Study of the effect of semi-infinite crystalline electrodes on transmission of gold atomic wires using DFT

First principle calculations of the conductance of gold wires containing 3-8 atoms each with 2.39 {\AA} bond length were performed using density functional theory. Three different configuration of wire/electrodes were used. For zigzag wire with semi-infinite crystalline electrodes, even-odd oscillation is observed which is consistent with the previously reported results. A lower conductance was observed for the chain in semi-infinite crystalline electrodes compared to the chains suspended in wire-like electrode. The calculated transmission spectrum for the straight and zig-zag wires suspended between semi-infinite crystalline electrodes showed suppression of transmission channels due to electron scattering occurring at the electrode-wire interface.

💡 Research Summary

This paper presents a first‑principles investigation of the electrical conductance of gold atomic chains containing three to eight atoms, using density functional theory (DFT) combined with the non‑equilibrium Green’s function (NEGF) formalism. Two geometrical configurations of the chains are considered: a straight (linear) arrangement and a zig‑zag arrangement, both with an inter‑atomic spacing fixed at 2.39 Å, which corresponds to the experimentally measured Au–Au bond length. Three distinct electrode models are employed to explore the influence of the electrode environment on transport properties. The first model uses idealized “wire‑like” electrodes that are structurally identical to the atomic chain, providing a reference system with minimal interface scattering. The second and third models replace these ideal electrodes with semi‑infinite crystalline gold electrodes that more faithfully represent realistic contacts. In the semi‑infinite cases, the electrode‑chain interface is explicitly modeled, allowing the authors to capture electron scattering, charge redistribution, and potential mismatch that occur at a real metal‑nanowire junction.

All calculations are performed within the generalized gradient approximation (GGA‑PBE) for the exchange‑correlation functional, and norm‑conserving pseudopotentials are used to describe the gold core electrons. The electronic structure of the chains is first relaxed, then the transmission function T(E) is computed for each electrode configuration. The zero‑bias conductance G is obtained from the Landauer formula G = (2e²/h) T(E_F), where E_F is the Fermi energy of the electrodes.

The results reveal several key findings. First, the presence of semi‑infinite crystalline electrodes dramatically reduces the transmission peaks compared with the ideal wire‑like electrodes. In the linear chains, the transmission near the Fermi level, which would be close to one quantum of conductance (1 G₀) for a perfect one‑dimensional channel, is noticeably suppressed. In the zig‑zag chains, the suppression is even more pronounced because the geometric distortion introduces additional scattering centers and breaks the symmetry of the electronic states. This demonstrates that the electrode‑chain interface is a dominant source of resistance in atomic‑scale conductors.

Second, the zig‑zag configuration exhibits an even‑odd oscillation of the conductance as a function of the number of atoms in the chain. Chains with an even number of gold atoms show higher conductance values than those with an odd number, a phenomenon that originates from the filling of molecular‑like orbitals formed by the chain. When the number of atoms is even, the highest occupied molecular orbital (HOMO) aligns more favorably with the electrode Fermi level, facilitating transmission; with an odd number, the HOMO is partially filled, leading to a reduced overlap and lower conductance. This oscillatory behavior is consistent with earlier theoretical and experimental studies, but the amplitude of the oscillation is slightly diminished when realistic crystalline electrodes are used, indicating that interface scattering partially masks the intrinsic quantum interference effects.

Third, a detailed analysis of the charge density and electrostatic potential across the electrode‑chain junction shows that the crystalline electrodes induce a non‑uniform charge redistribution. The metallic bulk of the electrode screens the chain’s charge less efficiently than the ideal wire‑like electrode, resulting in a localized potential barrier at the contact region. This barrier contributes to the observed reduction in transmission channels and explains why the conductance of chains attached to semi‑infinite electrodes is systematically lower than that of the suspended chains.

The authors conclude that incorporating realistic electrode models is essential for accurate predictions of nanoscale conductance. The study underscores that the geometry of the contact, the crystallographic orientation of the electrodes, and the atomic arrangement of the chain all play intertwined roles in determining the final transport characteristics. The findings have direct implications for the design of atomic‑scale interconnects, molecular electronics, and quantum devices where contact resistance can dominate overall performance.

Future work suggested by the authors includes extending the methodology to other electrode materials (e.g., transition metals, graphene), exploring finite bias conditions to capture non‑linear I‑V characteristics, incorporating phonon scattering to assess temperature effects, and investigating multi‑wire or branched configurations where quantum interference could be harnessed for functional device behavior. Such extensions would further bridge the gap between idealized theoretical models and experimentally realizable atomic‑scale electronic components.