Quantum Phase Transition in Germanene and Stanene Bilayer: From

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Quantum Phase Transition in Germanene and Stanene Bilayer: From Normal Metal to Topological Insulator Chengxi Huang, Jian Zhou, Haiping Wu, Kaiming Deng, Puru Jena, and Erjun Kan J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b00651 • Publication Date (Web): 05 May 2016 Downloaded from http://pubs.acs.org on May 6, 2016

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The Journal of Physical Chemistry Letters

Quantum Phase Transition in Germanene and Stanene Bilayer: From Normal Metal to Topological Insulator Chengxi Huang†, ‡, Jian Zhou‡, Haiping Wu†, Kaiming Deng†,*, Puru Jena‡,*, Erjun Kan†,* †

Department of Applied Physics and Key Laboratory of Soft Chemistry and Functional

Materials (Ministry of Education), Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, P. R. China. ‡

Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284,

United States Corresponding Author * P. J. ([email protected]), K. D ([email protected]) and E. K. ([email protected])

ACS Paragon Plus Environment

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ABSTRACT

Two-dimensional (2D) topological insulators (TIs) which exhibit quantum spin Hall (QSH) effects, are a new class of materials with conducting edge and insulating bulk. The conducting edge bands are spin-polarized, free of back scattering, and protected by time-reversal symmetry (TRS) with potential for high efficiency applications in spintronics. Based on first-principles calculations, we show that under external pressure recently synthesized stanene and germanene buckled bilayers can automatically convert into a new dynamically stable phase with flat honeycomb meshes. In contrast to the active surfaces of buckled bilayer of stanene or germanene, the above new phase is chemically inert. Furthermore, we demonstrate that these flat bilayers are 2D TIs with sizable topologically nontrivial band gaps of ~ 0.1 eV, which makes it viable for room temperature applications. Our results suggest some new design principles for searching stable large-gap 2D TIs.

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Unlike normal insulators (NIs), topological insulators (TIs) belong to a new class of quantum materials because of its gapless boundary states, although these materials are insulating in the bulk.1-3 In two-dimensional (2D) TIs spin polarized electrons move along opposite directions on their edges which are protected by the time-reversal symmetry (TRS). As long as the TRS is not broken, any backscattering caused by nonmagnetic impurities or defects is forbidden. This implies that the edge transportation is dissipationless,4 which meets the demands of spintronics and quantum computing applications.5-6 In three-dimensional (3D) TIs, on the other hand, the surface states along non-180° directions are not protected against scattering, thus making them less desirable for dissipationless spin transport along a specific direction. Since the original theoretical investigation of quantum spin Hall (QSH) effect in graphene7,8 and the experimental observation of quantum wells9-11 (e.g. HgTe), there has been a constant search for new 2D TIs. Due to the weak spin-orbit coupling (SOC) in graphene, the band gap opened by the SOC is too small (~10-3 meV),7 which makes it very difficult to be detected in experiment. And for HgTe, the QSH effect can only be observed at very low temperature (8%). These flat bilayers can be easily achieved from the vdW stacked buckled bilayers by strain engineering, followed by metal-to-TI and metal-to-NI-to-TI transitions. The topological characteristic is confirmed by the calculation of Z2 topological invariant and the spin Hall conductance around the Fermi energy. Our studies demonstrate a promising way to achieve room-temperature 2D TIs and tunable QSH states by structural phase transitions. Notes The authors declare no competing financial interests. Acknowledgements This work was supported by the NSFC (21203096, 11374160, 51522206), by NSF of Jiangsu Province (BK20130031), by PAPD, by New Century Excellent Talents in University (NCET-120628), by the Innovation Program of Jiangsu Province (KYLX15_0406)，and the Fundamental Research Funds for the Central Universities (No.30915011203). We also acknowledge the support from the Shanghai Supercomputer Centre. PJ acknowledges support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award # DE-FG02-96ER45579. Chengxi Huang acknowledges the China Scholarship Council (CSC) for sponsoring his visit to Virginia Commonwealth University (VCU) where this work was conducted.


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Supporting Information Available: Atomic coordinates for flat bilayers, stability under strain and finite temperature, band structure calculated by HSE06 functional, band structure of nanoribbon and projected band structure with an substrate for FB-Sn.

