Skip to main content
SpringerLink
Log in

Enhanced robustness of zero-line modes in graphene via magnetic field

  • Letter
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

We systematically studied the influence of magnetic field on zero-line modes (ZLMs) in graphene and demonstrated the physical origin of their enhanced robustness by employing nonequilibrium Green’s functions and the Landauer–Büttiker formula. We found that a perpendicular magnetic field can separate the wavefunctions of the counter-propagating kink states into opposite directions. Specifically, the separation vanishes at the charge neutrality point and increases as the Fermi level deviates from the charge neutrality point and can reach a magnitude comparable to the wavefunction spread at a moderate field strength. Such spatial separation of oppositely propagating ZLMs effectively suppresses backscattering and is more significant under zigzag boundary condition than under armchair boundary condition. Moreover, the presence of magnetic field enlarges the bulk gap and suppresses the bound states, thereby further reducing the scattering. These mechanisms effectively increase the mean free paths of the ZLMs to approximately 1 μm in the presence of a disorder.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. M. Bttiker, Edge-state physics without magnetic fields, Science 325(5938), 278 (2009)

    Article  Google Scholar 

  2. G. W. Semenoff, V. Semenoff, and F. Zhou, Domain walls in gapped graphene, Phys. Rev. Lett. 101(8), 087204 (2008)

    Article  ADS  Google Scholar 

  3. I. Martin, M. Blanter, and A. F. Morpurgo, Topological confinement in bilayer graphene, Phys. Rev. Lett. 100(3), 036804 (2008)

    Article  ADS  Google Scholar 

  4. W. Yao, S. A. Yang, and Q. Niu, Edge states in graphene: From gapped flat-band to gapless chiral modes, Phys. Rev. Lett. 102(9), 096801 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  5. M. Killi, S. Wu, and A. Paramekanti, Band structures of bilayer graphene superlattices, Phys. Rev. Lett. 107(8), 086801 (2011)

    Article  ADS  Google Scholar 

  6. Y. Ran, Y. Zhang, and A. Vishwanath, One-dimensional topologically protected modes in topological insulators with lattice dislocations, Nat. Phys. 5(4), 298 (2009)

    Article  Google Scholar 

  7. Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Experimental observation of quantum Hall effect and Berry’s phase in graphene, Nature 438, 201 (2005)

    Article  ADS  Google Scholar 

  8. K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer, U. Zeitler, J. C. Maan, G. S. Boebinger, P. Kim, and A. K. Geim, Room-temperature quantum Hall effect in graphene, Science 315(5817), 1379 (2007)

    Article  ADS  Google Scholar 

  9. C. Z. Chang, J. S. Zhang, X. Feng, J. Shen, Z. C. Zhang, M. H. Guo, K. Li, Y. B. Ou, P. Wei, L. L. Wang, Z. Q. Ji, Y. Feng, S. K. Ji, X. Chen, J. F. Jia, X. Dai, Z. Fang, S. C. Zhang, K. He, Y. Y. Wang, L. Lu, X. C. Ma, and Q. K. Xue, Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science 340(6129), 167 (2013)

    Article  ADS  Google Scholar 

  10. Z. Qiao, S. A. Yang, W. Feng, W. K. Tse, J. Ding, Y. Yao, J. Wang, and Q. Niu, Quantum anomalous Hall effect in graphene from Rashba and exchange effects, Phys. Rev. B 82(16), 161414R (2010)

    Google Scholar 

  11. L. Sheng, D. N. Sheng, and C. S. Ting, Spin-Hall effect in two-dimensional electron systems with Rashba spin-orbit coupling and disorder, Phys. Rev. Lett. 94(1), 016602 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  12. Z. H. Qiao, J. Jung, Q. Niu, and A. H. MacDonald, Electronic highways in bilayer graphene, Nano Lett. 11(8), 3453 (2011)

    Article  ADS  Google Scholar 

  13. T. Hou, G. H. Chen, W.K. Tse, C. G. Zeng, and Z. H. Qiao, Topological zero-line modes in folded bilayer graphene, arXiv: 1809.04036 (2018)

    Book  Google Scholar 

  14. K. Wang, Y. F. Ren, X. Z. Deng, S. A. Yang, J. Jung, and Z. H. Qiao, Gate-tunable current partition in graphenebased topological zero lines, Phys. Rev. B 95(24), 245420 (2017)

    Article  ADS  Google Scholar 

  15. Z. H. Qiao, J. Jung, C. Lin, Y. F. Ren, A. H. MacDonald, and Q. Niu, Current partition at topological channel intersections, Phys. Rev. Lett. 112(20), 206601 (2014)

    Article  ADS  Google Scholar 

  16. J. Li, K. Wang, K. J. McFaul, Z. Zern, Y. F. Ren, K. Watanabe, T. Taniguchi, Z. H. Qiao, and J. Zhu, Gate-controlled topological conducting channels in bilayer graphene, Nat. Nanotechnol. 11, 1060 (2016)

    Article  ADS  Google Scholar 

  17. M. Kim, J. H. Choi, S. H. Lee, K. Watanabe, T. Taniguchi, S. H. Jhi, and H. J. Lee, Valley-symmetrypreserved transport in ballistic graphene with gatedefined carrier guiding, Nat. Phys. 12(11), 1022 (2016)

    Article  Google Scholar 

  18. L. Ju, Z. Shi, N. Nair, Y. Lv, C. Jin, H. A. Velasco, M. C. Bechtel, A. Martin, J. Zettl, Analytis, and F. Wang, Topological valley transport at bilayer graphene domain walls, Nature 520(7549), 650 (2015)

    Article  ADS  Google Scholar 

  19. S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, 1997

    Google Scholar 

  20. M. P. L. Sancho, J. M. L. Sancho, and J. Rubio, Quick iterative scheme for the calculation of transfer matrices: Application to Mo(100), J. Phys. F Met. Phys. 14(5), 1205 (1984)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the National Key Research and Development Program (Grant No. 2017YFB0405703), the China Government Youth 1000-Plan Talent Program, and the National Natural Science Foundation of China (Grant No. 11474265). We are grateful to the Supercomputing Center of USTC for providing high-performance computing assistance.

Author information

Authors and Affiliations

  1. ICQD, Hefei National Laboratory for Physical Sciences at Microscale, and Synergetic Innovation Centre of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China

    Ke Wang, Tao Hou, Yafei Ren & Zhenhua Qiao

  2. CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics and Department of Physics, University of Science and Technology of China, Hefei, 230026, China

    Ke Wang, Tao Hou, Yafei Ren & Zhenhua Qiao

Authors
  1. Ke Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tao Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yafei Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhenhua Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenhua Qiao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, K., Hou, T., Ren, Y. et al. Enhanced robustness of zero-line modes in graphene via magnetic field. Front. Phys. 14, 23501 (2019). https://doi.org/10.1007/s11467-018-0869-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-018-0869-9

Keywords

Search

Navigation