Topological InsulatorsYew San Hor

1Department of Chemistryand

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 PhysicsPrinceton University

NSF-MRSEC DMR 0819860

TAR College, Kuala Lumpur, Malaysia13 July 2010

Albert Einstein

E = mc2

Photo by Ch’ng Ping Choon

Einstein’s house at Princeton 1935-55

Princeton Campus

Princeton Chemistry Department

Spring 2009

Princeton Physics Department

Ch’ng Ping Choon

Richard Feymann

Princeton Science Library

Princeton Condensed Matter GroupPhysics & Chemistry

NSF-MRSEC

Robert J. Cava

Matthias Prize for New Superconducting Materials 1996

Chemistry

Nai Phuan Ong

• Director of NSF MRSEC DMR 081986

• 2006 Kamerlingh Onnes Prize (For research accomplishments in HTc superconductor)

Physics

Zahid HasanDavid Hsieh

Bob Cava

Yew San Hor

t = 10-32 sec

Dirac equation (μ∂ μ + mc)ψ = 0

Relativistic energy

E2 = p2c2 + m2c4

E

k

E ~ k

Elementary particles

t ~ 300,000 years

t ~ 300,000 years

Condensed Matter

Non-relativistic energy

E~k2

E

k

Schroedinger Equation:Schroedinger Equation:

t ~ 1.5 × 1010 years

t ~ 1.5 × 1010 years

source: spie.org

LLss

EE

kk

Bulk InsulatorBulk Insulator

Strong Spin-OrbitCoupling

Strong Spin-OrbitCoupling

E~k2E~k2

BCBBCB

BVBBVB

LLss

EE

kk

Bulk InsulatorBulk Insulator

Strong Spin-OrbitCoupling

Strong Spin-OrbitCoupling

E~k2E~k2

BCBBCB

BVBBVB

EE

kkSVBSVB

SCBSCB

E~kE~kSurface ConductorSurface Conductor

…is a band insulator which is characterized by a topological

number and has Dirac-like excitations at its boundaries.

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.

Topology

=

sphere ellipsoid

Topology

=

Topologyin condensed matter electronic phases…

Electron spin property plays an important role.

Example:

AA BB

Insulatormaterial 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

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 ~ k2

BulkConduction Band

Bulk Valence Band

E ~ k

SurfaceConduction Band

SurfaceValence Band

Consider a simpler system 2D electron gas as an analogy

2D electron gas

No boundary

Applied B-field out of plane

When boundary is created, interface with vacuum state→ Edge state.

Electron charge → Quantum Hall effect

Conducting edge state

Insulator

Vacuum

…but this breaks Time Reversal Symmetry.

Electron charge → Quantum Hall effect

Broken Time Reversal Symmetry

Conducting edge state (Reversed with T operator)

Electron charge → Quantum Hall effect

Hall effect “charge”Electron charge → Quantum

Quantum Hall EffectClassical Hall Effect

Lorentz ForceF = -e x B

Hall conductancexy = -ne/B

Quantization of Hall conductance

xy = ie2/h

h/e2 = 25812.807

(Klaus von Klitzing, 1980)

1985 Nobel Prize in Physics

Fractional Quantum Hall Effect

Quantization of Hall conductance

xy = ie2/h

i = 1/3, 1/5, 5/2, 12/5 ..

(discovered in 1982)

Daniel Tsui Horst Stormer

Robert Laughlin

1998 Nobel Prize in Physics

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).

Semiconductor crisisGorden 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

So, we need to find a new material

New materials utilize electron spin property:

Topological Insulators

Topological Insulators

Spintronic devices

- apply electron spin property.

Quantum computer

- apply quantum mechanical phenomena.

- use qubit (quantum bit) instead of bit.

Topological Insulator

is also important for…

1. Quantum Spin Hall Effect.2. The search of Majorana fermion.3. Axion electrodynamic study.4. Magnetic monopole.

3D Topological Insulator

Bulk insulator

L

s

Strong spin-orbit couplingL

s

L

s

L

s

L

s

L

s

Large atomic number → Large orbital moment, L

No boundary

3D Topological Insulator

Bulk insulator

L

s

Strong spin-orbit coupling

L

s

L

s

3D Topological Insulator

Bulk insulator

L

s

Strong spin-orbit coupling

Etrap

Etrap

s

s

k1k2

k x Etrap ~ B

3D Topological Insulator

L

s

Etrap Etrap

s

s-k2 -k1

Time Reversal Symmetry

Invariant!

