Abstract
Dual topological insulator (DTI), which simultaneously hosts topological insulator (TI) and topological crystalline insulator (TCI) phases, has attracted extensive attention since it has a better robustness of topological nature and broad application prospects in spintronics. However, the realization of DTI phase in two-dimensional (2D) system is extremely scarce. By first-principles calculations, we predict that the 2D rectangular bismuth (R—Bi) bilayer is a novel DTI, featured by ℤ2 topological invariant ℤ2 = 1, mirror Chern number CM = −1, and metallic edge states within the bulk band gap. More interestingly, the TCI phase in bilayer is protected by horizontal glide mirror symmetries, rather than the usual mirror symmetry. The bulk band gap can be effectively tuned by vertical electric field and strain. Besides, the electric field can trigger the transition between TI and metallic phases for the bilayer, accompanied by the annihilation of TCI phase. On this basis, a topological field effect transistor is proposed, which can rapidly manipulate spin and charge carriers via electric field. The KBr(110) surface is demonstrated as an ideal substrate for the deposition of bilayer. These findings provide not only a new strategy for exploiting 2D DTI, but also a promising candidate for spintronic applications.
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References
J. E. Moore, The birth of topological insulators, Nature 464(7286), 194 (2010)
M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)
L. Fu, Topological crystalline insulators, Phys. Rev. Lett. 106(10), 106802 (2011)
Y. Ando, Topological insulator materials, J. Phys. Soc. Jpn. 82(10), 102001 (2013)
Y. Ando and L. Fu, Topological crystalline insulators and topological superconductors: From concepts to materials, Annu. Rev. Condens. Matter Phys. 6(1), 361 (2015)
C. Niu, P. M. Buhl, G. Bihlmayer, D. Wortmann, Y. Dai, S. Blügel, and Y. Mokrousov, Robust dual topological character with spin-valley polarization in a monolayer of the Dirac semimetal Na3Bi, Phys. Rev. B 95(7), 075404 (2017)
N. Mao, X. Hu, C. Niu, B. Huang, and Y. Dai, Dual topological insulator and insulator—semimetal transition in mirror-symmetric honeycomb materials, Phys. Rev. B 100(20), 205116 (2019)
N. Avraham, A. Kumar Nayak, A. Steinbok, A. Norris, H. Fu, Y. Sun, Y. Qi, L. Pan, A. Isaeva, A. Zeugner, C. Felser, B. Yan, and H. Beidenkopf, Visualizing coexisting surface states in the weak and crystalline topological insulator Bi2TeI, Nat. Mater. 19(6), 610 (2020)
I. Cucchi, A. Marrazzo, E. Cappelli, S. Riccò, F. Y. Bruno, S. Lisi, M. Hoesch, T. K. Kim, C. Cacho, C. Besnard, E. Giannini, N. Marzari, M. Gibertini, F. Baumberger, and A. Tamai, Bulk and surface electronic structure of the dual-topology semimetal Pt2HgSe3, Phys. Rev. Lett. 124(10), 106402 (2020)
M. Eschbach, M. Lanius, C. Niu, E. Młyńczak, P. Gospodarič, J. Kellner, P. Schüffelgen, M. Gehlmann, S. Döring, E. Neumann, M. Luysberg, G. Mussler, L. Plucinski, M. Morgenstern, D. Grützmacher, G. Bihlmayer, S. Blügel, and C. M. Schneider, Bi1Te1 is a dual topological insulator, Nat. Commun. 8(1), 14976 (2017)
J. I. Facio, S. K. Das, Y. Zhang, K. Koepernik, J. van den Brink, and I. C. Fulga, Dual topology in jacutingaite Pt2HgSe3, Phys. Rev. Mater. 3(7), 074202 (2019)
H. Lee, Y. G. Kang, M. C. Jung, M. J. Han, and K. J. Chang, Robust dual topological insulator phase in NaZnBi, NPG Asia Mater. 14(1), 36 (2022)
