Spin-orbit coupling in gold nanostructures

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Abstract

The effect of spin-orbit interaction accounting on the atomic and electronic structure of 0D (clusters), 1D (gold nanotubes), and 2D (monolayer) gold is reported. The relevance of the work lies in the fact that, on the one hand, gold nanostructures are widely used, in particular, in sensorics and medicine, on the other hand, due to limited computing resources, researchers may neglect some effects in the theoretical study of such objects, and it is important to understand what errors may be associated with such neglect. The study was conducted on a large set of objects: six isomers of the Au25 cluster, gold nanotubes of nine different radii, and a flat monolayer of gold, which made it possible to comprehensively evaluate the effect of spin-orbit interaction. It has been shown that the cohesive energies of all but the thinnest of the gold nanotubes range from the cohesive energy of gold nanoclusters to the cohesive energy of a gold monolayer. Accounting for the spin-orbit interaction leads to a decrease in the Au–Au interatomic distances and a change in the electronic structure of gold nanoobjects. At the same time, a significant change in the position of energy levels is possible for nanoclusters, reflecting a change in the cluster structure. For nanotubes and golden, only the splitting of energy levels occurs near the Fermi level.

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About the authors

E. R. Sozykina

South Ural State University

Author for correspondence.
Email: sozykinaer@susu.ru
Russian Federation, Chelyabinsk

S. A. Sozykin

South Ural State University

Email: sozykinaer@susu.ru
Russian Federation, Chelyabinsk

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Supplementary files

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2. Fig. 1. Models of (a) Au25,m clusters, where m = 1–6, (b) OZNT with chirality indices (n, 0), n = 3–10, and (c) Golden.

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3. Fig. 2. Average interatomic distances lAu–Au and relative energies ΔE of Au25 isomers. The index “soc” refers to the results obtained taking into account the spin-orbit interaction. ΔEref are the relative energies of the corresponding starting configurations of clusters according to [32].

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4. Fig. 3. Cohesion and formation energies of gold nanotubes as a function of their radius.

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5. Fig. 4. Energy levels of Au25 clusters with (red lines) and without (blue lines) spin-orbit interaction. Energy is measured from HOMO.

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6. Fig. 5. Band structure of gold nanotubes (n, 0), where n = 3–10. Red lines – taking into account spin-orbit interaction, blue – without it.

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7. Fig. 6. Band structure of golden without (blue dotted lines) and with (red lines) taking into account spin-orbit interaction.

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