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Van der Waals-coupled electronic states in incommensurate double-walled carbon nanotubes

Nature Physics volume 10, pages 737–742 (2014)Cite this article

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Abstract

Non-commensurate two-dimensional materials such as a twisted graphene bilayer or graphene on boron nitride, consisting of components that have no finite common unit cell, exhibit emerging moiré physics such as novel Van Hove singularities1,2,3, Fermi velocity renormalization4,5, mini Dirac points6 and Hofstadter butterflies7,8,9,10,11. Here we use double-walled carbon nanotubes as a model system for probing moiré physics in incommensurate one-dimensional systems, by combining structural and optical characterizations. We show that electron wavefunctions between incommensurate inner- and outer-wall nanotubes can hybridize strongly, contrary to the conventional wisdom of negligible electron hybridization due to destructive interference12,13. The chirality-dependent inter-tube electronic coupling is described by one-dimensional zone folding of the electronic structure of twisted-and-stretched graphene bilayers. Our results demonstrate that incommensurate van der Waals interactions can be important for engineering the electronic structure and optical properties of one-dimensional materials.

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Figure 1: Optical transitions of an individual chirality-defined DWNT.
Figure 2: Energy shifts of 99 transitions in 28 DWNTs compared with the corresponding constituent SWNT transitions.
Figure 3: Chirality dependence of inter-tube electronic coupling in an incommensurate DWNT.
Figure 4: Simulation of the inter-tube electronic coupling-induced optical transition shift for a (15,10) inner SWNT.

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Acknowledgements

This study was supported mainly by NSF grants (No. DMR-0846648 and DMR-1404865) and the NSF Center for Integrated Nanomechanical Systems (No. EEC-0832819). Support for the TEM characterization and sample preparation was provided by the Director, Office of Energy Research, Materials Sciences and Engineering Division of the US Department of Energy under Contract No. DE-AC02- 05CH11231.

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Author notes

  1. Kaihui Liu and Chenhao Jin: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA

    Kaihui Liu, Chenhao Jin, Xiaoping Hong, Jihoon Kim, Alex Zettl & Feng Wang

  2. Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    Alex Zettl & Feng Wang

  3. International Center for Quantum Materials and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China

    Enge Wang

Authors
  1. Kaihui Liu
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  3. Xiaoping Hong
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  7. Feng Wang
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Contributions

F.W., K.L. and C.J. conceived the project. K.L., J.K. and A.L. contributed to sample growth and characterization. K.L. carried out TEM measurements. K.L. and X.H. carried out optical measurements. K.L. and C.J. analysed the experimental data. C.J., E.W. and F.W. developed the theory. K.L., C.J. and F.W. wrote the manuscript. All authors discussed the results and commented on the paper.

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Correspondence to Feng Wang.

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The authors declare no competing financial interests.

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Liu, K., Jin, C., Hong, X. et al. Van der Waals-coupled electronic states in incommensurate double-walled carbon nanotubes. Nature Phys 10, 737–742 (2014). https://doi.org/10.1038/nphys3042

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