Abstract
The effect of spin—orbit coupling on the electron levels of (5, 3), (8, 7), (11, 3), (18, 11), (10, 5), (8, 8), and (13, 0) gold nanotubes of various diameters and chirality was studied in the framework of the relativistic version of the linear augmented cylindrical wave method. Spin-dependent band structures and electron state densities were calculated. Spin—orbit coupling is manifested as splitting of nonrelativistic dispersion curves. For the dispersion curve that crosses the Fermi level in the (5, 3) tube of the minimum radius, this splitting reaches 0.5 eV and decreases on going to low-lying valence band states. An increase in the radius and a decrease in the cylindrical surface curvature of these nanotubes suppress the spin—orbit splitting. All tubes possess a metal type band structure in which the number of conduction channels increases with increasing radius of the nanotube.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Y. Kondo and K. Takayanagi, Science 289, 606 (2000).
C. R. Bridges, P. M. DiCarmine, A. Fokina, et al., Chem. Mater., No. 1, 1127 (2013).
Y. Oshima, A. Onga, and K. Takayanagi, Phys. Rev. Lett. 91, 205503 (2003).
W. R. Hendren, A. Murphy, P. Evans, et al., J. Phys.: Condens. Matter 20, 362203 (2008).
H. W. Wang, C. F. Shieh, H. Y. Chen, et al., Nanotechnology 17, 2689 (2006).
C. R. Bridges, P. M. DiCarmine, and D. S. Seferos, Chem. Mater., No. 24, 963 (2012).
J. Kohl, M. Fireman, and D. M. O’ Carroll, Phys. Rev. B 84, 235118 (2011).
D. Huang, F. Liao, S. Molesa, et al., J. Electrochem. Soc. 150, 412 (2003).
X. Yang and J. Dong, Phys. Rev. B 71, 233403 (2005).
K. Zhang and H. Zhang, J. Phys. Chem. C 118, 635 (2014).
M. Valle, C. Tejedor, and G. Cuniberti, Phys. Rev. B 74, 045408 (2006).
Y. Oshima, K. Mouri, L. Guo, et al., J. Phys. Soc. Jpn. 75, 053705 (2006).
A. Sen, C. J. Lin, and C. C. Kaun, J. Phys. Chem. C 117, 13676 (2013).
T. Ono and K. Hirose, Phys. Rev. Lett. 94, 206806 (2005).
D. Z. Manrique, J. Cserti, and C. J. Lambert, Phys. Rev. B 81, 073103 (2010).
N. Liu, S. Jin, L. Guo, et al., Phys. Rev. B 95, 155311 (2017).
T. Ando, J. Phys. Soc. Jpn. 69, 1757 (2000).
X. Yang, J. Zhou, H. Weng, and J. Dong, Appl. Phys. Lett. 92, 023115 (2008).
Y. Mokrousov, G. Bihlmayer, and S. Blugel, Phys. Rev. B 72, 045402 (2005).
P. N. D’yachkov and D. V. Makaev, Phys. Rev. B 76, 195411 (2007).
P. N. D’yachkov, D. Z. Kutlubaev, and D. V. Makaev, Phys. Rev. B 82, 035426 (2010).
P. N. D’yachkov and D. V. Makaev, Int. J. Quantum Chem. 116, 316 (2016).
P. N. D’yachkov, Int. J. Quantum Chem. 116, 174 (2016).
L. O. Khoroshavin, D. O. Krasnov, P. N. D’yachkov, and E. M. Kol’tsova, Zh. Neorg. Khim. 62, 800 (2017).
J. C. Slater, The Self-Consistent Field for Molecules and Solids (McGaw-Hill, New York, 1974).
J. B. Conklin, L. E. Johnson, and G. W. Pratt, Phys. Rev. 137, 1283 (1965).
T. L. Loucks, Phys. Rev. 139, 1333 (1965).
O. K. Andersen, Phys. Rev. B 12, 3060 (1975).
D. D. Koelling and G. O. Arbman, J. Phys. F: Met. Phys. 5, 2041 (1975).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Krasnov, D.O., Khoroshavin, L.O. & D’yachkov, P.N. Spin—Orbit Coupling in Single-Walled Gold Nanotubes. Russ. J. Inorg. Chem. 64, 108–113 (2019). https://doi.org/10.1134/S0036023619010145
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0036023619010145