Critical currents in graphene ribbon Josephson's junctions

Abstract

The rapidly advancing technology of nanodevices has led to the production of smaller and smaller structures often called mesoscopic systems. These devices are large on the atomic scale, but sufficiently small that the electron wave function is coherent over the entire sample: the condition for coherence is that the electron traverses the wire without undergoing any collision with phonons or other electrons. Because the electron can lose energy and equilibrate with heat bath only via inelastic collisions, it is necessary to re-examine the conventional concept of energy dissipation in a resistor. We study the way in which the superconducting correlations are induced in graphene ribbon when it is placed between two superconductors, how such correlations may depend on complex edge structure of the ribbon, on the geometry of the experimental set-up and what is the role of Andreev's reflection in Josephson's effect at superconducting contacts.

Keywords:

• graphene
• quantum transport
• Josephson's junction
• critical currents

Notes

^1. Each carbon atom in the hexagonal lattice possess six electrons and in the graphite structure carbon has two 1s electrons, one 2p electron and three electrons. The three electrons forms the three bonds in the plane of the graphene sheet, leaving an unsaturated π orbital. This π orbital, perpendicular to the graphene surface, forms a delocalised π network across the nanoribbon, responsible for its electronic properties.

^2. At temperatures T < < T _F, i.e. for all temperatures at which the metal remains solid, the Fermi distribution differs appreciably from its zero-limit only in an energy shell of width ∼ around the Fermi energy , then only states within this shell contribute to reaction of the system to weak perturbation and for this reason, a critical role is played by the density of (single-particle) state per unit energy.

^3. There are two major ways to calculate : one is to use the non-equilibrium Green's function of the system; however, since G is a double variable function, computationally is not so expensive and is used for localised basis set methods; the other way to calculate is to solve the scattering equation , where H is the single particle Hamiltonian, and timely boundary conditions.

^4. As in [2], most theories suggest which is about π times smaller than the experimentally observed value .