Prediction of topological materials using firstprinciples band theory computations

Prediction of topological materials using firstprinciples band theory computations Hsin Lin Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore Department of Physics, National University of Singapore Sea urchin June 27 at SOCSIS 2016, Spetses, Greece

Singapore National Research Foundation Acknowledgement NUS: Shin-Ming Huang, Chi-Cheng Lee, Guoqing Chang, BaoKai Wang, Chuang-Han Hsu, Le Quy Duong, Bahadur Singh, Minggang Zeng, Wei-Feng Tsai NUS ECE: Gengchiau Liang s group M.Z. Hasan s group (Princeton Univ.): Su-Yang Xu, Ilya Belopolski, Nasser Alidoust, Madhab Neupane, Hao Zheng, Guang Bian, Daniel S. Sanchez Arun Bansil (Northeastern Univ.) Liang Fu (MIT) Vidya Madhavan (UIUC): Yoshinori Okada (Tohoku), Ilija Zeljkovic (Boston College) Rajendra Prasad (Indian Institute of Technology Kanpur) Tanmoy Das (Indian Institute of Physics, Bangalore) Han Hsu (National Central Univ., Taiwan) Feng-Chuan Chuang (NSYSU, Taiwan): Cheng-Yi Huang, Chia-Hsiu Hsu, Zhi-Quan Huang, Christian Crisostomo Horng-Tay Jeng (NTHU/IOP, Taiwan): Tay-Rong Chang, Peng-Jen Chen

Outline Introduction: band topology Z2 topological phase transition: TlBi(Se,S)2 Topological crystalline insulator: (Pb,Sn)Se Weyl semimetals: TaAs 2D topological materials : Spin filter/separator Conclusions

Energy Topological Insulators Fu & Kane, PRL 100, 096407 (2008) New possibilities for Fundamental physics Spintronics Quantum computing k x k y

Topology Gaussian curvature χ χ=2 χ=0 χ=-2

Energy [ev] Adiabatic transformation χ=2 χ=2 + +? + + EF L Γ X W L Γ X W

Energy [ev] Topological phase transition χ=2 χ=0 Trivial Critical Non-trivial + + 0 + + + EF L Γ X W L Γ X W

Bulk-boundary Correspondence Theorem Energy Energy Energy Metallic surface/edge states Z 2 :even EF Γ M Z 2 :odd EF Γ M Momentum k x k y time reversal: E(k, )=E(-k, )

Weyl semimetal Wan, Turner, Vishwanath, and Savrasov, PRB 2011

Bi 2 Se 3, Spin-orbit coupling Y. Xia et al., Nature Physics 5, 398 (2009).

Energy (ev) Surface calculation + surface probe First-principles calculations DFT (KKR, LAPW, Plane Wave) + Angle resolved photoemission (ARPES) Single-Dirac-cone surface states in topological insulator Bi 2 Se 3

Our Roadmap for 3D New Topological Materials 2 nd Gen, Bi 2 Se 3 /Bi 2 Te 3 : single Dirac cone, large bulk gap, but naturally doped with electrons or holes Nat. Phys. 5, 398 (2009); PRL 103, 146401 (2009); Nature 460, 1101 (2009). Half-Heuslers, Li 2 AgSb, quaternary chalcogenides, famatinites, ternary GeBi 2 Te 4, Bi 2 Te 2 Se families: tunability of lattice/dopants Nat. Mat. 9, 546 (2010); PRB 82, 125208 (2010); arxiv:1007.5111; New J. Phys. 13, 085017 (2011); New J. Phys. 13, 095005 (2011); PRB 85, 235406 (2012); PRB 87, 121202R (2013). TlBiSe 2 family: isolated single Dirac cone, topological phase transition PRL 105, 036404 (2010); Science 332, 560 (2011); PRB 86, 115208 (2012); Nat. Commun. 6, 6870 (2015); PRB (2016) (Pb/Sn)Te family: first topological crystalline insulator, topological phase transition. Nat. Commun. 3, 982 (2012); Nat. Commun. 3, 1192 (2012); PRB 87, 235317 (2013); Science 341, 1496 (2013); Nat. Phys. 10, 572 (2014); PRB 92, 075131 (2015); Nat. Commun. 6, 6559 (2015); Nat. Mat. 14, 318 (2015);

