For those junctions, it is predicted that IC∝ Δ1Δ2, leading to IC→ ∞ as Δ2→ ∞. A transition from a 0-junction to a π-junction is observed as χex(χex∼ 2 Eexd / ℏ vF) is increased. In a 0-junction, the spin supercurrents arising from the spin dependent Andreev energy levels do not vanish. This leads to IS= I↑+ I↓= 0 but with I↑= -I↓≠ 0. © 2009 Elsevier B.V. All rights reserved.