Current Applied Physics

Korean Physical Society (한국물리학회)
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Low-energy band structure very sensitive to the interlayer distance in Bernal-stacked tetralayer graphene

  • Received : 2018.04.11
  • Accepted : 2018.08.07
  • Published : 2018.11.30
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Abstract

We have investigated Bernal-stacked tetralayer graphene as a function of interlayer distance and perpendicular electric field by using density functional theory calculations. The low-energy band structure was found to be very sensitive to the interlayer distance, undergoing a metal-insulator transition. It can be attributed to the nearest-layer coupling that is more sensitive to the interlayer distance than are the next-nearest-layer couplings. Under a perpendicular electric field above a critical field, six electric-field-induced Dirac cones with mass gaps predicted in tight-binding models were confirmed, however, our density functional theory calculations demonstrate a phase transition to a quantum valley Hall insulator, contrasting to the tight-binding model prediction of an ordinary insulator.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea

References

  1. Y. Shi, S. Che, K. Zhou, S. Ge, Z. Pi, T. Espiritu, T. Taniguchi, K. Watanabe, Y. Barlas, R. Lake, C.N. Lau, Tunable Lifshitz transitions and multiband transport in tetralayer graphene, Phys. Rev. Lett. 120 (2018) 096802. https://doi.org/10.1103/PhysRevLett.120.096802
  2. A.L. Grushina, D.-K. Ki, M. Koshino, A.A.L. Nicolet, C. Faugeras, E. McCann, M. Potemski, A.F. Morpurgo, Insulating state in tetralayers reveals an even odd interaction effect in multilayer graphene, Nat. Commun. 69 (2015) 641.
  3. R.T. Weitz, M.T. Allen, B.E. Feldman, J. Martin, A. Yacoby, Broken-symmetry states in doubly gated suspended bilayer graphene, Science 330 (2010) 812. https://doi.org/10.1126/science.1194988
  4. A.S. Mayorov, D.C. Elias, M. Mucha-Kruczynski, R.V. Gorbachev, T. Tudorovskiy, A. Zhukov, S.V. Morozov, M.I. Katsnelson, V.I. Fal'ko, A.K. Geim, K.S. Novoselov, Interaction-driven spectrum reconstruction in bilayer graphene, Science 333 (2011) 860. https://doi.org/10.1126/science.1208683
  5. F. Zhang, J. Jung, G.A. Fiete, Q. Niu, A.H. MacDonald, Spontaneous quantum Hall states in chirally stacked few-layer graphene systems, Phys. Rev. Lett. 106 (2011) 156801. https://doi.org/10.1103/PhysRevLett.106.156801
  6. P. San-Jose, R.V. Gorbachev, A.K. Geim, K.S. Novoselov, F. Guinea, Stacking boundaries and transport in bilayer graphene, Nano Lett. 14 (2014) 2052. https://doi.org/10.1021/nl500230a
  7. M. Koshino, E. McCann, Landau level spectra and the quantum Hall effect of multilayer graphene, Phys. Rev. B 83 (2011) 165443. https://doi.org/10.1103/PhysRevB.83.165443
  8. T. Morimoto, M. Koshino, Gate-induced Dirac cones in multilayer graphenes, Phys. Rev. B 87 (2013) 085424. https://doi.org/10.1103/PhysRevB.87.085424
  9. M. Koshino, T. Ando, Electronic structures and optical absorption of multilayer graphenes, Solid State Commun. 149 (2009) 1123. https://doi.org/10.1016/j.ssc.2009.02.052
  10. E. McCann, M. Koshino, The electronic properties of bilayer graphene, Rep. Prog. Phys. 76 (2013) 056503. https://doi.org/10.1088/0034-4885/76/5/056503
  11. F. Zhang, A.H. MacDonald, E.J. Mele, Valley Chern numbers and boundary modes in gapped bilayer graphene, Proc. Natl. Acad. Sci. U.S.A. 110 (2013) 10546. https://doi.org/10.1073/pnas.1308853110
  12. M. Serbyn, D.A. Abanin, New Dirac points and multiple Landau level crossings in biased trilayer graphene, Phys. Rev. B 87 (2013) 115422. https://doi.org/10.1103/PhysRevB.87.115422
  13. K.W. Lee, C.E. Lee, Quantum valley Hall state in gas molecule-adsorbed bilayer graphene, Curr. Appl. Phys. 16 (2016) 160. https://doi.org/10.1016/j.cap.2015.11.011
  14. K.W. Lee, C.E. Lee, Density functional theory calculations of the electric-field-induced Dirac cones and quantum valley Hall state in ABA-stacked trilayer graphene, Phys. Rev. B 92 (2015) 245416. https://doi.org/10.1103/PhysRevB.92.245416
  15. M. Aoki, H. Amawashi, Dependence of band structures on stacking and field in layered graphene, Solid State Commun. 142 (2007) 123. https://doi.org/10.1016/j.ssc.2007.02.013
  16. K. Tang, R. Qin, J. Zhou, H. Qu, J. Zheng, R. Fei, H. Li, Q. Zheng, Z. Gao, J. Lu, Electric-field-induced energy gap in few-layer graphene, J. Phys. Chem. 115 (2011) 9458.
  17. D. Sanchez-Portal, P. Ordejon, E. Artacho, J.M. Soler, Density-functional method for very large systems with LCAO basis sets, Int. J. Quant. Chem. 65 (1997) 453. https://doi.org/10.1002/(SICI)1097-461X(1997)65:5<453::AID-QUA9>3.0.CO;2-V
  18. We used the pseudopotentials from https://www.icmab.es/siesta.
  19. J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23 (1981) 5048. https://doi.org/10.1103/PhysRevB.23.5048
  20. J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865. https://doi.org/10.1103/PhysRevLett.77.3865
  21. M. Dion, H. Rydberg, E. Schroder, D.C. Langreth, B.I. Lundqvist, Van der Waals density functional for general geometries, Phys. Rev. Lett. 92 (2004) 246401. https://doi.org/10.1103/PhysRevLett.92.246401
  22. G. Roman-Perez, J.M. Soler, Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotubes, Phys. Rev. Lett. 103 (2009) 096102. https://doi.org/10.1103/PhysRevLett.103.096102
  23. L. Kong, G. Roman-Perez, J.M. Soler, D.C. Langreth, Energetics and dynamics of H2 adsorbed in a nanoporous material at low temperature, Phys. Rev. Lett. 103 (2009) 096103. https://doi.org/10.1103/PhysRevLett.103.096103
  24. A.A. Mostofi, J.R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, N. Marzari, wannier90: a tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 178 (2008) 685. https://doi.org/10.1016/j.cpc.2007.11.016