Our Roadmap for 3D New Topological Materials TaAs family: first Weyl semimetal. Nat. Commun. (2015) ; Science (2015); Nat. Phys. (2015); Science Advances (2015); PRB (2015); ACS nano (2016); Nat. Commun. (2016); PRL (2016); SrSi 2 Weyl semimetal: Double Weyl, no mirrors PNAS (2016) (Mo,W)Te 2 : Type II Weyl semimetal Nat. Commun. (2016) Topological nodal-line semimetals: PbTaSe 2, TlTaSe 2 Nat. Commun. (2016) ; PRB 93, 121113 (2016); PRB 93, 245130 (2016) ; Ta 3 S 2 Weyl semimetal: largest separation between Weyl nodes. Science Advances (2016) Co 2 TiSi Heuslers: magnetic Weyl/nodal-line semimetal with high Curie temperature. arxiv 1603.01255 LaAlGe, CeAlGe: magnetic Type II Weyl semimetal arxiv 1603.07318, arxiv 1604.02124

Pseudo PbTe: TlBiTe 2 1Γ 3X 4L PbTe - - + SnTe - - - Both are Z 2 trivial. Te Tl (Pb) k z + [111] Te Bi (Pb) z x y k x + Γ L X k y H. Lin, R. S. Markiewicz, L. A. Wray, L. Fu, M. Z. Hasan, and A. Bansil, PRL (2010).

TlBiS 2 TlBiSe 2 H. Lin, R. S. Markiewicz, L. A. Wray, L. Fu, M. Z. Hasan, and A. Bansil, PRL (2010). S. Y. Xu, Y. Xia, L. A. Wray, S. Jia, F. Meier, J. H. Dil, J. Osterwalder, B. Slomski, A. Bansil, H. Lin, R. J. Cava, and M. Z. Hasan, Science (2011).

Topological phase transition in TlBi(S 1-δ Se δ ) 2 S. Y. Xu, Y. Xia, L. A. Wray, S. Jia, F. Meier, J. H. Dil, J. Osterwalder, B. Slomski, A. Bansil, H. Lin, R. J. Cava, and M. Z. Hasan, Science (2011).

Xu, Neupane, Belopolski, Liu, Alidoust, Bian, Jia, Landolt, Slomski, Dil, Shibayev, Basak, Chang, Jeng, Cava, Lin, Bansil, and Hasan, Nature Communications (2015). Preformed spin-polarized surface states (Theory) trivial critical Non-trivial Momentum k x (1/Å)

Preformed spin-polarized surface states (Experiment) Xu, Neupane, Belopolski, Liu, Alidoust, Bian, Jia, Landolt, Slomski, Dil, Shibayev, Basak, Chang, Jeng, Cava, Lin, Bansil, and Hasan, Nature Communications (2015). Trivial insulator TlBi(S 1-δ Se δ ) 2, δ=0.4

Summary Topological phase transition has been observed in TlBi(Se,S)2. Preformed spin polarized surface states developed on the trivial side.

Energy Crystal symmetry protected Dirac node Metallic surface/edge states Z 2 TI TCI -i +i EF Γ X Γ Momentum X Mirror eigenvalues ±i

Topological crystalline insulator (Pb,Sn)Te 1Γ 3X 4L PbTe - - + SnTe - - - T. H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Nature Communications 3, 982 (2012).

Intrinsic band inversion in SnTe T. H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Nature Communications 3, 982 (2012).

Surface states and four Dirac cones Y. J. Wang, W.-F. Tsai, H. Lin, S.-Y. Xu, M. Neupane, M. Z. Hasan, and A. Bansil, PRB 87, 235317 (2013). T. H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Nature Communications 3, 982 (2012).

Experimental observation Xu, Liu, Alidoust, Qian, Neupane, Denlinger, Wang, Wray, Cava, Lin, Marcinkova, Morosan, Bansil, Hasan, Nature Communications 3, 1192 (2012).

Energy Lifshitz transition and Van Hove singularities Y. Okada, M. Serbyn, H. Lin, D. Walkup, W. Zhou, C. Dhital, M. Neupane, S.Y. Xu, Y.J. Wang, R. Sankar, F.C. Chou, A. Bansil, M. Z. Hasan, S. D. Wilson, L. Fu, V. Madhavan, Science 341, 1496 (2013). Y. J. Wang, W.-F. Tsai, H. Lin, S.-Y. Xu, M. Neupane, M. Z. Hasan, and A. Bansil, PRB 87, 235317 (2013). T. H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Nature Communications 3, 982 (2012).

Two coaxial Dirac-cone model Te Sn Sn Sn Te Te Chen Fang, Matthew J. Gilbert, Su-Yang Xu, B. Andrei Bernevig, M. Z. Hasan, PRB 88, 125141 (2013). Junwei Liu, Wenhui Duan, and Liang Fu, Phys. Rev. B 88, 241303(R) (2013). Y. J. Wang, W.-F. Tsai, H. Lin, S.-Y. Xu, M. Neupane, M. Z. Hasan, and A. Bansil, PRB 87, 235317 (2013).

