Tunable topological quantum states in three- and two-dimensional materials

Abstract

We review our theoretical advances in tunable topological quantum states in three- and twodimensional materials with strong spin–orbital couplings. In three-dimensional systems, we propose a new tunable topological insulator, bismuth-based skutterudites in which topological insulating states can be induced by external strains. The orbitals involved in the topological band-inversion process are the d- and p-orbitals, unlike typical topological insulators such as Bi₂Se₃and BiTeI, where only the p-orbitals are involved in the band-inversion process. Owing to the presence of large d-electronic states, the electronic interaction in our proposed topological insulator is much stronger than that in other conventional topological insulators. In two-dimensional systems, we investigated 3d-transition-metal-doped silicene. Using both an analytical model and first-principles Wannier interpolation, we demonstrate that silicene decorated with certain 3d transition metals such as vanadium can sustain a stable quantum anomalous Hall effect. We also predict that the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition-metal-doped silicenes where the energy band inversion occurs. These findings provide realistic materials in which topological states could be arbitrarily controlled.

Graphical abstract

Keywords

first-principles calculations / topological insulator / quantum anomalous Hall effect

References

[1] B. A. Bernevig, T. A. Hughes, and S. C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science314(5806), 1757 (2006)

[2] H. Lin, L. A. Wray, Y. Xia, S. Y. Xu, S. Jia, R. J. Cava, A. Bansil, and M. Z. Hasan, Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena, Nat. Mater.9(7), 546 (2010)

[3] S. Chadov, X. L. Qi, J. Kubler, G. H. Fecher, C. Felser, and S. C. Zhang, Tunable multifunctional topological insulators in ternary Heusler compounds, Nat. Mater.9(7), 541 (2010)

[4] X. L. Qi, T. L. Hughes, and S. C. Zhang, Topological field theory of time-reversal invariant insulators, Phys. Rev. B78(19), 195424 (2008)

[5] H. J. 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)

[6] M. Yang and W. M. Liu, The d-p band-inversion topological insulator in bismuth-based skutterudites, Scientific Reports4, 5153 (2014)

[7] L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B76(4), 045302 (2007)

[8] Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys.5(6), 398 (2009)

[9] Y. L. Chen, Studies on the electronic structures of threedimensional topological insulators by angle resolved photoemission spectroscopy, Front. Phys.7(2), 175 (2012)

[10] B. H. Yan, L. Muchler, X. L. Qi, S. C. Zhang, and C. Felser, Topological insulators in filled skutterudites, Phys. Rev. B85(16), 165125 (2012)

[11] C. C. Liu, W. X. Feng, and Y. G. Yao, Quantum spin Hall effect in silicene and two-dimensional germanium, Phys. Rev. Lett.107(7), 076802 (2011)

[12] F. D. Sun, X. L. Yu, J. W. Ye, H. Fan, and W. M. Liu, Topological quantum phase transition in synthetic non-abelian gauge potential: Gauge invariance and experimental detections, Scientific Reports3, 2119 (2013)

[13] F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett.61(18), 2015 (1988)

[14] C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Quantum anomalous Hall effect in Hg_1-yMn_yTe quantum wells, Phys. Rev. Lett.101(14), 146802 (2008)

[15] Z. H. Qiao, W. Tse, H. Jiang, Y. G. Yao, and Q. Niu, Twodimensional topological insulator state and topological phase transition in bilayer graphene, Phys. Rev. Lett.107(25), 256801 (2011)

[16] R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, and Z. Fang, Quantized anomalous Hall effect in magnetic topological insulators, Science329(5987), 61 (2010)

[17] X. L. Zhang, L. F. Liu, and W. M. Liu, Quantum anomalous Hall effect and tunable topological states in 3d transition metals doped silicene, Scientific Reports3, 2908 (2013)

[18] Y. Y. Zhang, J. P. Hu, B. A. Bernevig, X. R. Wang, X. C. Xie, and W. M. Liu, Localization and the Kosterlitz– Thouless transition in disordered graphene, Phys. Rev. Lett.102(10), 106401 (2009)

[19] R. Y. Liao, Y. X. Yu, and W. M. Liu, Tuning the tricritical point with spin-orbit coupling in polarized fermionic condensates, Phys. Rev. Lett.108(8), 080406 (2012)

[20] J. M. Zhang, W. G. Zhu, Y. Zhang, D. Xiao, and Y. G. Yao, Tailoring magnetic doping in the topological insulator Bi₂Se₃, Phys. Rev. Lett.109(26), 266405 (2012)

