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**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

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Albert Einstein E = mc2

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**Photo by Ch’ng Ping Choon**

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

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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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Richard Feymann Ch’ng Ping Choon

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**Princeton Science Library**

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**Princeton Condensed Matter Group**

Physics & Chemistry NSF-MRSEC

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**Matthias Prize for New Superconducting Materials 1996**

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

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**Physics Nai Phuan Ong Director of NSF MRSEC DMR 081986**

2006 Kamerlingh Onnes Prize (For research accomplishments in HTc superconductor) Nai Phuan Ong

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Zahid Hasan Yew San Hor David Hsieh Bob Cava

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The Big Bang Theory

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The Big Bang Theory

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**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

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**Schroedinger Equation:**

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

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t ~ 1.5 × 1010 years

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**New condensed matter phase**

t ~ 1.5 × 1010 years New condensed matter phase

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**Topological Insulators**

source: spie.org

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**Topological Insulators**

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

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**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

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**Topological Insulators**

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

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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 = sphere ellipsoid

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Topology =

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**Topology in condensed matter electronic phases… Electron spin property**

plays an important role. Example: A B

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**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

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**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

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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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**Insulator Vacuum Conducting edge state**

…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) Broken Time Reversal Symmetry Electron charge → Quantum Hall effect

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**Electron charge → Quantum**

Hall effect “charge”

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**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

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**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 ..

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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 *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

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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**

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

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**3D Topological Insulator**

Bulk insulator Strong spin-orbit coupling

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**3D Topological Insulator**

Etrap Etrap k x Etrap ~ B s k1 k2 s L s Bulk insulator Strong spin-orbit coupling

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**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

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**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

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**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)

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**(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

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**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

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**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?

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Imperfect World

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**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

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**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

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**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)

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**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)

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**Fine tuning in Bi2-xCaxSe3**

How about transport properties? Bi2Se3 Bi1.9975Ca0.0025Se3 Bi1.99Ca0.01Se3 Nature 460, 1101 (2009)

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**Bi2-xCaxSe3 transport properties**

Non-metallic. Onset at T~130 K. Metallic behavior. PRL 103, (2009)

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**Quasi-periodic fluctuations**

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

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**Annealing temperature: 400 – 440 C (1 week)**

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

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**Transport property of Bi2Te3**

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

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**Dirac States in topological insulator Bi2Te3**

EB EB kx kx H H H H dxx/dH Non-metallic Metallic 2D Fermi Surface 3D Bulk State Science (in press)

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**Bi2Se3 can be doped to become more conducting…**

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

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superconductor By C.Kane (U Penn.)

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

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**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.

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**STM topography of Cu0.15Bi2Se3**

T = 4.2 K Cu clusters on surface. Cu atoms intercalated between layers

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**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.

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**Superconductivity of CuxBi2Se3**

SC phase is not fully connected. PRL (2010)

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**Strongly type II superconductor**

Upper critical field Hc2 is anisotropic

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**Bi2Se3 topological insulator + CuxBi2Se3 superconductor Majorana Fermionic Physics.**

(?)

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**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

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**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

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**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

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**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)

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**STM topography of Bi1.91Mn0.09Te3**

Black triangles: substitutional Mn on Bi sites. No Mn-clustering is found.

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**DC Magnetization of Bi2-xMnxTe3**

TC ~ 9 – 12 K for x = 0.04 and 0.09

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**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)

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**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 (?).

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**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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Majorana Fermions and Topological Insulators

Majorana Fermions and Topological Insulators

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