Observed spin texture Xu, Liu, Alidoust, Qian, Neupane, Denlinger, Wang, Wray, Cava, Lin, Marcinkova, Morosan, Bansil, Hasan, Nature Communications 3, 1192 (2012).

Orbital contribution Sn p z Te p x Y. J. Wang, W.-F. Tsai, H. Lin, S.-Y. Xu, M. Neupane, M. Z. Hasan, and A. Bansil, PRB 87, 235317 (2013). Xu, Liu, Alidoust, Qian, Neupane, Denlinger, Wang, Wray, Cava, Lin, Marcinkova, Morosan, Bansil, Hasan, Nature Communications 3, 1192 (2012).

Interference patterns I. Zeljkovic, Y. Okada, C.-Y. Huang, R. Sankar, D. Walkup, W. Zhou, M. Serbyn, F. C. Chou, W. F. Tsai, H. Lin, A. Bansil, L. Fu, M. Z. Hasan. V. Madhavan, Nat. Phys. (2014).

Matrix element effect I. Zeljkovic, Y. Okada, C.-Y. Huang, R. Sankar, D. Walkup, W. Zhou, M. Serbyn, F. C. Chou, W. F. Tsai, H. Lin, A. Bansil, L. Fu, M. Z. Hasan. V. Madhavan, Nat. Phys. (2014).

Interference patterns I. Zeljkovic, Y. Okada, C.-Y. Huang, R. Sankar, D. Walkup, W. Zhou, M. Serbyn, F. C. Chou, W. F. Tsai, H. Lin, A. Bansil, L. Fu, M. Z. Hasan. V. Madhavan, Nat. Phys. (2014).

Landau Levels Y. Okada, M. Serbyn, H. Lin, D. Walkup, W. Zhou, C. Dhital, M. Neupane, S.Y. Xu, Y.J. Wang, R. Sankar, F.C. Chou, A. Bansil, M. Z. Hasan, S. D. Wilson, L. Fu, V. Madhavan, Science 341, 1496 (2013).

Gapped Dirac cones Y. Okada, M. Serbyn, H. Lin, D. Walkup, W. Zhou, C. Dhital, M. Neupane, S.Y. Xu, Y.J. Wang, R. Sankar, F.C. Chou, A. Bansil, M. Z. Hasan, S. D. Wilson, L. Fu, V. Madhavan, Science 341, 1496 (2013).

Topological phase transition Pb 1-x Sn x Se I. Zeljkovic, Y. Okada, M. Serbyn, R. Sankar, D. Walkup, W. Zhou, J. Liu, G. Chang, Y. J. Wang, M. Z. Hasan, F. Chou, H. Lin, A. Bansil, L. Fu, and V. Madhavan, Nature Materials 14, 318 (2015).

Gap size as a function of doping I. Zeljkovic, Y. Okada, M. Serbyn, R. Sankar, D. Walkup, W. Zhou, J. Liu, G. Chang, Y. J. Wang, M. Z. Hasan, F. Chou, H. Lin, A. Bansil, L. Fu, and V. Madhavan, Nature Materials 14, 318 (2015).

Surface state penetration depth I. Zeljkovic, Y. Okada, M. Serbyn, R. Sankar, D. Walkup, W. Zhou, J. Liu, G. Chang, Y. J. Wang, M. Z. Hasan, F. Chou, H. Lin, A. Bansil, L. Fu, and V. Madhavan, Nature Materials 14, 318 (2015).

Finite size slab Ab initio calculations for Electronic Band Structures Wannierization Semi-infinite slab Material-specific Tight-binding Hamiltonians Surface state Calculations Angle-resolved photoemission (ARPES) and Scanning tunneling Spectroscopy (STS)

Break TRS Reversal Symmetry Magnetic pyrochlore iridates (Y 2 Ir 2 O 7 ) Weyl semimetal without Time- 2-in/2- out Mag. hetero-structure Wan, Turner, Vishwanath, and Savrasov, PRB 2011 Burkov & Balents, PRL (2011)

TaAs

Weyl semimetal without Breaking Time-reversal TaAs class: (Ta,Nb)(As,P) Stoichiometric compound Symmetry I4 1 md (C 4v ) No inversion symmetry C 4 rotation axis 2 mirror planes, xz & yz Huang et al., Nat. Comm., 6, 7373 (2015)

band structure of TaAs (a) body-centerd tetragonal structure of TaAs. (b) Brillouin zone. (c) band structure of TaAs without SO. (d) band with SO.