[21] Z. F. Wang, Z. Liu, and F. Liu, Quantum anomalous Hall effect in 2D organic topological insulators, Phys. Rev. Lett.110(19), 196801 (2013)

[22] 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, Science340(6129), 167 (2013)

[23] L. Fu and C. L. Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator, Phys. Rev. Lett.100(9), 096407 (2008)

[24] R. P. Tiwari, U. Zülicke, and U. Bruder, Majorana fermions from Landau quantization in a superconductor and topological-insulator hybrid structure, Phys. Rev. Lett.110(18), 186805 (2013)

[25] W. X. Feng, D. Xiao, J. Ding, and Y. G. Yao, Threedimensional topological insulators in IIII-VI2 and II-IVV2 chalcopyrite semiconductors, Phys. Rev. Lett.106(1), 016402 (2011)

[26] W. L. Liu, X. Peng, C. Tang, L. Sun, K. Zhang, and J. Zhong, Anisotropic interactions and strain-induced topological phase transition in Sb₂Se₃ and Bi₂Se₃, Phys. Rev. B84(24), 245105 (2011)

[27] G. Seyfarth, J. Brison, M. A. Méasson, J. Flouquet, K. Izawa, Y. Matsuda, H. Sugawara, and H. Sato, Multiband superconductivity in the heavy fermion compound PrOs₄Sb₁₂, Phys. Rev. Lett.95(10), 107004 (2005)

[28] M. Matsumoto and M. Koga, Exciton mediated superconductivity in PrOs₄Sb₁₂, J. Phys. Soc. Jpn.73(5), 1135 (2004)

[29] J. C. Smith, S. Banerjee, V. Pardo, and W. E. Pickett, Dirac point degenerate with massive bands at a topological quantum critical point, Phys. Rev. Lett.106(5), 056401 (2011)

[30] G. Kresse and J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B54(16), 11169 (1996)

[31] G. Kresse and J. Furthmuller, Efficiency of abinitio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci.6(1), 15 (1996)

[32] A. Kjekshus, T. Rakke, S. Rundqvist, T. Ostvold, A. Bjorseth, and D. L. Powell, Compounds with the skutterudite type crystal structure (III): Structural data for arsenides and antimonides, Acta Chem. Scand. A28a, 99 (1974)

[33] There are n_Ir = 4 Ir atoms and n_Bi = 12 Bi atoms in an IrBi3 primitive cell. At GGA level, E_Ir = -8.69 eV for crystalline Ir with space group FM3 ¯M and E_Bi = -3.70 eV for crystalline Bi with space group IM3 ¯M. From Fig. 1(d) we read E_IrBi3 = –82.81 eV. Substituting the above values in Eq. (1), we arrived at the binding energy E_b= –3.65 eV.

[34] A. Becke and E. Johnson, A simple effective potential for exchange, J. Chem. Phys.124(22), 221101 (2006)

[35] F. Tran and P. Blaha, Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential, Phys. Rev. Lett.102(22), 226401 (2009)

[36] W. X. Feng, D. Xiao, Y. Zhang, and Y. G. Yao, Half-Heusler topological insulators: A first principles study with the Tran–Blaha modified Becke–Johnson density functional, Phys. Rev. B82(23), 235121 (2010)

[37] D. Doennig, W. E. Pickett, and R. Pentcheva, Confinementdriven transitions between topological and Mott phases in (LaNiO₃)N/(LaAlO₃)M(111) superlattices, Phys. Rev. B89, 12110(R) (2014)

[38] J. Werner and F. F. Assaad, Interaction-driven transition between topological states in a Kondo insulator, Phys. Rev. B88(3), 035113 (2013)

[39] A. Go, W. Witczak-Krempa, G. S. Jeon, K. Park, and Y. B. Kim, Correlation effects on 3d topological phases: From bulk to boundary, Phys. Rev. Lett.109(6), 066401 (2012)

[40] H. M. Weng, J. Z. Zhao, Z. J. Wang, Z. Fang, and X. Dai, Topological crystalline Kondo insulator in mixed valence ytterbium borides, Phys. Rev. Lett.112(1), 016403 (2014)

[41] K. Miyamoto, A. Kimura, K. Kuroda, T. Okuda, K. Shimada, H. Namatame, M. Taniguchi, and M. Donath, Spinpolarized Dirac-cone-like surface state with d character at W(110), Phys. Rev. Lett.108(6), 066808 (2012)