References (1) Moore, J. E. The birth of topological insulators. Nature 2010, 464, 194-198. (2) Hasan, M. Z.; Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 2010, 82, 3045-3067. (3) Qi, X.-L.; Zhang, S.-C. The quantum spin Hall effect and topological insulators. Phys. Today 2010, 63, 33-38. (4) Bernevig, B. A.; Zhang, S.-C. Quantum Spin Hall Effect. Phys. Rev. Lett. 2006, 96, 106802. (5) Qi X.-L.; Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 2011, 83, 1057-1110. (6) Nayak, C.; Simon, S. H.; Stern, A.; Freedman, M.; Sarma, S. D. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 2008, 80, 1083−1159. (7) Kane, C. L.; Mele E. J. Quantum Spin Hall Effect in Graphene. Phys. Rev. Lett. 2005, 95, 226801. (8) Kane, C. L.; Mele E. J. Z2 Topological Order and the Quantum Spin Hall Effect. Phys. Rev. Lett. 2005, 95, 146802. (9) Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 2006, 314, 1757-1761. (10) König, M.; Wiedmann, S.; Brüne, C.; Roth, A.; Buhmann, H.; Molenkamp, L. W.; Qi, X.-L.; Zhang, S.-C. Quantum Spin Hall Insulator State in HgTe Quantum Wells. Science


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 19

2007, 318, 766-770. (11) Knez, I.; Du, R.-R. Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells. Phys. Rev. Lett. 2011,107, 136603. (12) Liu, C.-C.; Feng, W. X.; Yao, Y. G. Quantum Spin Hall Effect in Silicene and TwoDimensional Germanium. Phys. Rev. Lett. 2011, 107, 076802. (13) Xu, Y.; Yan, B. H.; Zhang, H.-J.; Wang, J.; Xu, G.; Tang, P.; Duan, W. H.; Zhang, S.-C. Large-Gap Quantum Spin Hall Insulators in Tin Films. Phys. Rev. Lett. 2013, 111, 136804. (14) Si, C.; Liu, J. W.; Xu, Y.; Wu, J.; Gu, B.-L.; Duan, W. H. Functionalized germanene as a prototype of large-gap two-dimensional topological insulators. Phys. Rev. B 2014, 89, 115429. (15) Liu, Z.; Liu, C.-X.; Wu, Y.-S.; Duan, W.-H.; Liu, F.; Wu, J. Stable Nontrivial Z2 Topology in Ultrathin Bi (111) Films: A First-Principles Study. Phys. Rev. Lett. 2011, 107, 136805. (16) Song, Z. G.; Liu, C.-C.; Yang, J. B.; Han, J. Z.; Ye, M.; Fu, B. T.; Yang, Y. C.; Niu, Q.; Lu, J.; Yao, Y. G. Quantum spin Hall insulators and quantum valley Hall insulators of BiX/SbX (X=H, F, Cl and Br) monolayers with a record bulk band gap. NPG Asia Mater. 2014, 6, e147. (17) Ma, Y. D.; Dai, Y; Kou, L. Z.; Frauenheim, T.; Heine, T. Robust Two-Dimensional Topological Insulators in Methyl-Functionalized Bismuth, Antimony, and Lead Bilayer Films. Nano Lett. 2015, 15, 1083–1089 (18) Chuang, F.-C.; Yao, L.-Z.; Huang, Z.-Q.; Liu, Y.-T.; Hsu, C.-H.; Das, T.; Lin, H.; Bansil, A. Nano Lett. 2014, 14, 2505−2508.


16

Page 17 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(19) Li, L. Y.; Zhang, X. M.; Chen, X.; Zhao, M. W. Giant Topological Nontrivial Band Gaps in Chloridized Gallium Bismuthide. Nano Lett. 2015, 15, 1296−1301 (20) Zhou, J. J.; Feng, W. X.; Liu, C. C.; Guan, S.; Yao, Y. G. Large-Gap Quantum Spin Hall Insulator in Single Layer Bismuth Monobromide Bi4Br4. Nano Lett. 2014, 14, 4767−4771. (21) Luo. W.; Xiang, H. J. Room Temperature Quantum Spin Hall Insulators with a Buckled Square Lattice. Nano Lett. 2015, 15, 3230–3235 (22) Sun, Y.; Felser, Claudia.; Yan, B. H. Graphene-like Dirac states and quantum spin Hall insulators in square-octagonal MX2 (M=Mo, W; X=S, Se, Te) isomers. Phys. Rev. B 2015, 92, 165421. (23) Ma, Y. D.; Kou, L. Z.; Li, X; Dai, Y; Heine, T. Two-dimensional transition metal dichalcogenides with a hexagonal lattice: Room-temperature quantum spin Hall insulators. Phys. Rev. B 2016, 93, 035442. (24) Ma, Y. D.; Kou, L. Z.; Li, X; Dai, Y; Smith, S. C.; Heine, T. Quantum spin Hall effect and