Weyl points and topological chiral charge in TaAs: (a) Position of WPS and nodal ringin TaAs. (e) A schematic for projected WPS on (001) surface. (f) spin texture

ARPES Results W2: W1: Xu et al., arxiv:1502.03807; Science (2015)

Surface States of TaAs

Interference patterns (Theory) Chang, Xu, Zheng, Lee, Huang, Belopolski, Sanchez, Bian, Alidoust, Chang, Hsu, Jeng, Bansil, Lin, and Hasan, PRL (2016).

Removing Fermi arcs Chang, Xu, Zheng, Lee, Huang, Belopolski, Sanchez, Bian, Alidoust, Chang, Hsu, Jeng, Bansil, Lin, and Hasan, PRL (2016).

Fermi arcs interference patterns Chang, Xu, Zheng, Lee, Huang, Belopolski, Sanchez, Bian, Alidoust, Chang, Hsu, Jeng, Bansil, Lin, and Hasan, PRL (2016).

Chang, Xu, Zheng, Lee, Huang, Belopolski, Sanchez, Bian, Alidoust, Chang, Hsu, Jeng, Bansil, Lin, and Hasan, PRL (2016).

Interference patterns for NbP Zheng, Xu,Bian,Guo,Chang, Sanchez, Belopolski, Lee, Huang, Zhang, Sankar, Alidoust, Chang,Wu,Neupert,Chou,Jeng,Yao,Bansil, Jia, Lin, Hasan, ACS nano (2016).

Allowing inter-orbital scattering Chang, Xu, Zheng, Lee, Huang, Belopolski, Sanchez, Bian, Alidoust, Chang, Hsu, Jeng, Bansil, Lin, and Hasan, PRL (2016).

LaAlGe Xu, Alidoust, Chang, Lu, Singh, Belopolski, Sanchez, Zhang, Bian, Zheng, Husanu, Bian, Huang, Hsu, Chang, Jeng, Bansil, Strocov, Lin, Jia and Hasan, arxiv:1603.07318

LaAlGe Xu, Alidoust, Chang, Lu, Singh, Belopolski, Sanchez, Zhang, Bian, Zheng, Husanu, Bian, Huang, Hsu, Chang, Jeng, Bansil, Strocov, Lin, Jia and Hasan, arxiv:1603.07318

Summary 3D Topological phase transition is realized in TlBi(S 1-δ Se δ ). Preformed spin polarized surface states developed on the trivial side. Ge(Sb,Bi)2Te4 family is another material candidate for topological phase transition. First material realization of TCI in SnTe family Surface states exhibit gapless Dirac cones with Dirac nodes protected by mirror symmetry. Spin and orbital texture can be understood by a twocoaxial-dirac-cone model, giving matrix-element effect in interference patterns. Stoichiometric Weyl semimetals are found in TaAs and LaAlGe family. Fermi arcs surface states are observed Interference patterns are observed in NbP.

2D topological materials Group V: [New Journal of Physics 16, 105018 (2014)] ultrathin Bi(110) films [Nano Letters 15, 80 (2015)]; Bi/Sb honeycombs on SiC(0001)[New Journal of Physics 17, 025005 (2015)]; Bi films on Ge(111) [Surface Science 626, 68 (2014)]; 2D TCI in Sb/Bi planar honeycombs [Scientific Reports 6, 18993 (2016)] Group IV: 100% spin polarization [Nature Communications 4, 1500 (2013)]; silicene on a semiconducting Bi/Si(111)- 3x 3 substrate[physical Review B 90, 245433 (2014)], hydrogenated ultra-thin tin films [New Journal of Physics 16, 115008 (2014)] III-V: bilayers of Group III Elements with Bi [Nano Letters 14, 2505 (2014)]; III-V on Si(111) [Scientific Reports 5, 15463 (2015)]; Hydrogenated III-V [Nano Letters 15, 6568 (2015)] Thin films of 3D TI: TlBiS2 films [Journal of Applied Physics 116, 033704 (2014)]; Bi2Se3 films[nature Communications 5, 3841 (2014)], QAH [Journal of Applied Physics 117, 17C741 (2015), Physical Review B 92, 115205 (2015)] Au/Si(111) substrate [Physical Review B 93, 035429 (2016)]

2D material with graphene-like structure Without SO z K x c With SO Compare with graphene: sp 2 sp 3 C.C. Liu et al., PRB 84 (2011) & PRL 107 (2011) K 56