[42] C. J. Kang, J. Kim, K. Kim, J.-S. Kang, J. D. Denlinger, and B. I. Min, Band symmetries of mixed valence topological insulator: SmB₆, arXiv: 1312.5898 (2013)

[43] S. Okamoto, Wenguang Zhu, Y. Nomura, R. Arita, Di Xiao, and N. Nagaosa, Correlation effects in (111) bilayers of perovskite transition-metal oxides, arXiv: 1401.0009 (2014)

[44] G. Chen and M. Hermele, Magnetic orders and topological phases from f-d exchange in pyrochlore iridates, Phys. Rev. B86(23), 235129 (2012)

[45] Y. H. Chen, H. S. Tao, D. X. Yao, and W. M. Liu, Kondo metal and ferrimagnetic insulator on the triangular Kagome lattice, Phys. Rev. Lett.108(24), 246402 (2012)

[46] K. Niwa, D. Nomichi, M. Hasegawa, T. Okada, T. Yagi, and T. Kikegawa, Compression behaviors of binary skutterudite CoP₃ in noble gases up to 40 GPa at room temperature, Inorg. Chem.50(8), 3281 (2011)

[47] A. Smalley, M. L. Jespersen, and D. C. Johnson, Synthesis and structural evolution of RuSb₃, a new metastable skutterudite compound, Inorg. Chem.43(8), 2486 (2004)

[48] T. Caillat, J. P. Fleurial, and A. Borshchevsky, Bridgmansolution crystal growth and characterization of the skutterudite compounds CoSb₃ and RhSb₃, J. Cryst. Growth166(1-4), 722 (1996)

[49] M. Akasaka, T. Iida, G. Sakuragi, S. Furuyama, M. Noda, S. Matsui, M. Ota, H. Suzuki, H. Sato, Y. Takanashi, and S. Sakuragi, Effects of post-annealing on thermoelectric properties of p-type CoSb₃ grown by the vertical Bridgman method, J. Alloys Compd.386(1-2), 228 (2005)

[50] H. Takizawa, K. Miura, M. Ito, B. Suzuki, and T. Endo, Atom insertion into the CoSb skutterudite host lattice under high pressure, J. Alloys Compd.282(1-2), 79 (1999)

[51] X. X. Xi, C. Ma, Z. Liu, Z. Chen, W. Ku, H. Berger, C. Martin, D. B. Tanner, and G. L. Carr, Signatures of a pressure-induced topological quantum phase transition in BiTeI, Phys. Rev. Lett.111(15), 155701 (2013)

[52] Y. Nakamoto, H. Sumiya, T. Matsuoka, K. Shimizu, T. Irifune, and Y. Ohishi, Generation of Multi-megabar pressure using nano-polycrystalline diamond anvils, Jpn. J. Appl. Phys.46(25), L640 (2007)

[53] J. L. Zhu, J. L. Zhang, P. P. Kong, S. J. Zhang, X. H. Yu, J. L. Zhu, Q. Q. Liu, X. Li, R. C. Yu, R. Ahuja, W. G. Yang, G. Y. Shen, H. K. Mao, H. M. Weng, X. Dai, Z. Fang, Y. S. Zhao, and C. Q. Jin, Superconductivity in topological insulator Sb₂Te₃ induced by pressure, Scientific Reports3, 2016 (2013)

[54] J. J. Hamlin, J. R. Jeffries, N. P. Butch, P. Syers, D. A. Zocco, S. T. Weir, Y. K. Vohra, J. Paglione, and M. B. Maple, High pressure transport properties of the topological insulator Bi₂Se₃, J. Phys.: Condens. Matter24(3), 035602 (2012)

[55] Y. Q. Li, K. H. Wu, J. R. Shi, and X. C. Xie, Electron transport properties of three-dimensional topological insulators, Front. Phys.7(2), 165 (2012)

[56] B. Dóra and R. Moessner, Dynamics of the spin Hall effect in topological insulators and graphene, Phys. Rev. B83(7), 073403 (2011)

[57] P. Cheng, C. Song, T. Zhang, Y. Zhang, Y. Wang, J. F. Jia, J. Wang, Y. Wang, B. F. Zhu, X. Chen, X. Ma, K. He, L. Wang, X. Dai, Z. Fang, X. Xie, X. L. Qi, C. X. Liu, S. C. Zhang, and Q. K. Xue, Landau quantization of topological surface states in Bi₂Se₃, Phys. Rev. Lett.105(7), 076801 (2010)