Bulk insulator

Strong spin-orbit coupling

When T-operator is applied…

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

• Bi • Bi1-xSbx • Sb• Bi2Se3 • Bi2Te3

• Sb2Te3• will look for more…

Nature 452, 970 (2008)

Science 321, 547 (2008)

Nature Physics 5, 398 (2009)

Bi

Bi2Se3

Bi0.9Sb0.1

Bi1-xSbx

Topological insulators

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)

EE

EE

kkSVBSVB

SCBSCB

E~kE~kDirac surface stateDirac surface state

ARPES

Surface Dirac-like spin current.Zero net current, but spin-polarization,protected by Time Reversal Symmetry

k

E

Gaplesssurfacestate

EF

Challenging problem for

Dirac surface state transport measurements

Why not bulk insulator?

Bulk electron is measured

BCB

Imperfect World

Defect chemistry in Bi2Se3

SeSe → VSe●● + Se (gas) + 2 e-

defect

n-type Bi2Se3

10 nm

e-e-

STM

Bi

Se

Se

Bi

Se

Se

Se

Se

Se

Se

Bi

Bi

Bi

Ca-doped in Bi2Se3

2Ca

defect

n-type Bi2Se3

10 nm

e-e- → 2CaBi’ + 2h•

p-type Bi2Se3 STM

Bi

Se

Se

Bi

Se

Se

Se

Se

Se

Se

Bi

Bi

Bi

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 79 195208 (2009)

n- to p-type Bi2-xCaxSe3 topological insulator

X=0

X=0.02

X = 0

X=0.02k

E

k

E

PRB 79 195208 (2009)

x = 0x = 0.005, 0.02, 0.05

Fine tuning in Bi2-xCaxSe3

Bi2Se3 Bi1.9975Ca0.0025Se3 Bi1.99Ca0.01Se3

Nature 460, 1101 (2009)

Metallic behavior.

Non-metallic.Onset at T~130 K.

x = 0.0025x > 0.005x = 0

PRL 103, 246601 (2009)

Bi2-xCaxSe3 transport properties

Bi1.9975Ca0.0025Se3

Quasi-periodic fluctuations

Surface state?

PRL 103 246601 (2009)

Te annealing of Bi2Te3

Annealing temperature: 400 – 440 C (1 week)

Te powder As-grown Bi2Te3 crystal

Transport property of Bi2Te3

kx (Å-1)

EB (

eV)

Fine tuning of Bi2Te3+

As-grown

EF S1S2

S3

S4

Dirac States in topological insulator Bi2Te3

Science (in press)

Non-metallic Metallic

kx

EB

EB

kx

dxx

/dH

HHHH

HH

HH

2D Fermi Surface 3D Bulk State

On the other hand…

Bi2Se3 can be doped to become more conducting…

Superconductor

Cu-intercalated Bi2Se3

By C.Kane (U Penn.)

superconductor

CuxBi2Se3

Cux

Cux

Cux

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.

STM topography of Cu0.15Bi2Se3

T = 4.2 K

Cu clusters on surface. Cu atoms intercalated between layers

Superconductivity of CuxBi2Se3

Superconductivity only found in 0.1 < x < 0.3

Tc~3.8 K

~20 % SC phase

SC phase is not fully connected.

PRL 104 057001 (2010)

Superconductivity of CuxBi2Se3

Upper critical field Hc2 is anisotropic

Strongly type II superconductor

Bi2Se3 topological insulator+

CuxBi2Se3 superconductor

Majorana Fermionic Physics.

(?)

Topological magnetic insulators

• Motivated by:• Axion electrodynamics theory → E x B.• Magnetic monopole → symmetries of Maxwell’s

equations.• by Zhang group (Stanford), arXiv:0908.1537v1

Ferromagnetism in Bi2-xMnxTe3

For axion electrodynamics

1. Quantum Spin Hall Effect: (b) Transport measurements

Point charge

Vacuum

Topologicalinsulator

Magnetic monopole induced

Surface currentinduced

S. C. Zhang, Science 323 1184 (2009)

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

Mn-doped Bi2Te3

Mn-substituted Bi2Te3 (Bi2-xMnxTe3)

Bi/Mn

Te

Te

Bi/Mn

Te

Te

Te

Te

Te

Te

Bi/Mn

Bi/Mn

Bi/Mn

STM topography of Bi1.91Mn0.09Te3

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

DC Magnetization of Bi2-xMnxTe3

TC ~ 9 – 12 K for x = 0.04 and 0.09

ARPES

Topological surface state is still present. Dispersion relation of the state is changed in a subtle fashion.

T=15 K

PRB 81,195203 (2010)

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 (?).

AcknowledgementsCava 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 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 2006.Fu, Kane, Mele, PRL 2007.Moore, Nature 2010.Bjorken, Relativistic Quantum Mechanics.