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Topological Insulators Yew San Hor 1 Department of Chemistry and J. G. Checkelsky 2, A. Richardella 2, J. Seo 2, P. Roushan 2, D. Hsieh 2, Y. Xia 2, M. Z. Hasan 2, A. Yazdani 2, N. P. Ong 2, and R. J. Cava 1 2 Department of Physics Princeton University NSF-MRSEC DMR TAR College, Kuala Lumpur, Malaysia 13 July 2010

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Albert Einstein E = mc 2

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Photo by Chng Ping Choon Einsteins house at Princeton

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Princeton Campus

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Princeton Chemistry Department Spring 2009

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Princeton Physics Department

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Chng Ping Choon Richard Feymann

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Princeton Science Library

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Princeton Condensed Matter Group Physics & Chemistry NSF-MRSEC

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

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

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Zahid Hasan David Hsieh Bob Cava Yew San Hor

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t = sec Dirac equation ( μ μ + mc)ψ = 0 Relativistic energy E 2 = p 2 c 2 + m 2 c 4 E k E ~ k Elementary particles t ~ 300,000years t ~ 300,000 years

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Condensed Matter Non-relativistic energy E~k 2 E k Schroedinger Equation:

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t ~ 1.5 × years

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source: spie.org

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L L s s E E k k Bulk Insulator Strong Spin-Orbit Coupling Strong Spin-Orbit Coupling E~k2E~k2 E~k2E~k2 BCB BVB

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L L s s E E k k Bulk Insulator Strong Spin-Orbit Coupling Strong Spin-Orbit Coupling E~k2E~k2 E~k2E~k2 BCB BVB EE kk SVB SCB E~kE~k E~kE~k Surface Conductor

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

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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.

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Topology = sphereellipsoid

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Topology =

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

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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

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Topological Insulators Bulk band insulators. Ingredients: Strong spin-orbit coupling. Time reversal symmetry. E k E k Gapless surface state Gapped bulk insulator Gapless Dirac excitations at its boundaries. E ~ k 2 Bulk Conduction Band Bulk Valence Band E ~ k Surface Conduction Band Surface Valence Band

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Consider a simpler system 2D electron gas as an analogy

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2D electron gas No boundary

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

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

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

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Hall effect charge Electron charge Quantum

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Quantum Hall Effect Classical Hall Effect Lorentz Force F = -e x B Hall conductance xy = -ne/B Quantization of Hall conductance xy = ie 2 /h h/e 2 = (Klaus von Klitzing, 1980) 1985 Nobel Prize in Physics

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

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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).

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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

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So, we need to find a new material

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New materials utilize electron spin property: Topological Insulators

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

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

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

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

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3D Topological Insulator Bulk insulator L s Strong spin-orbit coupling E trap s s k1k1 k2k2 k x E trap ~ B

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3D Topological Insulator L s E trap s s -k 2 -k 1 Time Reversal Symmetry Invariant! Bulk insulator Strong spin-orbit coupling When T-operator is applied…

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

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Bi Bi 1-x Sb x Sb Bi 2 Se 3 Bi 2 Te 3 Sb 2 Te 3 will look for more… Nature 452, 970 (2008) Science 321, 547 (2008) Nature Physics 5, 398 (2009) Bi Bi 2 Se 3 Bi 0.9 Sb 0.1 Bi 1-x Sb x Topological insulators

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

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

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

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Imperfect World

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Defect chemistry in Bi 2 Se 3 Se Se V Se + Se (gas) + 2 e - defect n-type Bi 2 Se 3 10 nm e-e- e-e- STM Bi Se Bi Se Bi

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Ca-doped in Bi 2 Se 3 2Ca defect n-type Bi 2 Se 3 10 nm e-e- e-e- 2Ca Bi + 2h p-type Bi 2 Se 3 STM Bi Se Bi Se Bi

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

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n- to p-type Bi 2-x Ca x Se 3 topological insulator X=0 X=0.02 X = 0 X=0.02 k E k E PRB (2009) x = 0 x = 0.005, 0.02, 0.05

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Fine tuning in Bi 2-x Ca x Se 3 Bi 2 Se 3 Bi Ca Se 3 Bi 1.99 Ca 0.01 Se 3 Nature 460, 1101 (2009)

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Metallic behavior. Non-metallic. Onset at T~130 K. x = x > x = 0 PRL 103, (2009) Bi 2-x Ca x Se 3 transport properties

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Bi Ca Se 3 Quasi-periodic fluctuations Surface state? PRL (2009)

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Te annealing of Bi 2 Te 3 Annealing temperature: 400 – 440 C (1 week) Te powderAs-grown Bi 2 Te 3 crystal

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Transport property of Bi 2 Te 3 k x (Å -1 ) E B (eV) Fine tuning of Bi 2 Te 3+ As-grown EFEF S1 S2 S3 S4

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Dirac States in topological insulator Bi 2 Te 3 Science (in press) Non-metallic Metallic kxkx EBEB EBEB kxkx d xx /dH H H H H H H H H 2D Fermi Surface3D Bulk State

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On the other hand… Bi 2 Se 3 can be doped to become more conducting… Superconductor Cu-intercalated Bi 2 Se 3

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By C.Kane (U Penn.) superconductor

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Cu x Bi 2 Se 3 Cu x

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Cu-doped Bi 2 Se 3 crystal growth Mixtures of high purity elements Bi, Cu, Se in sealed vacuum quartz tubes. Melt at 850 o C overnight. Slow cooling: o C for 24 hours. Quench in cold water at 620 o C.

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STM topography of Cu 0.15 Bi 2 Se 3 T = 4.2 K Cu clusters on surface. Cu atoms intercalated between layers

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Superconductivity of Cu x Bi 2 Se 3 Superconductivity only found in 0.1 < x < 0.3 T c ~3.8 K ~20 % SC phase

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SC phase is not fully connected. PRL (2010) Superconductivity of Cu x Bi 2 Se 3

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Upper critical field H c2 is anisotropic Strongly type II superconductor

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Bi 2 Se 3 topological insulator + Cu x Bi 2 Se 3 superconductor Majorana Fermionic Physics. (?)

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Topological magnetic insulators Motivated by: Axion electrodynamics theory E x B. Magnetic monopole symmetries of Maxwells equations. by Zhang group (Stanford), arXiv: v1 Ferromagnetism in Bi 2-x Mn x Te 3

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

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

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Mn-doped Bi 2 Te 3 Mn-substituted Bi 2 Te 3 (Bi 2-x Mn x Te 3 ) Bi/Mn Te Bi/Mn Te Bi/Mn

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STM topography of Bi 1.91 Mn 0.09 Te 3 Black triangles: substitutional Mn on Bi sites. No Mn-clustering is found.

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DC Magnetization of Bi 2-x Mn x Te 3 T C ~ 9 – 12 K for x = 0.04 and 0.09

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

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Summary Ca-doped Bi 2 Se 3 Topological Insulator. suppress bulk conductance to show up Dirac electron surface state. Cu-added Bi 2 Se 3 Superconductor. interface with Bi 2 Se 3 to have proximity effect, Majorana fermionic physics (?). Mn-doped Bi 2 Te 3 Magnetic topological insulator. in search for magnetic monopole (?) and axion electrodynamics studies (?).

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Acknowledgements Cava group: 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 Ulyana Sorokopoud Linda Peoples Funding agencies: Air Force Office of Scientific Research (AFOSR). Materials Research Science & Engineering Centers (MRSEC). Thank you References: Bernevig, Hughes, Zhang, Science Fu, Kane, Mele, PRL Moore, Nature Bjorken, Relativistic Quantum Mechanics.

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