Nano Research

, Volume 3, Issue 8, pp 545–556 | Cite as

Strain effects in graphene and graphene nanoribbons: The underlying mechanism

Open Access
Research Article


A tight-binding analytic framework is combined with first-principles calculations to reveal the mechanism underlying the strain effects on electronic structures of graphene and graphene nanoribbons (GNRs). It provides a unified and precise formulation of the strain effects under various circumstances-including the shift of the Fermi (Dirac) points, the change in band gap of armchair GNRs with uniaxial strain in a zigzag pattern and its insensitivity to shear strain, and the variation of the k-range of edge states in zigzag GNRs under uniaxial and shear strains which determine the gap behavior via the spin polarization interaction.


Graphene graphene nanoribbons (GNRs) band gap strain first-principles calculations tight-binding model 


  1. [1]
    Geim, A. K.; Novoselov, K. S. The rise of graphene. Nat. Mater. 2007, 6, 183–191.CrossRefPubMedADSGoogle Scholar
  2. [2]
    Cresti, A.; Nemec, N.; Biel, B.; Niebler, G.; Triozon, F.; Cuniberti, G.; Roche, S. Charge transport in disordered graphene-based low dimensional materials. Nano Res. 2008, 1, 361–394.CrossRefGoogle Scholar
  3. [3]
    Yan, Q. M.; Huang, B.; Yu, J.; Zheng, F. W.; Zang, J.; Wu, J.; Gu, B. L.; Liu, F.; Duan, W. H. Intrinsic current-voltage characteristics of graphene nanoribbon transistors and effect of edge doping. Nano Lett. 2007, 7, 1469–1473.CrossRefPubMedADSGoogle Scholar
  4. [4]
    Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666–669.CrossRefPubMedADSGoogle Scholar
  5. [5]
    Biel, B.; Blase, X.; Triozon, F.; Roche, S. Anomalous doping effects on charge transport in graphene nanoribbons. Phys. Rev. Lett. 2009, 102, 096803.CrossRefPubMedADSGoogle Scholar
  6. [6]
    Pereira, V. M.; Neto, A. H. C. Strain engineering of graphene’s electronic structure. Phys. Rev. Lett. 2009, 103, 046801.CrossRefPubMedADSGoogle Scholar
  7. [7]
    Ferralis, N.; Maboudian, R.; Carraro, C. Evidence of structural strain in epitaxial graphene layers on 6H-SiC(0001). Phys. Rev. Lett. 2008, 101, 156801.CrossRefPubMedADSGoogle Scholar
  8. [8]
    Borysiuk, J.; Bozek, R.; Strupinski, W.; Wysmolek, A.; Grodecki, K.; Steapniewski, R.; Baranowski, J. M. Transmission electron microscopy and scanning tunneling microscopy investigations of graphene on 4H-SiC(0001). J. Appl. Phys. 2009, 105, 023503.CrossRefADSGoogle Scholar
  9. [9]
    Sun, G. F.; Jia, J. F.; Xue, Q. K.; Li, L. Atomic-scale imaging and manipulation of ridges on epitaxial graphene on 6H-SiC(0001). Nanotechnology 2009, 20, 355701.CrossRefPubMedADSGoogle Scholar
  10. [10]
    Jun, S. Density-functional study of edge stress in graphene. Phys. Rev. B 2008, 78, 073405.CrossRefADSGoogle Scholar
  11. [11]
    Huang, B.; Liu, M.; Su, N. H.; Wu, J.; Duan, W. H.; Gu, B. L.; Liu, F. Quantum manifestations of graphene edge stress and edge instability: A first-principles study. Phys. Rev. Lett. 2009, 102, 166404.CrossRefPubMedADSGoogle Scholar
  12. [12]
    Lee, C.; Wei, X. D.; Kysar, J. W.; Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 2008, 321, 385–388.CrossRefPubMedADSGoogle Scholar
  13. [13]
    Mohiuddin, T. M. G.; Lombardo, A.; Nair, R. R.; Bonetti, A.; Savini, G.; Jalil, R.; Bonini, N.; Basko, D. M.; Galiotis, C.; Marzari, N.; Novoselov, K. S.; Geim, A. K.; Ferrai, A. C. Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation. Phys. Rev. B 2009, 79, 205433.CrossRefADSGoogle Scholar
  14. [14]
    Ni, Z. H.; Yu, T.; Lu, Y. H.; Wang, Y. Y.; Feng, Y. P.; Shen, Z. X. Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2008, 2, 2301–2305.CrossRefPubMedGoogle Scholar
  15. [15]
    Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, J. M.; Kim, K. S.; Ahn, J. -H.; Kim, P.; Choi, J. -Y.; Hong, B. H. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 2009, 457, 706–710.CrossRefPubMedADSGoogle Scholar
  16. [16]
    Bao, W. Z.; Miao, F.; Chen, Z.; Zhang, H.; Jang, W. Y.; Dames, C.; Lau, C. N. Controlled ripple texturing of suspended graphene and ultrathin graphite membranes. Nat. Nanotechnol. 2009, 4, 562–566.CrossRefPubMedADSGoogle Scholar
  17. [17]
    Lee, M. L.; Fitzgerald, E. A.; Bulsara, M. T.; Currie, M. T.; Lochtefeld, A. Strained Si, SiGe, and Ge channels for highmobility metal-oxide-semiconductor field-effect transistors. J. Appl. Phys. 2005, 97, 011101.CrossRefADSGoogle Scholar
  18. [18]
    Yang, L.; Han, J. Electronic structure of deformed carbon nanotubes. Phys. Rev. Lett. 2000, 85, 154–157.CrossRefPubMedADSGoogle Scholar
  19. [19]
    Minot, E. D.; Yaish, Y.; Sazonova, V.; Park, J. Y.; Brink, M.; McEuen, P. L. Tuning carbon nanotube band gaps with strain. Phys. Rev. Lett. 2003, 90, 156401.CrossRefPubMedADSGoogle Scholar
  20. [20]
    Teague, M. L.; Lai, A. P.; Velasco, J.; Hughes, C. R.; Beyer, A. D.; Bockrath, M. W.; Lau, C. N.; Yeh, N. C. Evidence for strain-induced local conductance modulations in single-layer graphene on SiO2. Nano Lett. 2009, 9, 2542–2546.CrossRefPubMedADSGoogle Scholar
  21. [21]
    Chang, C. P.; Wu, B. R.; Chen, R. B.; Lin, M. F. Deformation effect on electronic and optical properties of nanographite ribbons. J. Appl. Phys. 2007, 101, 063506.CrossRefADSGoogle Scholar
  22. [22]
    Gui, G.; Li, J.; Zhong, J. X. Band structure engineering of graphene by strain: First-principles calculations. Phys. Rev. B 2008, 78, 075435.CrossRefADSGoogle Scholar
  23. [23]
    Farjam, M.; Rafii-Tabar, H. Comment on “Band structure engineering of graphene by strain: First-principles calculations”. Phys. Rev. B 2009, 80, 167401.CrossRefADSGoogle Scholar
  24. [24]
    Gui, G.; Li, J.; Zhong, J. X. Reply to “Comment on ‘Band structure engineering of graphene by strain: First-principles calculations.’”. Phys. Rev. B 2009, 80, 167402.CrossRefADSGoogle Scholar
  25. [25]
    Sun, L.; Li, Q. X.; Ren, H.; Su, H. B.; Shi, Q. W.; Yang, J. L. Strain effect on electronic structures of graphene nanoribbons: A first-principles study. J. Chem. Phys. 2008, 129, 074704.CrossRefPubMedADSGoogle Scholar
  26. [26]
    Pereira, V. M.; Neto, A. H. C.; Peres, N. M. R. Tight-binding approach to uniaxial strain in graphene. Phys. Rev. B 2009, 80, 045401.CrossRefADSGoogle Scholar
  27. [27]
    Mohr, M.; Papagelis, K.; Maultzsch, J.; Thomsen, C. Two-dimensional electronic and vibrational band structure of uniaxially strained graphene from ab initio calculations. Phys. Rev. B 2009, 80, 205410.CrossRefADSGoogle Scholar
  28. [28]
    Hod, O.; Scuseria, G. E. Electromechanical properties of suspended graphene nanoribbons. Nano Lett. 2009, 9, 2619–2622.CrossRefPubMedADSGoogle Scholar
  29. [29]
    Alam, K. Uniaxial strain effects on the performance of a ballistic top gate graphene nanoribbon on insulator transistor. IEEE Trans. Nanotechnol. 2009, 8, 528–534.CrossRefGoogle Scholar
  30. [30]
    Pellegrino, F. M. D.; Angilella, G. G. N.; Pucci, R. Strain effect on the optical conductivity of graphene. Phys. Rev. B 2010, 81, 035411.CrossRefADSGoogle Scholar
  31. [31]
    Choi, S. M.; Jhi, S. H.; Son, Y. W. Effects of strain on electronic properties of graphene. Phys. Rev. B 2010, 81, 081407.CrossRefADSGoogle Scholar
  32. [32]
    Rasuli, R.; Rafii-Tabar, H.; Zad, A. I. Strain effect on quantum conductance of graphene nanoribbons from maximally localized Wannier functions. Phys. Rev. B 2010, 81, 125409.CrossRefADSGoogle Scholar
  33. [33]
    Poetschke, M.; Rocha, C. G.; Torres, L. E. F. F.; Roche, S.; Cuniberti, G. Modeling graphene-based nanoelectromechanical devices. Phys. Rev. B 2010, 81, 193404.CrossRefADSGoogle Scholar