I. Matsuda, K. Yaji, A. A. Taskin, M. D’angelo, R. Yukawa, Y. Ohtsubo, P. Le Fèvre, F. Bertran, S. Yoshizawa, A. Taleb-Ibrahimi, A. Kakizaki, Y. Ando, and F. Komori, Surface state of the dual topological insulator \({\rm{B}}{{\rm{i}}_{0.91}}{\rm{S}}{{\rm{b}}_{0.09}}(11\bar 2)\), Physica B 516, 100 (2017)
T. Rauch, M. Flieger, J. Henk, I. Mertig, and A. Ernst, Dual topological character of chalcogenides: Theory for Bi2Te3, Phys. Rev. Lett. 112(1), 016802 (2014)
J. C. Y. Teo, L. Fu, and C. L. Kane, Surface states and topological invariants in three-dimensional topological insulators: Application to Bi1−xSbx, Phys. Rev. B 78(4), 045426 (2008)
C. Fang and L. Fu, New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic, Phys. Rev. B 91(16), 161105 (2015)
H. Kim and S. Murakami, Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice, Phys. Rev. B 102(19), 195202 (2020)
J. Ma, C. Yi, B. Lv, Z. J. Wang, S. Nie, L. Wang, L. Kong, Y. Huang, P. Richard, P. Zhang, K. Yaji, K. Kuroda, S. Shin, H. Weng, B. A. Bernevig, Y. Shi, T. Qian, and H. Ding, Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb, Sci. Adv. 3(5), e1602415 (2017)
Z. Wang, A. Alexandradinata, R. J. Cava, and B. A. Bernevig, Hourglass fermions, Nature 532(7598), 189 (2016)
Y. L. Chen, M. Kanou, Z. K. Liu, H. J. Zhang, J. A. Sobota, D. Leuenberger, S. K. Mo, B. Zhou, S. L. Yang, P. S. Kirchmann, D. H. Lu, R. G. Moore, Z. Hussain, Z. X. Shen, X. L. Qi, and T. Sasagawa, Discovery of a single topological Dirac fermion in the strong inversion asymmetric compound BiTeCl, Nat. Phys. 9(11), 704 (2013)
B. Yan, M. Jansen, and C. Felser, A large-energy-gap oxide topological insulator based on the superconductor BaBiO3, Nat. Phys. 9(11), 709 (2013)
H. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys. 5(6), 438 (2009)
M. M. Otrokov, I. I. Klimovskikh, H. Bentmann, D. Estyunin, A. Zeugner, Z. S. Aliev, S. Gaß, A. U. B. Wolter, A. V. Koroleva, A. M. Shikin, M. Blanco-Rey, M. Hoffmann, I. P. Rusinov, A. Y. Vyazovskaya, S. V. Eremeev, Y. M. Koroteev, V. M. Kuznetsov, F. Freyse, J. Sánchez-Barriga, I. R. Amiraslanov, M. B. Babanly, N. T. Mamedov, N. A. Abdullayev, V. N. Zverev, A. Alfonsov, V. Kataev, B. Büchner, E. F. Schwier, S. Kumar, A. Kimura, L. Petaccia, G. Di Santo, R. C. Vidal, S. Schatz, K. Kißner, M. Ünzelmann, C. H. Min, S. Moser, T. R. F. Peixoto, F. Reinert, A. Ernst, P. M. Echenique, A. Isaeva, and E. V. Chulkov, Prediction and observation of an antiferromagnetic topological insulator, Nature 576(7787), 416 (2019)
C. Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L. L. Wang, Z. Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S. C. Zhang, K. He, 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)
F. Reis, G. Li, L. Dudy, M. Bauernfeind, S. Glass, W. Hanke, R. Thomale, J. Schäfer, and R. Claessen, Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material, Science 357(6348), 287 (2017)
Y. Lu, W. Xu, M. Zeng, G. Yao, L. Shen, M. Yang, Z. Luo, F. Pan, K. Wu, T. Das, P. He, J. Jiang, J. Martin, Y. P. Feng, H. Lin, and X. Wang, Topological properties determined by atomic buckling in self-assembled ultrathin Bi(110), Nano Lett. 15(1), 80 (2015)
Y. Bai, L. Cai, N. Mao, R. Li, Y. Dai, B. Huang, and C. Niu, Doubled quantum spin Hall effect with high-spin Chern number in α-antimonene and α-bismuthene, Phys. Rev. B 105(19), 195142 (2022)
L. Kou, X. Tan, Y. Ma, H. Tahini, L. Zhou, Z. Sun, D. Aijun, C. Chen, and S. C. Smith, Tetragonal bismuth bilayer: A stable and robust quantum spin Hall insulator, 2D Mater. 2, 045010 (2015)
