Strain induced topological transitions in twisted double bilayer graphene

Abstract

We theoretically study the band structures and the valley Chern numbers of the AB–AB and AB–BA stacked twisted double bilayer graphene under heterostrain effect. In the absence of heterostrain, due to the constrains by the spatial symmetries, the central two flat bands of the AB–AB are topological trivial bands, while in the AB–BA they have a finite Chern number. The heterostrain breaks all the point group symmetries and the constrains are lifted, hence the topological properties of the two arrangements can be tuned by different strain magnitudes ϵ and directions ϕ. The heterostrain has dissimilar impacts on the Chern numbers of the AB–AB and AB–BA, owing to their different band gaps, and these gaps can be modified by a vertical electric field. Our results show that the topological transitions for both arrangements occur in the ϵ range of 0.1%–0.4%, which can be realized in the graphene-based sample.

Graphical abstract

Keywords

valley Chern number / twisted double bilayer graphene / flat bands / heterostrain

References

[1] Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature 556(7699), 43 (2018)

[2] 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, and P. Jarillo-Herrero, Correlated insulator behaviour at half-flling in magic-angle graphene superlattices, Nature 556(7699), 80 (2018)

[3] X. M. Liu, Z. Hao, E. Khalaf, J. Y. Lee, Y. Ronen, H. Yoo, D. Haei Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, Tunable spin-polarized correlated states in twisted double bilayer graphene, Nature 583(7815), 221 (2020)

[4] C. Shen, Y. Chu, Q. Wu, N. Li, S. Wang, Y. Zhao, J. Tang, J. Liu, J. Tian, K. Watanabe, T. Taniguchi, R. Yang, Z. Y. Meng, D. Shi, O. V. Yazyev, and G. Zhang, Correlated states in twisted double bilayer graphene, Nat. Phys. 16(5), 520 (2020)

[5] 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, and F. Wang, Signatures of gate-tunable superconductivity in trilayer graphene moiré superlattice, Nature 572(7768), 215 (2019)

[6] H. C. Po, L. J. Zou, A. Vishwanath, and T. Senthil, Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene, Phys. Rev. X 8(3), 031089 (2018)

[7] Y. H. Zhang, D. Mao, and T. Senthil, Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous Hall effect and a lattice model, Phys. Rev. Res. 1(3), 033126 (2019)

[8] Y. H. Zhang, D. Mao, Y. Cao, P. Jarillo-Herrero, and T. Senthil, Nearly flat Chern bands in moiré superlattices, Phys. Rev. B 99(7), 075127 (2019)

[9] X. Lu, P. Stepanov, W. Yang, M. Xie, M. A. Aamir, I. Das, C. Urgell, K. Watanabe, T. Taniguchi, G. Zhang, A. Bachtold, A. H. MacDonald, and D. K. Efetov, Superconductors, orbital magnets and correlated states in magicangle bilayer graphene, Nature 574(7780), 653 (2019)

[10] C. L. Tschirhart, M. Serlin, H. Polshyn, A. Shragai, Z. Xia, J. Zhu, Y. Zhang, K. Watanabe, T. Taniguchi, M. E. Huber, and A. F. Young, Imaging orbital ferromagnetism in a moiré Chern insulator, Science 372(6548), 1323 (2021)

[11] H. Polshyn, J. Zhu, M. A. Kumar, Y. Zhang, F. Yang, C. L. Tschirhart, M. Serlin, K. Watanabe, T. Taniguchi, A. H. MacDonald, and A. F. Young, Electrical switching of magnetic order in an orbital Chern insulator, Nature 588(7836), 66 (2020)

[12] G. R. Chen, A. L. Sharpe, E. J. Fox, Y. H. Zhang, S. Wang, L. Jiang, B. Lyu, H. Li, K. Watanabe, T. Taniguchi, Z. Shi, T. Senthil, D. Goldhaber-Gordon, Y. Zhang, and F. Wang, Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice, Nature 579(7797), 56 (2020)

[13] A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney, K. Watanabe, T. Taniguchi, M. A. Kastner, and D. Goldhaber-Gordon, Emergent ferromagnetism near threequarters filling in twisted bilayer graphene, Science 365(6453), 605 (2019)

[14] M. Serlin, C. L. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. F. Young, Intrinsic quantized anomalous Hall effect in a moiré heterostructure, Science 367(6480), 900 (2020)

[15] F. R. Geisenhof, F. Winterer, A. M. Seiler, J. Lenz, T. Xu, F. Zhang, and R. T. Weitz, Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene, Nature 598(7879), 53 (2021)

[16] E. Tang, J. W. Mei, and X. G. Wen, High-temperature fractional quantum Hall states, Phys. Rev. Lett. 106(23), 236802 (2011)

[17] K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett. 106(23), 236803 (2011)

[18] T. Neupert, L. Santos, C. Chamon, and C. Mudry, Fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 106(23), 236804 (2011)

