Conduction properties of extended defect states in Dirac materials

Abstract

We demonstrate the existence of localized states in close vicinity of a linear defect in graphene. These states have insulating or conducting character. Insulating states form a flat band, while conducting states present a slowdown of the group velocity which is not originated by many-body interactions and it is controlled by the interface properties. For appropriate boundary conditions, the conducting states exhibit momentum-valley locking and protection from backscattering effects. These findings provide a contribution to the recent discussion on the origin of correlated phases in graphene.

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Fig. 1

Notes

  1. 1.

    Throughout this work, symbols \( {\mathbb{I}} \) and \( \sigma_{x,y,z} \) are used to indicate the \( 2 \times 2 \) identity matrix and the Pauli matrices, respectively. The symbol \( \otimes \) is used to indicate the Kronecker product of matrices. The notation \( p_{x} = - i\hbar \partial_{x} \) and \( p_{y} = - i\hbar \partial_{y} \) is introduced for quantum operators associated with the linear momentum components. Complex conjugation operator is denoted by \( {\mathcal{K}} \), while \( A^{t} \) denotes the transpose of \( A \).

References

  1. 1.

    R.P. Feynman, Int. J. Theor. Phys. 21, 467 (1982)

    Article  Google Scholar 

  2. 2.

    E. Fermi, J. Pasta, S. Ulam, Studies of Non Linear Problems, Los-Alamos internal report, document LA-1940 (1955)

  3. 3.

    A. Ekert, R. Jozsa, Rev. Mod. Phys. 68(3), 733 (1996)

    ADS  Article  Google Scholar 

  4. 4.

    V.S. Denchev, S. Boixo, S.V. Isakov, N. Ding, R. Babbush, V. Smelyanskiy, J. Martinis, H. Neven, Phys. Rev. X 6, 031015 (2016)

    Google Scholar 

  5. 5.

    S. Das Sarma, S. Adam, E.H. Hwang, E. Rossi, Rev. Mod. Phys. 83, 407 (2011)

    ADS  Article  Google Scholar 

  6. 6.

    M. Polini, F. Guinea, M. Lewenstein, H.C. Manoharan, V. Pellegrini, Nat. Nanotechnol. 8, 625 (2013)

    ADS  Article  Google Scholar 

  7. 7.

    P.E. Allain, J.N. Fuchs, Eur. Phys. J. B 83, 301 (2011)

    ADS  Article  Google Scholar 

  8. 8.

    T.M. Rusin, W. Zawadzki, Phys. Rev. B 78, 125419 (2008)

    ADS  Article  Google Scholar 

  9. 9.

    F.V. Tikhonenko, A.A. Kozikov, A.K. Savchenko, R.V. Gorbachev, Phys. Rev. Lett. 103, 226801 (2009)

    ADS  Article  Google Scholar 

  10. 10.

    P.M. Ostrovsky, I.V. Gornyi, A.D. Mirlin, Phys. Rev. B 77, 195430 (2008)

    ADS  Article  Google Scholar 

  11. 11.

    V.V. Cheianov, V. Fal’ko, B.L. Altshuler, Science 315, 1252 (2007)

    ADS  Article  Google Scholar 

  12. 12.

    Y. Cao, V. Fatemi, A. Demir, S. Fang, S.L. Tomarken, J.Y. Luo, J.D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R.C. Ashoori, P. Jarillo-Herrero, Nature 556, 80 (2018)

    ADS  Article  Google Scholar 

  13. 13.

    Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, P. Jarillo-Herrero, Nature 556, 43 (2018)

    ADS  Article  Google Scholar 

  14. 14.

    G. Chen, A.L. Sharpe, P. Gallagher, I.T. Rosen, E.J. Fox, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi, J. Jung, Z. Shi, D. Goldhaber-Gordon, Y. Zhang, F. Wang, Nature (2019). https://doi.org/10.1038/s41586-019-1393-y

    Article  Google Scholar 

  15. 15.

    G. Tarnopolsky, A.J. Kruchkov, A. Vishwanath, Phys. Rev. Lett. 122, 106405 (2019)

    ADS  Article  Google Scholar 

  16. 16.

    A. Luican-Mayer, J.E. Barrios-Vargas, J.T. Falkenberg, G. Auts, A.W. Cummings, D. Soriano, G. Li, M. Brandbyge, O.V. Yazyev, S. Roche, E.Y. Andrei, 2D Materials 3, 031005 (2016)

    Article  Google Scholar 

  17. 17.

    T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004)

    Google Scholar 

  18. 18.

    H. Suzuura, T. Ando, Phys. Rev. Lett. 89, 266603 (2002)

    ADS  Article  Google Scholar 

  19. 19.

    F. Romeo, A. Di Bartolomeo, Materials 11, 1660 (2018)

    ADS  Article  Google Scholar 

  20. 20.

    C.W.J. Beenakker, Phys. Rev. Lett. 97, 067007 (2006)

    ADS  Article  Google Scholar 

  21. 21.

    J. Lahiri, Y. Lin, P. Bozkurt, I.I. Oleynik, M. Batzill, Nat. Nanotechnol. 5, 326 (2010)

    ADS  Article  Google Scholar 

  22. 22.

    T. Ochiai, M. Onoda, Phys. Rev. B 80, 155103 (2009)

    ADS  Article  Google Scholar 

  23. 23.

    Daniel Torrent, José Sánchez-Dehesa, Phys. Rev. Lett. 108, 174301 (2012)

    ADS  Article  Google Scholar 

  24. 24.

    Penglin Gao, Daniel Torrent, Francisco Cervera, Pablo San-Jose, José Sánchez-Dehesa, Johan Christensen, Phys. Rev. Lett. 123, 196601 (2019)

    ADS  Article  Google Scholar 

  25. 25.

    Xin Li, Yan Meng, Wu Xiaoxiao, Sheng Yan, Yingzhou Huang, Shuxia Wang, Weijia Wen, Appl. Phys. Lett. 113, 203501 (2018)

    ADS  Article  Google Scholar 

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Acknowledgements

Discussions with R. De Luca and M. Salerno are gratefully acknowledged. This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

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Correspondence to Francesco Romeo.

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Romeo, F. Conduction properties of extended defect states in Dirac materials. Eur. Phys. J. Plus 135, 446 (2020). https://doi.org/10.1140/epjp/s13360-020-00491-9

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