R. W. Zhang, C. W. Zhang, W. X. Ji, S. S. Yan, and Y. G. Yao, First-principles prediction on bismuthylene monolayer as a promising quantum spin Hall insulator, Nanoscale 9(24), 8207 (2017)
X. Kong, L. Li, O. Leenaerts, X. J. Liu, and F. M. Peeters, New group-V elemental bilayers: A tunable structure model with four-, six-, and eight-atom rings, Phys. Rev. B 96(3), 035123 (2017)
G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54(16), 11169 (1996)
G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal—amorphous-semiconductor transition in germanium, Phys. Rev. B 49(20), 14251 (1994)
G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59(3), 1758 (1999)
S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem. 27(15), 1787 (2006)
J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45(23), 13244 (1992)
S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H—Pu, J. Chem. Phys. 132(15), 154104 (2010)
S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32(7), 1456 (2011)
A. A. Soluyanov and D. Vanderbilt, Wannier representation of Z2 topological insulators, Phys. Rev. B 83(3), 035108 (2011)
A. A. Soluyanov and D. Vanderbilt, Computing topological invariants without inversion symmetry, Phys. Rev. B 83(23), 235401 (2011)
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)
M. P. L. Sancho, J. M. L. Sancho, J. M. L. Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, J. Phys. F Met. Phys. 15(4), 851 (1985)
J. Liu, T. H. Hsieh, P. Wei, W. Duan, J. Moodera, and L. Fu, Spin-filtered edge states with an electrically tunable gap in a two-dimensional topological crystalline insulator, Nat. Mater. 13(2), 178 (2014)
J. Liu, X. Qian, and L. Fu, Crystal field effect induced topological crystalline insulators in monolayer IV—VI semiconductors, Nano Lett. 15(4), 2657 (2015)
C. Niu, P. M. Buhl, G. Bihlmayer, D. Wortmann, S. Blügel, and Y. Mokrousov, Topological crystalline insulator and quantum anomalous Hall states in IV–VI-based monolayers and their quantum wells, Phys. Rev. B 91(20), 201401 (2015)
L. Yan, C. M. Lopez, R. P. Shrestha, E. A. Irene, A. A. Suvorova, and M. Saunders, Magnesium oxide as a candidate high-κ gate dielectric, Appl. Phys. Lett. 88(14), 142901 (2006)
A. Posadas, F. J. Walker, C. H. Ahn, T. L. Goodrich, Z. Cai, and K. S. Ziemer, Epitaxial MgO as an alternative gate dielectric for SiC transistor applications, Appl. Phys. Lett. 92(23), 233511 (2008)
T. Hirahara, G. Bihlmayer, Y. Sakamoto, M. Yamada, H. Miyazaki, S. I. Kimura, S. Blügel, and S. Hasegawa, Interfacing 2D and 3D topological insulators: Bi(111) bilayer on Bi2Te2, Phys. Rev. Lett. 107(16), 166801 (2011)
F. Yang, L. Miao, Z. F. Wang, M. Y. Yao, F. Zhu, Y. R. Song, M. X. Wang, J. P. Xu, A. V. Fedorov, Z. Sun, G. B. Zhang, C. Liu, F. Liu, D. Qian, C. L. Gao, and J. F. Jia, Spatial and energy distribution of topological edge states in single Bi(111) bilayer, Phys. Rev. Lett. 109(1), 016801 (2012)
F. Zhu, W. Chen, Y. Xu, C. Gao, D. Guan, C. Liu, D. Qian, S. C. Zhang, and J. Jia, Epitaxial growth of two-dimensional stanene, Nat. Mater. 14(10), 1020 (2015)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 12004137), the Taishan Scholar Project of Shandong Province (No. ts20190939), and the Natural Science Foundation of Shandong Province (Grant No. ZR2020QA052).
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Li, S., Ji, W., Zhang, J. et al. Two-dimensional rectangular bismuth bilayer: A novel dual topological insulator. Front. Phys. 18, 43301 (2023). https://doi.org/10.1007/s11467-023-1262-x
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DOI: https://doi.org/10.1007/s11467-023-1262-x