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Coupling of spin and orbital motion of electrons in carbon nanotubes


Electrons in atoms possess both spin and orbital degrees of freedom. In non-relativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion, leading to the well-known fine structure in their spectra. The electronic states in defect-free carbon nanotubes are widely believed to be four-fold degenerate1,2,3,4,5,6,7,8,9,10, owing to independent spin and orbital symmetries, and also to possess electron–hole symmetry11. Here we report measurements demonstrating that in clean nanotubes the spin and orbital motion of electrons are coupled, thereby breaking all of these symmetries. This spin–orbit coupling is directly observed as a splitting of the four-fold degeneracy of a single electron in ultra-clean quantum dots. The coupling favours parallel alignment of the orbital and spin magnetic moments for electrons and antiparallel alignment for holes. Our measurements are consistent with recent theories12,13 that predict the existence of spin–orbit coupling in curved graphene and describe it as a spin-dependent topological phase in nanotubes. Our findings have important implications for spin-based applications in carbon-based systems, entailing new design principles for the realization of quantum bits (qubits) in nanotubes and providing a mechanism for all-electrical control of spins14 in nanotubes.

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Figure 1: Few-electron carbon nanotube quantum dot devices.
Figure 2: Excited-state spectroscopy of a single electron in a nanotube dot.
Figure 3: The many-electron ground states and their explanation by spin-orbit interaction.
Figure 4: Theoretical model for spin–orbit interaction in nanotubes and the energy level spectroscopy of a single hole.

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We thank E. Altman, Y. Gefen, C. L. Henley, Y. Meir, E. Mueller, Y. Oreg, E. I. Rashba, A. Stern and B. Trauzettel for discussions. This work was supported by the NSF through the Center for Nanoscale systems, and by the MARCO Focused Research Center on Materials, Structures and Devices. Samples were fabricated at the Cornell node of the National Nanofabrication Users Network, funded by NSF.

Author Contributions F.K. and S.I. fabricated the devices and performed the experiments. F.K., S.I., D.C.R. and P.L.M. analysed the data and co-wrote the paper. All authors discussed the results and commented on the manuscript.

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Correspondence to P. L. McEuen.

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Supplementary Information

The file contains Supplementary Discussion and Supplementary Figures S1-S2 with Legends. This document discusses how the one-electron and one-hole quantum dots are identified, and how the few-electron addition spectra are affected by higher longitudinal modes. Two Figures further compare quantum dots localized over different gate electrodes and schematically contrast the effects of spin-orbit coupling and KK’ scattering. (PDF 299 kb)

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Kuemmeth, F., Ilani, S., Ralph, D. et al. Coupling of spin and orbital motion of electrons in carbon nanotubes. Nature 452, 448–452 (2008).

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