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

Physics 2, 108 (2009)

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

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

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

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

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

Parity analysis

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

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

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

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

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.

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

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

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

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

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

Quasiparticle interference (QPI) Without matrix elementWith matrix element

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

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).

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.

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).

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).

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

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:

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

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

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

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

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

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, (2010). 1 Γ 3X 4L PbTe (trivial) SnTe (trivial)

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, (2010). Band folding

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]

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

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.

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