[19] Y. F. Wang, Z. C. Gu, C. D. Gong, and D. N. Sheng, Fractional quantum Hall effect of hard-core bosons in topological flat bands, Phys. Rev. Lett. 107(14), 146803 (2011)

[20] N. R. Chebrolu, B. L. Chittari, and J. Jung, Flat bands in twisted double bilayer graphene, Phys. Rev. B 99(23), 235417 (2019)

[21] G. W. Burg, J. Zhu, T. Taniguchi, K. Watanabe, A. H. MacDonald, and E. Tutuc, Correlated insulating states in twisted double bilayer graphene, Phys. Rev. Lett. 123(19), 197702 (2019)

[22] M. H. He, Y. H. Li, J. Q. Cai, Y. Liu, K. Watanabe, T. Taniguchi, X. Xu, and M. Yankowitz, Symmetry breaking in twisted double bilayer graphene, Nat. Phys. 17(1), 26 (2021)

[23] Y. W. Choi and H. J. Choi, Intrinsic band gap and electrically tunable flat bands in twisted double bilayer graphene, Phys. Rev. B 100, 201402(R) (2019)

[24] X. M. Liu, C. L. Chiu, J. Y. Lee, G. Farahi, K. Watanabe, T. Taniguchi, A. Vishwanath, and A. Yazdani, Spectroscopy of a tunable moiré system with a correlated and topological flat band, Nat. Commun. 12(1), 2732 (2021)

[25] M. Koshino, Band structure and topological properties of twisted double bilayer graphene, Phys. Rev. B 99(23), 235406 (2019)

[26] G. Y. Luo, L. Wen, X. Y. Lv, and Z. Li, Tunable optical property and flat bands in twisted double bilayer graphene, Phys. Lett. A 416, 127670 (2021)

[27] Z. Bi, N. Yuan, and L. Fu, Designing flat band by strain, Phys. Rev. B 100(3), 035448 (2019)

[28] L. Huder, A. Artaud, T. Le Quang, G. T. de Laissardière, A. G. M. Jansen, G. Lapertot, C. Chapelier, and V. T. Renard, Electronic spectrum of twisted graphene layers under heterostrain, Phys. Rev. Lett. 120(15), 156405 (2018)

[29] A. Kerelsky, L. McGilly, D. M. Kennes, L. Xian, M. Yankowitz, S. Chen, K. Watanabe, T. Taniguchi, J. Hone, C. Dean, A. Rubio, and A. N. Pasupathy, Magic angle spectroscopy, arXiv: 1812.08776 (2018)

[30] M. Yankowitz, S. Chen, H. Polshyn, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Tuning superconductivity in twisted bilayer graphene, arXiv: 1808.07865 (2018)

[31] E. McCann and M. Koshino, The electronic properties of bilayer graphene, Rep. Prog. Phys. 76(5), 056503 (2013)

[32] P. Moon and M. Koshino, Optical absorption in twisted bilayer graphene, Phys. Rev. B 87(20), 205404 (2013)

[33] Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng and Z. X. Shen, Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening, ACS Nano 2(11), 2301 (2008)

[34] S. B. Cronin, A. K. Swan, M. S. Unlu, B. B. Goldberg, M. S. Dresselhaus, and M. Tinkham, Measuring the uniaxial strain of individual single-wall carbon nanotubes: Resonance Raman spectra of atomic-force-microscope modified single-wall nanotubes, Phys. Rev. Lett. 93(16), 167401 (2004)

[35] N. N. T. Nam and M. Koshino, Lattice relaxation and energy band modulation in twisted bilayer graphene, Phys. Rev. B 96(7), 075311 (2017)

[36] Z. Ma, S. Li, Y. W. Zheng, M. M. Xiao, H. Jiang, J. H. Gao, and X. C. Xie, Topological flat bands in twisted trilayer graphene, Sci. Bull. (Beijing) 66(1), 18 (2021)

[37] J. Liu, Z. Ma, J. Gao, and X. Dai, Quantum valley hall effect, orbital magnetism, and anomalous hall effect in twisted multilayer graphene systems, Phys. Rev. X 9(3), 031021 (2019)

[38] Z. B. Dai, Y. He, and Z. Q. Li, Effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene, Phys. Rev. B 104(4), 045403 (2021)

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

[40] S. Cho, S. D. Kang, W. Kim, E. S. Lee, S. J. Woo, K. J. Kong, I. Kim, H. D. Kim, T. Zhang, J. A. Stroscio, Y. H. Kim, and H. K. Lyeo, Thermoelectric imaging of structural disorder in epitaxial graphene, Nat. Mater. 12(10), 913 (2013)

[41] S. S. Sunku, G. X. Ni, B. Y. Jiang, H. Yoo, A. Sternbach, A. S. McLeod, T. Stauber, L. Xiong, T. Taniguchi, K. Watanabe, P. Kim, M. M. Fogler, and D. N. Basov, Photonic crystals for nano-light in moiré graphene superlattices, Science 362(6419), 1153 (2018)

RIGHTS & PERMISSIONS

2022 Higher Education Press