[58] C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett.95(22), 226801 (2005)

[59] C. L. Kane and E. J. Mele, Z₂ topological order and the quantum spin Hall effect, Phys. Rev. Lett.95(14), 146802 (2005)

[60] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature438(7065), 197 (2005)

[61] S. Cahangirov, M. Topsakal, E. Aktürk, H. Sahin, and S. Ciraci, Two- and one-dimensional honeycomb structures of silicon and germanium, Phys. Rev. Lett.102(23), 236804 (2009)

[62] M. Ezawa, Valley-polarized metals and quantum anomalous Hall effect in silicene, Phys. Rev. Lett.109(5), 055502 (2012)

[63] M. Ezawa, A topological insulator and helical zero mode in silicene under an inhomogeneous electric field, New J. Phys.14(3), 033003 (2012)

[64] M. Tahir and U. Schwingenschlögl, Valley polarized quantum Hall effect and topological insulator phase transitions in silicene, Scientific Reports3, 1075 (2013)

[65] W. F. Tsai, C.Y. Huang, T.R. Chang, H. Lin, H.T. Jeng, and A. Bansil, Gated silicene as a tunable source of nearly 100% spin-polarized electrons, Nat. Commun.4, 1500 (2013)

[66] L. Chen, B. J. Feng, and K. H. Wu, Observation of a possible superconducting gap in silicene on Ag(111) surface, Appl. Phys. Lett.102(8), 081602 (2013)

[67] M. I. Katsnelson, V. Y. Irkhin, L. Chioncel, A. I. Lichtenstein, and R. A. de Groot, Half-metallic ferromagnets: From band structure to many-body effects, Rev. Mod. Phys.80(2), 315 (2008)

[68] D. Xiao, W. Yao, and Q. Niu, Valley-contrasting physics in graphene: Magnetic moment and topological transport, Phys. Rev. Lett.99(23), 236809 (2007)

[69] P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B50(24), 17953 (1994)

[70] C. C. Liu, H. Jiang, and Y. Yao, Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin, Phys. Rev. B84(19), 195430 (2011)

[71] I. V. Solovyev, P. H. Dederichs, and V. I. Anisimov, Corrected atomic limit in the local-density approximation and the electronic structure of d impurities in Rb, Phys. Rev. B50(23), 16861 (1994)

[72] V. I. Anisimov, F. Aryasetiawan, and A. I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: The LDA+ U method, J. Phys.: Condens. Matter9(4), 767 (1997)

[73] K. T. Chan, J. B. Neaton, and M. L. Cohen, Firstprinciples study of metal adatom adsorption on graphene, Phys. Rev. B77(23), 235430 (2008)

[74] J. Ding, Z. Qiao, W. Feng, Y. Yao, and Q. Niu, Engineering quantum anomalous/valley Hall states in graphene via metal-atom adsorption: An ab-initio study, Phys. Rev. B84(19), 195444 (2011)

[75] H. M. Weng, T. Ozaki, and K. Terakuta, Theoretical analysis of magnetic coupling in sandwich clusters V_n(C₆H₆)_n+1, J. Phys. Soc. Jpn.77(1), 014301 (2008)

[76] T. O. Wehling, A. V. Balatsky, M. I. Katsnelson, A. I. Lichtenstein, and A. Rosch, Orbitally controlled Kondo effect of Co adatoms on graphene, Phys. Rev. B81(11), 115427 (2010)

[77] H. Zhang, C. Lazo, S. Blügel, S. Heinze, and Y. Mokrousov, Electrically tunable quantum anomalous Hall effect in graphene decorated by 5d transition-metal adatoms, Phys. Rev. Lett.108(5), 056802 (2012)

[78] Z. H. Qiao, S. A. Yang, W. X. Feng, W.-K. Tse, J. Ding, Y. G. Yao, J. Wang, and Q. Niu, Quantum anomalous Hall effect in graphene from Rashba and exchange effects, Phys. Rev. B82, 161414(R) (2010)

[79] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-Dimensional periodic potential, Phys. Rev. Lett.49(6), 405 (1982)

[80] D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys.82(3), 1959 (2010)

[81] A. Mostofi, J. R. Yates, Y. S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Wannier90: A tool for obtaining maximally-localized Wannier functions, Comput. Phys. Commun.178(9), 685 (2008)

[82] X. Wang, J. R. Yates, I. Souza, and D. Vanderbilt, Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation, Phys. Rev. B74(19), 195118 (2006)

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