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Quantum Spin Hall Effect in Two-Dimensional Transition Metal Dichalcogenides Xiaofeng Qian Et Al

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Quantum Spin Hall Effect in Two-Dimensional Transition Metal Dichalcogenides Xiaofeng Qian Et Al RESEARCH | REPORTS magnitude too slow to produce v-weakening, 3. S. Siman-Tov, E. Aharonov, A. Sagy, S. Emmanuel, Geology 41, 22. J.-P. Gratier, D. K. Dysthe, F. Renard, Adv. Geophys. 54,47–179 except perhaps at temperatures of 500° to 700°C 703–706 (2013). (2013). 4. S. A. F. Smith et al., Geology 41,63–66 (2013). 23. J. R. Farver, R. A. Yund, Contrib. Mineral. Petrol. 123,77–91 reached in experiments at coseismic slip veloc- – 4 5 14 19 5. M. Fondriest et al., Geology 41, 1175 1178 (2013). (1996). ities ( , , , ). 6. J. D. Kirkpatrick, C. D. Rowe, J. C. White, E. E. Brodsky, Geology 24. N. R. Tao et al., Acta Mater. 50, 4603–4616 (2002). The internal polycrystalline substructure of 41, 1015–1018 (2013). 25. L. A. Kennedy, J. C. White, Geology 29, 1027–1030 (2001). the nanospherules and nanofibers that we ob- 7. J. P. Evans, M. R. Prante, S. U. Janecke, A. K. Ault, D. L. Newell, 26. R. L. Penn, J. F. Banfield, Science 281, 969–971 (1998). Geology 42, 623–626 (2014). 27. H. Zhang, J. F. Banfield, CrystEngComm 16, 1568–1578 served bears a striking similarity to microstruc- – 24 8. C. H. Scholz, Nature 391,37 42 (1998). (2014). tures found in shocked ductile metals ( ). As 9. B. A. Verberne, C. He, C. J. Spiers, Bull. Seismol. Soc. Am. 100, 28. N. Gehrke, H. Cölfen, N. Pinna, M. Antonietti, N. Nassif, in metals, the well-known ductility of calcite 2767–2790 (2010). Cryst. Growth Des. 5, 1317–1319 (2005). (25) may allow the ~5- to 20-nm substructure to 10. B. A. Verberne et al., Geology 41, 863–866 (2013). 29. N. H. de Leeuw, S. C. Parker, J. Chem. Soc. Faraday Trans. 93, – – form by progressive development of nano–cell 11. B. A. Verberne et al., Pure Appl. Geophys. 171, 2617 2640 467 475 (1997). (2014). 30.M.F.Ashby,R.A.Verrall,Acta Metall. Mater. 21,149–163 (1973). walls from dense dislocation networks gener- 12. X. Chen, A. S. Madden, B. R. Bickmore, Z. Reches, Geology 41, ated by crystal plasticity. Plastic deformation, 739–742 (2013). ACKNOWLEDGMENTS fracturing, and abrasion presumably generated 13. R. Han, T. Hirose, T. Shimamoto, Y. Lee, J.-i. Ando, Geology 39, WethankA.Niemeijer,J.Chen,V.Toy,andH.deBresser.H.King – the observed nanospherules from the starting 599 602 (2011). is thanked for the AFM measurements and P. van Krieken for 14. G. Di Toro et al., Nature 471, 494–498 (2011). “gouge.” To explain the chaining of nanospher- the thermogravimetric analysis. B.A.V. was supported by grant 15. R. Würschum, S. Herth, U. Brossmann, Adv. Eng. Mater. 5, 2011-75, awarded by the Netherlands Research Centre for – ules, producing the observed fiber structure and 365 372 (2003). Integrated Solid Earth Sciences; O.P. by Veni grant 863.13.006, – CPO, we note that oriented attachment at co- 16. S. C. Tjong, H. Chen, Mater. Sci. Eng. Rep. 45,1 88 (2004). awarded by the Netherlands Organisation for Scientific Research herent nanoparticle interfaces is widely reported 17. A. R. Niemeijer, C. J. Spiers, J. Geophys. Res. 112, B10405 (NWO); and D.A.M.D.W. by ISES grant 2011-74. NWO funded (2007). the FIB-SEM. All data are available in the supplementary materials. as a mechanism by which nanocrystallites can 18. Materials and methods are available as supplementary 26 27 rapidly coalesce to form single crystals ( , ), materials on Science Online. SUPPLEMENTARY MATERIALS 28 . 19. K. Oohashi et al., Geology 42, 787–790 (2014). also in calcite ( ) On this basis, we suggest www.sciencemag.org/content/346/6215/1342/suppl/DC1 20. C. J. Spiers, S. De Meer, A. R. Niemeijer, X. Zhang, in that the strong anisotropy in the surface energy Materials and Methods Physicochemistry of Water in Geological and Biological Supplementary Text of calcite produced similar preferred sintering Systems – Structures and Properties of Thin Aqueous Films, Figs. S1 to S8 (neck growth) at high-energy crystallographic in- S. Nakashima, C. J. Spiers, L. Mercury, P. A. Fenter, Tables S1 to S2 terfaces between neighboring spherules (Fig. 3, M. F. Hochella Jr, Eds. (Universal Academy Press, Tokyo, – – References (31 40) B and C), leading to dynamic chaining and align- 2004), pp. 129 158. 21. X. Zhang, C. J. Spiers, C. J. Peach, J. Geophys. Res. 115, 21 July 2014; accepted 11 November 2014 29 on December 21, 2014 ment of the lowest-energy (104) plane ( ) par- B09217 (2010). 