  34. [34]
    Hossain, M. Z. Quantum conductance modulation in graphene by strain engineering. Appl. Phys. Lett. 2010, 96, 143118.CrossRefADSGoogle Scholar
  35. [35]
    Lu, Y.; Guo, J. Band gap of strained graphene nanoribbons. Nano Res. 2010, 3, 189–199.CrossRefGoogle Scholar
  36. [36]
    de Andres, P. L.; Verges, J. A. First-principles calculation of the effect of stress on the chemical activity of graphene. Appl. Phys. Lett. 2008, 93, 171915.CrossRefADSGoogle Scholar
  37. [37]
    Kresse, G.; Furthmüller, J. Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 1996, 6, 15–50.CrossRefGoogle Scholar
  38. [38]
    Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758–1775.CrossRefADSGoogle Scholar
  39. [39]
    Perdew, J. P.; Wang, Y. Accurate and simple analytic representation of the electron-gas correlation-energy. Phys. Rev. B 1992, 45, 13244–13249.CrossRefADSGoogle Scholar
  40. [40]
    Harrison, W. A. Electronic structure and the properties of solids: The physics of the chemical bond; Dover Publications: New York, 1989.Google Scholar
  41. [41]
    Ribeiro, R. M.; Pereira, V. M.; Peres, N. M. R.; Briddon, P. R.; Neto, A. H. C. Strained graphene: Tight-binding and density functional calculations. New J. Phys. 2009, 11, 115002.CrossRefADSGoogle Scholar
  42. [42]
    Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 2009, 81, 109–162.CrossRefADSGoogle Scholar
  43. [43]
    Hasegawa, Y.; Konno, R.; Nakano, H.; Kohmoto, M. Zero modes of tight-binding electrons on the honeycomb lattice. Phys. Rev. B 2006, 74, 033413.CrossRefADSGoogle Scholar
  44. [44]
    Son, Y. W.; Cohen, M. L.; Louie, S. G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 2006, 97, 216803.CrossRefPubMedADSGoogle Scholar
  45. [45]
    Saito, R.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Electronic-structure of chiral graphene tubules. Appl. Phys. Lett. 1992, 60, 2204–2206.CrossRefADSGoogle Scholar
  46. [46]
    Mintmire, J. W.; Dunlap, B. I.; White, C. T. Are fullerene tubules metallic? Phys. Rev. Lett. 1992, 68, 631–634.CrossRefADSGoogle Scholar
  47. [47]
    Zheng, F. W.; Liu, Z. R.; Wu, J.; Duan, W. H.; Gu, B. L. Scaling law of the giant Stark effect in boron nitride nanoribbons and nanotubes. Phys. Rev. B 2008, 78, 085423.CrossRefADSGoogle Scholar
  48. [48]
    Wakabayashi, K.; Fujita, M.; Ajiki, H.; Sigrist, M. Electronic and magnetic properties of nanographite ribbons. Phys. Rev. B 1999, 59, 8271–8282.CrossRefADSGoogle Scholar
  49. [49]
    Son, Y. W.; Cohen, M. L.; Louie, S. G. Half-metallic graphene nanoribbons. Nature 2006, 444, 347–349.CrossRefPubMedADSGoogle Scholar
  50. [50]
    Zheng, F. W.; Zhou, G.; Liu, Z. R.; Wu, J.; Duan, W. H.; Gu, B. L.; Zhang, S. B. Half metallicity along the edge of zigzag boron nitride nanoribbons. Phys. Rev. B 2008, 78, 205415.CrossRefADSGoogle Scholar
  51. [51]
    Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. Peculiar localized state at zigzag graphite edge. J. Phys. Soc. Jpn. 1996, 65, 1920–1923.CrossRefADSGoogle Scholar
  52. [52]
    Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys. Rev. B 1996, 54, 17954–17961.CrossRefADSGoogle Scholar
  53. [53]
    Gunlycke, D.; Areshkin, D. A.; Li, J. W.; Mintmire, J. W.; White, C. T. Graphene nanostrip digital memory device. Nano Lett. 2007, 7, 3608–3611.CrossRefPubMedADSGoogle Scholar

Copyright information

© Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yang Li
    • 1
    • 2
  • Xiaowei Jiang
    • 1
    • 2
  • Zhongfan Liu
    • 1
  • Zhirong Liu
    • 1
  1. 1.College of Chemistry and Molecular Engineering, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, and Beijing National Laboratory for Molecular SciencesPeking UniversityBeijingChina
  2. 2.School of PhysicsPeking UniversityBeijingChina

Personalised recommendations