Quantum spin Hall (2D Topological insulator) Fu and Kane s parity analysis:prb 76, 045302 (2007) Parity of each valence band Sign of parity product Z 2 = 1 Z 2 = 1 Gap (mev) 8 23 M M Γ K M Z 2 = 1 72 Z 2 = 0 554 The 2D systems of Si, Ge, and Sn are 2D QSH materials, whereas Pb is not C.C. Liu et al., PRB 84 (2011) & PRL 107 (2011)

Under E Field: Inversion Symmetry Breaking Gap evolution z A B x Drummond et al., PRB 85, 12 The gap size reduces linearly as we turn on the electric field: At E z = E c, the gap reduces to zero As E z > E c, the system reopens a gap

E-field tunable topological phase transition E z = 0 0 < E z < E c E z = E c E z > E c AB AB QSH phase QSH phase Critical phase BB AA Band insulator silicene Bi 2 Se 3

A low-energy effective description 1 st term = Hopping term 2 nd term = Intrinsic NNN SOC 3 rd term = Rashba NNN SOC 4 th term = Staggered sublattice potential 5 th term = Zeeman splitting 4 th term turns out driving the transition between QSH and trivial BI C.-C. Liu, H. Jiang and Y. Yao, PRB 84, 195430 (2011). W.-F. Tsai, C.-Y. Huang, T.-R. Chang, H. Lin, H.-T. Jeng, and A. Bansil, Nature Communications 4:1500 (2013).

Quantum spin Hall: spin separator Spin polarized conducting edge states Silicene Spin Separator

Gapless edge states G. Gupta, H. Lin, A. Bansil, M. B. A. Jalil, C.-Y. Huang, W.-F. Tsai, and G.C. Liang, Applied Physics Letters 104,032410 (2014).

High efficiency spin separator G. Gupta, H. Lin, A. Bansil, M. B. A. Jalil, C.-Y. Huang, W.-F. Tsai, and G.C. Liang, Applied Physics Letters 104,032410 (2014).

Field-tunable spin separator G. Gupta, H. Lin, A. Bansil, M. B. A. Jalil, C.-Y. Huang, W.-F. Tsai, and G.C. Liang, Applied Physics Letters 104,032410 (2014).

Field-tunable High Efficiency Spin Filter Basic idea (from bulk property): E z > 0 K K K

Field-tunable High Efficiency Spin Filter Basic idea (from bulk property): E z > 0 h K μ 0 K K

Quantum Point Contact E F μ 0 K K K K *In Rycerz et al., Nat. Phys. 3 (2007), edge state property is used in graphene!

Conductance (e 2 /h) High-efficiency spin filter Iterative Green s function method for two-terminal conductance [T. Ando, PRB 44 (1991)] Spin polarization L s =0 L s =8 μ 0 /t W.-F. Tsai, C.-Y. Huang, T.-R. Chang, H. Lin, H.-T. Jeng, and A. Bansil, Nature Communications 4:1500 (2013).

Robustness against weak (nonmagnetic) disorder Disorder-averaged spin polarization as a function of the maximum strength of the random onsite potential V w. Disorder-averaged spin polarization as a function of the perrcentage of edge vacancies r in the constriction. W.-F. Tsai, C.-Y. Huang, T.-R. Chang, H. Lin, H.-T. Jeng, and A. Bansil, Nature Communications 4:1500 (2013).

TlBi, InBi, GaBi Chuang, Yao, Huang, Liu, Hsu, Das, Lin, and Bansil, Nano Letters 14, 2505 (2014)

At various hydrogen coverages, TlBi remains topologically nontrivial Christian P. Crisostomo, Liang-Zi Yao, Zhi-Quan Huang, Chia-Hsiu Hsu, Feng-Chuan Chuang, Hsin Lin, Marvin A. Albao, and Arun Bansil, Nano Letters 15, 6568 (2015)

Robust band inversion at Γ Christian P. Crisostomo, Liang-Zi Yao, Zhi-Quan Huang, Chia-Hsiu Hsu, Feng-Chuan Chuang, Hsin Lin, Marvin A. Albao, and Arun Bansil, Nano Letters 15, 6568 (2015)

Summary At low energies, silicene can be described by two nearly fully spin-polarized (massless/massive) Dirac cones in the presence of the perpendicular E field Quantum spin Hall insulators can be used as a spin separator. It is possible to localize conducting channels anywhere in the 2D silicene by applying an inhomogeneous electric field. The proposed spin filter gives rise to nearly 100% spinpolarized currents via gate control More functional electronic devices based on 2D spin-orbit thin films can be anticipated in the future!

Thank you for your attention!