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Topological Insulators

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1 Topological Insulators
TAR College, Kuala Lumpur, Malaysia 13 July 2010 Topological Insulators Yew San Hor 1Department of Chemistry and 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

2

3

4 Albert Einstein E = mc2

5 Photo by Ch’ng Ping Choon
Einstein’s house at Princeton Photo by Ch’ng Ping Choon

6 Princeton Campus

7 Princeton Chemistry Department
Spring 2009

8

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

14 Physics Nai Phuan Ong 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

16

17 The Big Bang Theory

18 The Big Bang Theory

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

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

21 t ~ 1.5 × 1010 years

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

23 Topological Insulators
source: spie.org

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

25 Topological Insulators
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 Topological Insulators
…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: A B

31 Insulator Topological Insulator A new class of 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
Bulk band insulators. E Bulk Conduction Band Gapped bulk insulator 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 Vacuum Conducting edge state
…but this breaks Time Reversal Symmetry. Electron charge → Quantum Hall effect

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

38 Electron charge → Quantum
Hall effect “charge”

39 Quantum Hall Effect Classical Hall Effect (Klaus von Klitzing, 1980)
Quantization of Hall conductance xy = ie2/h Lorentz Force F = -e x B h/e2 =  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 *Size limit *Heat dissipation
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
Bulk insulator Strong spin-orbit coupling

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

51 3D Topological Insulator
Electron spin Quantum spin Hall effect Surface Dirac-like spin current. Zero net current, but spin-polarization, protected by Time Reversal Symmetry L s L s L s Bulk insulator Strong spin-orbit coupling

52 Topological insulators
Bi Bi1-xSbx Sb Bi2Se3 Bi2Te3 Sb2Te3 will look for more… Bi Bi1-xSbx Science 321, 547 (2008) Bi2Se3 Bi0.9Sb0.1 Nature Physics 5, 398 (2009) Nature 452, 970 (2008)

53 (Angle-resolved photoemission spectroscopy)
Basics of ARPES (Angle-resolved photoemission spectroscopy) ARPES is surface sensitive Can measure E vs k of bulk and surface states separately h Damascelli et al. RMP 2003

54 E~k E E k Dirac surface state ARPES SCB SVB
Surface Dirac-like spin current. Zero net current, but spin-polarization, protected by Time Reversal Symmetry SCB E~k k E Dirac surface state SVB ARPES

55 transport measurements
Challenging problem for Dirac surface state transport measurements E EF BCB Gapless surface state k Bulk electron is measured Why not bulk insulator?

56 Imperfect World

57 Defect chemistry in Bi2Se3
SeSe → VSe●● + Se (gas) + 2 e- e- Bi Se Bi Se Se Bi Se Bi Se Se 10 nm defect Bi STM n-type Bi2Se3 Se

58 STM Ca-doped in Bi2Se3 → 2CaBi’ + 2h• 2Ca Se e- e- Bi Se Bi Se Se Bi
10 nm defect Bi STM n-type Bi2Se3 p-type Bi2Se3 Se

59 Bi2-xCaxSe3 Crystal growth
1st step: (i) stoichiometric mixture of Bi and Se in vacuum quartz tube. (ii) melting at 800 oC for 16 hours. (iii) air-quenching to room temperature. 2nd step: (i) add Ca to Bi2-xSe3 and sealed in vacuum quartz tube. (ii) 400 oC for 16 hours. (iii) 800 oC for 1 day. (iv) 1 day slow cooling to 550 oC. (v) stay at 550 oC for 3 days. PRB (2009)

60 n- to p-type Bi2-xCaxSe3 topological insulator
Can we perform the fine tuning in order to bring the Fermi level to lie in the band gap and hit the Dirac point? X=0.02 k k x = 0 x = 0.005, 0.02, 0.05 PRB (2009)

61 Fine tuning in Bi2-xCaxSe3
How about transport properties? Bi2Se3 Bi1.9975Ca0.0025Se3 Bi1.99Ca0.01Se3 Nature 460, 1101 (2009)

62 Bi2-xCaxSe3 transport properties
Non-metallic. Onset at T~130 K. Metallic behavior. PRL 103, (2009)

63 Quasi-periodic fluctuations
Bi1.9975Ca0.0025Se3 Quasi-periodic fluctuations Surface state? PRL (2009)

64 Annealing temperature: 400 – 440 C (1 week)
Te annealing of Bi2Te3 Te powder As-grown Bi2Te3 crystal Annealing temperature: 400 – 440 C (1 week)

