First-principles calculation of the Andreev conductance of carbon wires

Abstract

We developed a first-principles approach based on nonequilibrium Green's function (NEGF) combined with density functional theory (DFT) to investigate quantum transport properties of normal-metal--superconductor (N-S) hybrid systems. As an application of our theory, we investigated the Andreev conductance of atomic wires consisting of 4--15 carbon atoms in contact with one normal Al lead and another superconducting Al lead from first principles. Numerical results show that the Andreev conductance oscillates between an even and odd number of carbon atoms. In the presence of the superconducting lead, the self-consistent scattering potential of the N-S system can be very different from that of the corresponding normal system. Furthermore, a small change of scattering potential can give rise to a significant change of Andreev conductance. For an even number of carbon atoms, the change of scattering potential gives rise to a 4--7% difference in conductance, while when the number of carbon atoms $n$ is odd, a 14--30% change of conductance is observed due to the potential change. We find that the charge transfer plays an important role in N-S systems. For the carbon wire with normal Al contacts, there is a significant charge transfer in real space that is responsible for the even-odd oscillation in conductance. When a superconducting lead is present, the charge is redistributed in momentum space, although it is almost not changed in real space. For even $n$, a $10%$ change of charge density at Fermi level is found mainly in the lead region. For odd $n$, however, the change of charge density at Fermi level is even more than $30%$ near the first, third, etc., carbon atoms. Since less charge density is available at Fermi level, there is a decrease in conductance for all carbon wires, especially for the wires with odd number of carbon atoms. Our results indicate that the self-consistent calculation of the scattering potential is necessary to obtain an accurate Andreev conductance of N-S hybrid structures.