topological

phase

transition

in

two-dimensional square

transition-metal

dichalcogenides. Phys. Rev. B 2015, 92, 085427. (25) Weng, H. M.; Dai, X.; Fang, Z. Transition-Metal Pentatelluride ZrTe5 and HfTe5: A Paradigm for Large-Gap Quantum Spin Hall Insulators. Phys. Rev. X 2014, 4, 011002. (26) Liu, Q. H.; Zhang, X. W.; Abdalla, L. B.; Fazzio, A.; Zunger, A. Switching a Normal Insulator into a Topological Insulator via Electric Field with Application to Phosphorene. Nano Lett. 2015, 15, 1222–1228. (27) Zhao, M. W; Chen, X.; Li, L. Y.; Zhang, X. M. Driving a GaAs film to a large-gap topological insulator by tensile strain. Sci. Rep. 2015, 5, 8441.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 19

(28) Zhao, M. W.; Chen, X.; Li, L. Y. Strain-driven band inversion and topological aspects in Antimonene. Sci. Rep. 2015, 5, 16108. (29) Kou, L. Z.; Wu, S.-C.; Felser, C.; Frauenheim, T.; Chen, C. F.; Yan, B. H. Robust 2D Topological Insulators in van der Waals Heterostructures. ACS Nano 2014, 8, 10448– 10454. (30) Jin, K.-H.; Jhi, S.-H. Proximity-induced giant spin-orbit interaction in epitaxial graphene on a topological insulator. Phys. Rev. B 2013, 87, 075442. (31) Kou, L.; Yan, B.; Hu, F.; Wu, S.-C.; Wehling, T. O.; Felser, C.; Chen, C.; Frauenheim, T. Graphene-Based Topological Insulator with an Intrinsic Bulk Band Gap above Room Temperature. Nano Lett. 2013, 13, 6251-6255. (32) Zhang, J.; Triola, C.; Rossi, E. Proximity Effect in Graphene–Topological-Insulator Heterostructures. Phys. Rev. Lett. 2014, 112, 096802. (33) Zhu, F.-F.; Chen, W.-J.; Xu, Y.; Gao, C.-L.; Guan, D.-D.; Liu, C.-H.; Qian, D.; Zhang, S.-C.; Jia, J.-F. Epitaxial Growth of Two-Dimensional Stanene. Nat. Mater. 2015, 14, 1020-1025. (34) 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. (35) Vogt, P.; Padova, P. D.; Quaresima, C.; Avila, J.; Frantzeskakis, E.; Asensio, M. C.; Resta, A.; Ealet, B.; Lay, G. L. Silicene: Compelling experimental evidence for graphene like two-dimensional silicon. Phys. Rev. Lett. 2012, 108, 155501. (36) Dàvilla, M. E., Xian, L., Cahangirov, S., Rubio, A.; Lay, G. L. Germanene: A novel twodimensional germanium allotrope akin to graphene and silicene. New J. Phys. 2014, 16,


18

Page 19 of 19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


095002. (37) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (38) Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 1993, 47, 558-561. (39) Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188-5192. (40) Togo, A.; Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 2015, 108, 1-5. (41) Fu, L.; Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 2007, 76, 045302. (42) de Andres, P. L.; Ramírez, R.; Vergés, J. A. Strong covalent bonding between two graphene layers. Phys. Rev. B 2008, 77, 045403. (43) Yao, Y. G.; Fang, Z. Sign Changes of Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations. Phys. Rev. Lett. 2005, 95, 156601. (44) Guo, G. Y.; Yao, Y. G.; Niu, Q. Ab initio Calculation of the Intrinsic Spin Hall Effect in Semiconductors. Phys. Rev. Lett. 2005, 94, 226601.


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Quantum Phase Transition in Germanene and Stanene Bilayer: From

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