1. Search for New Topological Insulator Materials April 14, 2011 at NTNU Hsin Lin Northeastern University

2. Physics 2, 108 (2009) http://physics.aps.org/articles/v2/108

3. Outline Introduction Topological insulator materials – Bi 2 Te 3 spin texture, hexagonal warping – Half-Heuslers, Li 2 AgSb – GeBi 2 Te 4 – TlBiSe 2 Topological phase transition Conclusions

4. Topological Insulators New possibilities for – Fundamental physics – Spintronics – Quantum computing – Novel magnetism and superconductivity – Applications

5. χ Topology Gaussian curvature Berry connection Berry curvature geodesic curvature χ=2χ=0 χ=-2

6. Adiabatic transformation χ=2 Energy [eV] L Γ X W EFEF + + + + ?

7. Topological transition χ=2χ=0 Trivial Non-trivial Critical Energy [eV] L Γ X W EFEF 0 + + + + +

8. Parity analysis

9. Metallic surface/edge states Z 2 :odd Z 2 :even Γ M Energy EFEF Γ M Energy EFEF time reversal: E(k, ↑ )=E(-k, ↓ )

10. Topological phase transition S.-Y. Su et al., Science Express online 31 March 2011 [DOI:10.1126/science.1201607]

11. Determining Band topology Z 2 value: integral over valence bands Adiabatic transformation Parity analysis (inversion symmetry) Surface state dispersion

12. First-principles calculations DFT/LDA (KKR, LAPW) Tight binding models (Wannier functions) Spectroscopies: Angle resolved photoemission (ARPES) Scanning tunneling microscopy/spectroscopy (STM/STS) Resonant inelastic X-ray scattering (RIXS) Compton profile (CP) First-principles matrix element effect Including interactions beyond DFT/LDA Theoretical Roadmap

13. First-principles calculations DFT/LDA (KKR, LAPW) Angle resolved photoemission (ARPES) Surface calculation + surface probe + Energy (eV) Single-Dirac-cone surface states in topological insulator Bi 2 Se 3 Prof. Hasan at Princeton U.Prof. Bansil at Northeastern U.

14. Our Roadmap for New TIs Bi/Sb: multiple FSs, disorder scattering 2 nd Gen, Bi 2 Se 3 /Bi 2 Te 3 : single Dirac cone, large bulk gap, but naturally doped with electrons or holes Half-Heuslers, Li 2 AgSb: tunability of lattice/dopants GeBi 2 Te 4 families: many compounds, single Dirac cone inside gap, more insulating than Bi 2 Se 3 /Bi 2 Te 3 TlBiSe 2 family: single Dirac cone, Dirac point in gap, topological phase transition

15. Specific TI families Discovered Bi 2 Se 3 –Nat. Phys. 5, 398 (2009). –PRL 103, 146401 (2009). –Nature 460, 1101 (2009). Half-Heusler –Nat. Mat. 9, 546 (2010). –PRB 82, 125208 (2010). TlBiSe 2 –PRL 105, 036404 (2010). –Science in press. [DOI:10.1126/science.1201607] Li 2 AgSb - arXiv:1004.0999 GeBi 2 Te 4 - arXiv:1007.5111

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

17. Bi 2 Te 3 ARPES D. Hsieh et al., Physical Review Letters 103, 146401 (2009). Singly degenerate surface state

18. Energy kxkx kyky Ideal Dirac cone kyky kxkx E=const. +k ↑ -k ↓ one-to-one spin- momentum locked backward scattering suppressed

19. Quasiparticle interference (QPI) Without matrix elementWith matrix element

20. Hsieh et al., NATURE 460, 1101 (2009).

21. E=200 meV Energy [meV] out-of-plane spin polarization (%) E=150 meV E=50 meV kxkx kyky k x [1/Å] k y [1/Å] Bi 2 Te 3 surface state with spin polarization Γ M K M. Z. Hasan, H. Lin, and A. Bansil, Physics 2, 108 (2009).

