Topological Insulators

1. Yew San Hor 1Department of Chemistry and Topological Insulators TAR College, Kuala Lumpur, Malaysia 13 July 2010 J. G. Checkelsky2, A. Richardella2, J. Seo2, P. Roushan2, D. Hsieh2, Y. Xia2, M. Z. Hasan2, A. Yazdani2, N. P. Ong2, and R. J. Cava1 2Department of Physics Princeton University NSF-MRSEC DMR 0819860

4. Albert Einstein E = mc2

5. Einstein’s house at Princeton 1935-55 Photo by Ch’ng Ping Choon

6. Princeton Campus

7. Princeton Chemistry Department Spring 2009

9. Princeton Physics Department

10. Richard Feymann Ch’ng Ping Choon

11. Princeton Science Library

12. Princeton Condensed Matter Group Physics & Chemistry NSF-MRSEC

13. Chemistry Matthias Prize for New Superconducting Materials 1996 Robert J. Cava

14. Physics • Director of NSF MRSEC DMR 081986 • 2006 Kamerlingh Onnes Prize (For research accomplishments in HTc superconductor) Nai Phuan Ong

15. Zahid Hasan Yew San Hor David Hsieh Bob Cava

17. The Big Bang Theory

18. The Big Bang Theory

19. t = 10-32 sec t ~ 300,000years Relativistic energy E2 = p2c2 + m2c4 Elementary particles E k Dirac equation (μ∂μ + mc)ψ = 0 E ~ k

20. Non-relativistic energy t ~ 300,000years Schroedinger Equation: E Condensed Matter k E~k2

21. t ~ 1.5 × 1010 years

22. t ~ 1.5 × 1010 years New condensed matter phase

23. Topological Insulators source: spie.org

24. Bulk Insulator L E s BCB k BVB Strong Spin-Orbit Coupling E~k2 Topological Insulators

25. E Bulk Insulator SCB E~k k L E Surface Conductor s SVB BCB k BVB Strong Spin-Orbit Coupling E~k2 Topological Insulators

26. …is a band insulator which is characterized by a topological number and has Dirac-like excitations at its boundaries. Topological Insulators

27. Topology …is the mathematical study of the spatial properties that are preserved under continuous deformations of objects, for examples, twisting and stretching, but no tearing or gluing.

28. Topology = sphere ellipsoid

29. Topology =

30. Topology in condensed matter electronic phases… Electron spin property plays an important role. Example: B A

31. Insulator material does not conduct electric current 1.Band Insulator (valence band completely filled). 2. Peierls Insulator (lattice deformation). 3. Mott Insulator (Coulomb repulsion). 4. Anderson Insulator (impurity scattering). A new class of insulator Topological Insulator

32. Topological Insulators E Bulk Conduction Band Gapped bulk insulator • Bulk band insulators. E ~ k2  k Bulk Valence Band • Gapless Dirac excitations at its boundaries. E Surface Conduction Band Gapless surface state E ~ k k Ingredients: Strong spin-orbit coupling. Time reversal symmetry. Surface Valence Band

33. Consider a simpler system 2D electron gas as an analogy

34. 2D electron gas No boundary

35. Applied B-field out of plane When boundary is created, interface with vacuum state → Edge state. Electron charge → Quantum Hall effect

36. Insulator Conducting edge state Vacuum …but this breaks Time Reversal Symmetry. Electron charge → Quantum Hall effect

37. Conducting edge state (Reversed with T operator) Broken Time Reversal Symmetry Electron charge → Quantum Hall effect

38. “charge” Electron charge → Quantum Hall effect

39. Classical Hall Effect Quantum Hall Effect (Klaus von Klitzing, 1980) Quantization of Hall conductance xy = ie2/h Lorentz Force F= -e x B h/e2 = 25812.807  Hall conductance xy = -ne/B 1985 Nobel Prize in Physics

40. Fractional Quantum Hall Effect (discovered in 1982) Daniel Tsui Horst Stormer 1998 Nobel Prize in Physics Quantization of Hall conductance xy = ie2/h Robert Laughlin i = 1/3, 1/5, 5/2, 12/5 ..

41. Devices utilize electron charge property: Semiconductor Transistor, AT&T Bell Labs (1947). Single Crystal Germanium (1952). Single Crystal Silicon (1954). IC device, Texas Instrument (1958). IC Product, Fairchild Camera (1961). Microprocessor, Intel (1971). Personal Computer (1975).

42. Semiconductor crisis Gorden Moore (co-founder of Intel 1964): Number of transistors doubled every 12 months while price unchanged. In 1980s, number of transistors doubled every 18 months. *Size limit *Heat dissipation

43. So, we need to find a new material

44. New materials utilize electron spin property:Topological Insulators

45. Topological Insulators Spintronic devices - apply electron spin property. Quantum computer - apply quantum mechanical phenomena. - use qubit (quantum bit) instead of bit.

46. Topological Insulator is also important for… 1. Quantum Spin Hall Effect. 2. The search of Majorana fermion. 3. Axion electrodynamic study. 4. Magnetic monopole.

47. 3D Topological Insulator Strong spin-orbit coupling L L s s L s L s L s L s Bulk insulator No boundary Large atomic number → Large orbital moment, L

48. 3D Topological Insulator L L s s L s Bulk insulator Strong spin-orbit coupling

49. 3D Topological Insulator Etrap Etrap k x Etrap ~ B s k2 k1 s L s Bulk insulator Strong spin-orbit coupling

50. 3D Topological Insulator Etrap Etrap s -k2 -k1 s When T-operator is applied… Time Reversal Symmetry Invariant! Bulk insulator s Strong spin-orbit coupling L