65 Transport property of Bi2Te3
EB (eV) S3 S2 EF S1 As-grown kx (Å-1) Fine tuning of Bi2Te3+

66 Dirac States in topological insulator Bi2Te3
EB EB kx kx H H H H dxx/dH Non-metallic Metallic 2D Fermi Surface 3D Bulk State Science (in press)

67 Bi2Se3 can be doped to become more conducting…
On the other hand… Bi2Se3 can be doped to become more conducting… Superconductor Cu-intercalated Bi2Se3

68 superconductor By C.Kane (U Penn.)

69 Cux CuxBi2Se3 Cux We did a little different approach in doping on Bi2Se3. Cux

70 Cu-doped Bi2Se3 crystal growth
Mixtures of high purity elements Bi, Cu, Se in sealed vacuum quartz tubes. Melt at 850 oC overnight. Slow cooling: 850 → 620 oC for 24 hours. Quench in cold water at 620 oC.

71 STM topography of Cu0.15Bi2Se3
T = 4.2 K Cu clusters on surface. Cu atoms intercalated between layers

72 Superconductivity of CuxBi2Se3
Superconductivity only found in 0.1 < x < 0.3 Tc~3.8 K ~20 % SC phase We focus on the superconductivity of CuxBi2Se3.

73 Superconductivity of CuxBi2Se3
SC phase is not fully connected. PRL (2010)

74 Strongly type II superconductor
Upper critical field Hc2 is anisotropic

75 Bi2Se3 topological insulator + CuxBi2Se3 superconductor  Majorana Fermionic Physics.
(?)

76 Topological magnetic insulators
Motivated by: Axion electrodynamics theory → E x B. Magnetic monopole → symmetries of Maxwell’s equations. by Zhang group (Stanford), arXiv: v1 Ferromagnetism in Bi2-xMnxTe3

77 For axion electrodynamics
Point charge Surface current induced Vacuum Topological insulator S. C. Zhang, Science (2009) Magnetic monopole induced 1. Quantum Spin Hall Effect: (b) Transport measurements

78 Axion electrodynamics
Sharp tip acts as a point charge Induced surface current E field Gold-copper alloy contacts TI crystal I+ V+ V- I- Schematic diagram for the studies of axion electrodynamics 1. Quantum Spin Hall Effect: (b) Transport measurements

79 Mn-substituted Bi2Te3 (Bi2-xMnxTe3)
Mn-doped Bi2Te3 Te Bi/Mn Te Bi/Mn Te Te Bi/Mn Te Bi/Mn Te Te Bi/Mn Te Mn-substituted Bi2Te3 (Bi2-xMnxTe3)

80 STM topography of Bi1.91Mn0.09Te3
Black triangles: substitutional Mn on Bi sites. No Mn-clustering is found.

81 DC Magnetization of Bi2-xMnxTe3
TC ~ 9 – 12 K for x = 0.04 and 0.09

82 ARPES Topological surface state is still present.
T=15 K Topological surface state is still present. Dispersion relation of the state is changed in a subtle fashion. PRB 81, (2010)

83 Summary ● Ca-doped Bi2Se3 → Topological “Insulator”.
suppress bulk conductance to show up Dirac electron surface state. ● Cu-added Bi2Se3 → Superconductor. interface with Bi2Se3 to have proximity effect, Majorana fermionic physics (?). ● Mn-doped Bi2Te3 → Magnetic topological insulator. in search for magnetic monopole (?) and axion electrodynamics studies (?).

84 Acknowledgements References: Thank you Cava group: Funding agencies:
Professor Robert Cava Tyrel McQueen (JHU) Don Vincent West (U Penn) Anthony Williams David Grauer (UC Berkeley) Jared Allred Shuang Jia Siân Dutton Esteban Climent-Pascual Martin Bremholm Ni Ni Ulyana Sorokopoud Linda Peoples Funding agencies: Air Force Office of Scientific Research (AFOSR). Materials Research Science & Engineering Centers (MRSEC). References: Bernevig, Hughes, Zhang, Science 2006. Fu, Kane, Mele, PRL 2007. Moore, Nature 2010. Bjorken, Relativistic Quantum Mechanics. Thank you


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