10.1126/science.1259003 allel to the shear plane, and thus to the observed fibrous structure and CPO. In principle, the mechanism of frictional slip that we propose (Fig. 3, A to C, and fig. S1) is SOLID STATE THEORY similar to the Ashby-Verrall model for super- plasticity by diffusion-accommodated grain bound- ary sliding (GBS) (Fig. 3D) (30), but allows for Quantum spin Hall effect in frictional GBS and for intergranular cavitation (porosity generation by dilatation) when diffu- sive mass transport is too slow to accommodate two-dimensional transition www.sciencemag.org GBS. Our findings imply that nanocrystalline PSZs developed in calcite faults can produce metal dichalcogenides v-weakening, and hence seismogenic fault fric- tion, by a mechanism of cooperative nanogran- Xiaofeng Qian,1* Junwei Liu,2* Liang Fu,2† Ju Li1† ular or nanofiber flow plus diffusive mass transfer (Fig. 3, A to C), even in the upper crust where Quantum spin Hall (QSH) effect materials feature edge states that are topologically temperatures are generally considered too low to protected from backscattering. However, the small band gap in materials that Downloaded from support diffusion or superplasticity at active fault have been identified as QSH insulators limits applications. We use first-principles slip rates. The reason that these processes are calculations to predict a class of large-gap QSH insulators in two-dimensional observed in our experiments is because diffusive transition metal dichalcogenides with 1T′ structure, namely, 1T′-MX2 with M = mass transfer is dramatically accelerated by the (tungsten or molybdenum) and X = (tellurium, selenium, or sulfur). A structural nanogranular nature of the slip-zone rock that distortion causes an intrinsic band inversion between chalcogenide-p and metal-d forms, and by water-enhanced grain boundary bands. Additionally, spin-orbit coupling opens a gap that is tunable by vertical electric diffusion. A similar mechanism can also be en- field and strain. We propose a topological field effect transistor made of van der Waals visaged to operate at coseismic slip rates, where heterostructures of 1T′-MX2 and two-dimensional dielectric layers that can be the high temperatures generated will promote rapidly switched off by electric field through a topological phase transition instead solid-state diffusion. Given the abundant recent of carrier depletion. observations of nanogranular fault surfaces in tectonically active terrains (1–7), and the anom- alously high rates of diffusion found in nano- he discovery of graphene (1) has fuelled forming vdW heterostructures (9), which offer materials (15, 16), the proposed mechanism may vigorous investigation of two-dimensional unprecedented opportunities for exploring quan- be relevant not only to faults cutting calcite-rich (2D) materials (2), revealing a wide range tum electronics at the nanoscale. rockssuchaslimestones,but to crustal seismo- of extraordinary properties (3–5)andfunc- T 1 genesis in general. tionalities (6, 7). Owing to their atomic Department of Nuclear Science and Engineering and thickness, 2D materials can be horizontally pat- Department of Materials Science and Engineering, Massachusetts terned through chemical and mechanical tech- Institute of Technology, Cambridge, MA 02139, USA. REFERENCES AND NOTES 2 niques (8). Moreover, the weak van der Waals Department of Physics, Massachusetts Institute of Technology, 1. J. S. Chester, F. M. Chester, A. K. Kronenberg, Nature 437, Cambridge, MA 02139, USA. 133–136 (2005). (vdW) interaction between adjacent layers en- *These authors contributed equally to this work. †Corresponding 2. K.-F. Ma et al., Nature 444, 473–476 (2006). ables vertical stacking of different 2D materials, author. E-mail: [email protected] (L.F.); [email protected] (J.L.) 1344 12 DECEMBER 2014 • VOL 346 ISSUE 6215 sciencemag.org SCIENCE RESEARCH | REPORTS Quantum spin Hall (QSH) insulators (10–16) 1H-MX2 1T-MX2 1T’-MX2 have an insulating bulk but conducting edge states that are topologically protected from back- scattering by time-reversal symmetry. Quantized X1 conductance through QSH edge states have been experimentally demonstrated in HgTe/CdTe M (13, 14) and InAs/GaSb (17, 18) quantum wells. This could in principle provide an alternative route to quantum electronic devices with low X2 dissipation. However, the realization of such QSH-based devices for practical applications is impeded by three critical factors: (i) band gaps of existing QSH insulators are too small, which limits the operating regime to low tem- peratures. This has motivated efforts to search y for large-gap QSH insulators (19–26); (ii) the small number of conducting channels (e2/h per edge, where e istheelementarychargeandh is ’ x Planck sconstant)resultsinasmallsignal-to- noise ratio; and (iii) efficient methods of fast z on/off switching are lacking. Here, we use first-principles calculations to show that 2D materials can provide a practical platform for developing topological electronic x devices that may potentially overcome the above hurdles. Specifically, we predict a class of large- Fig. 1. Atomistic structures of monolayer transition metal dichalcogenides MX2. M stands for gap (~0.1 eV) QSH insulators in 2D transition (W, Mo) and X stands for (Te, Se, S). (A) 1H-MX2 in ABA stacking with P6m2 space group. (B) 1T-MX2 metal dichalcogenides (TMDCs) MX2 with M = in ABC stacking with P3m2 space group. (C)1T′-MX2, distorted 1T-MX2, where the distorted M atoms (W, Mo) and X = (Te, Se, S).
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