22. Fe doped Bi 2 Te 3 STM interference pattern Exp. Theory Collaboration with Prof. Madhavan STM group at Boston college Y. Okada et. al. Phys. Rev. Lett. in press.

23. x y z Band insulator Semimetal EFEF s-like J=3/2 Γ Γ TrivialNon-trivial Γ Topological insulator Hg Te CdTeHgTeDistorted HgTe Pt Sb Lu H. Lin et al., Nature Materials 9, 546 (2010).

24. Half-Heuslers LuPtSbYAuPb abc TiNiSn L Γ X W EFEF Energy (eV) Γ8Γ8 Γ6Γ6 L Γ X W d YPtSb a 0 +2%a 0 Momentum H. Lin et al., Nature Materials 9, 546 (2010).

25. Half-Heusler family H. Lin et al., Nature Materials 9, 546 (2010).

26. Li 2 AgSb x y z Sb Ag Li Te Hg Energy (eV) EFEF a 0 +3%a 0 K Γ T K Γ T K Γ T a 0 +3%a 0 c 0 +3%c 0 Momentum H. Lin et al., arXiv:1004.0999

27. 7-atom layer Te Bi Te Ge Te quintuple layer Te Bi Te Bi Te 124023 GeBi 2 Te 4 Bi 2 Te 3 S.-Y. Su et al., arXiv:1007.5111

28. 9-atom layer Te Bi Te Ge Te quintuple layer Te Bi Te Bi Te 225147 Ge Te 7-atom layer quintuple layer 7-atom layer Te Bi Te Ge Te S.-Y. Su et al., arXiv:1007.5111

29. GeBi 2 Te 4 K Γ M Energy (eV) S.-Y. Su et al., arXiv:1007.5111

30. PbBi 4 Te 7 K Γ M Energy (eV) S.-Y. Su et al., arXiv:1007.5111

31. GeBi 2 Te 4 ARPES S.-Y. Su et al., arXiv:1007.5111

32. Pseudo PbTe: TlBiTe 2 x y z Te (Pb) + + kyky kxkx kzkz Γ L X [111] Tl Te Bi (Pb) H. Lin et al., Physical Review Letters 105, 036404 (2010). 1 Γ 3X 4L PbTe (trivial) --+--+ SnTe (trivial) ------

33. A PbTe supercell PbSnTe 2 TlSbTe 2 L Γ X W Energy [eV] EFEF EFEF BC D L Γ X W Energy [eV] Momentum PbTe SnTe L Γ X E GF PbSnTe 2 TlSbTe 2 EFEF EFEF H. Lin et al., Physical Review Letters 105, 036404 (2010). Band folding

34. AB Trivial Energy [eV] Non-trivial Momentum K Γ M _ _ _ L Γ X W + + + + D C Energy [eV] Direct Gap [eV] V a [eV] EFEF EFEF F TlSbTe 2 Z 2 =-1 Critical L Γ X W 0 + E Z 2 =1Z 2 =-1 Z 2 =1 Z 2 =-1 z Te [Å]

35. S.-Y. Su et al., Science Express online 31 March 2011 [DOI:10.1126/science.1201607]

38. Conclusion We have found several families of topological insulator materials, including Bi 2 Se 3, Half-Heusler compounds, TlBiSe 2, Li 2 AgSb, GeBi 2 Te 4. Unconventional spin texture on single-Dirac-cone topological surface states. Topological insulator materials –Heavy atoms (large spin-orbit coupling) –Structural similarity –Parity analysis and band structure engineering “Best” topological insulator materials –GeBi 2 Te 4 and Bi 2 Te 2 Se –Fermi level inside the bulk gap –Dirac point inside the bulk gap Topological phase transition observed in TlBi(S 1- δ Se δ ) system.

39. x y z Hg Te HgTe YPtSb Hg Te Kr H. Lin et al., Nature Materials 9, 546 (2010). Pt Sb Y KrHgTe Two tricks for adiabatic transformation Insert noble-gas atoms Change nuclear charge Z continuously