Direct Probing the Electronic Structures of

Topological Insulators

Yulin Chen SLAC National Accelerator Laboratory

Stanford University

APS March Meeting Tutorial 20 March 2011

Condensed matter physics Understand the collective properties of assemblies of particles

Conductor Insulator Semi-conductor

…

Superconductor

Electronic structures

Insulator Conductor

Kx

Ky

E

An Insulator that conducts

What is a topological insulator (TI)

3D real space Band structure

In gap 2D surface state

Conduction

band

Valence

band

Band structure

In gap 1D surface state

Valence band

Conduction band

2D real space

Why “topological”

Sphere Torus

Regular insulator Topological insulator

Topologically distinct objects

No back-scattering rule (by non-magnetic impurities)

“Locking” between current & spin

Unique surface state properties of TIs

Robustness of the topological surface state

Surface state in topological insulator

robust Surface state in regular insulator

vulnerable

(Wilczek, 1987)

(Qi, et. al., 2009)

(Qi, Hughes & Zhang, 2008)

Majorana Fermion

Akhmerov, Nilsson, & Beenakker, 2009

Scientific implications

Image magnetic monopole from a source charge

Half charge on a magnetic domain wall

Axion electrodynamics

……

Application potentials

Electronics more efficient (Longer functional time)

Spintronics without magnet (Faster & less consumption)

Quantum Computation

……

Higher density integrated circuit

Thermoelectric generators

Theory: Kane, Fu, Zhang, Qi, Moore, Roy, Nagosa, Franz, Lee, Dai, Fang, …

Materials: Molenkamp, Cava, Fisher, Cui, Lee, Ando…

Transport: Molenkamp, Ong, Fisher, Cui, Ando, Morpurgo, Jarillo-Herrero…

ARPES: Hasan, Hsieh, Shen, Chen, Xue, Taniguchi Boresenko, Nuh Gedik…

STM: Yazdani, Kapitulnik, Xue, Hanaguri, Manoharan…

Optical: Basov, Paglione …

Intensive research activities

World wide effort:

ARPES

Transport STM/STS

Optical Spectroscopy

Theory Development

Material Development

…

How to find TIs Search for the unique band structure

Topological insulator

Regular conductor

Regular insulator

How to “see” band structures Angle Resolved Photoemission Spectroscopy (ARPES)

Z

e-

q hn

Heinrich Hertz Albert Einstein

ARPES: k-space Microscope

Energy Conservation EB= hn - Ekin - F

Momentum Conservation K|| = k||+ G||

General principle

𝐼𝑃𝐸𝑆 ∝ 𝐹(𝑇) ∙ 𝛿(𝐸𝑓−𝐸𝑖−ℏ𝜔) ∙ | 𝝍𝒇, 𝑵𝑯𝒊𝒏𝒕 𝝍𝒊, 𝑵

|𝟐

𝐹(𝑇) ∙ | 𝝓𝒇,𝑬𝒌 𝑯𝒊𝒏𝒕 𝝓𝒊,𝒌 |2 𝝍𝒇𝒌𝑺(𝑵−𝟏)|𝝍𝒊

𝒌 (𝑵−𝟏) |2

𝑆 𝛿(𝐸𝑓,𝐸𝑘+𝐸𝑆(𝑁−1)−𝐸𝑖−ℏ𝜔)

+ (Suddent approximation)

|𝜓𝑖, 𝑁 = |𝜙𝑖,𝑘 |𝜓𝑖𝑘(𝑁−1)

|𝜓𝑓, 𝑁 = |𝜙𝑓,𝐸𝑘 |𝜓𝑓𝑘(𝑁−1)

+

𝐹(𝑇) ∙ 𝛿(𝐸𝑓−𝐸𝑖−ℏ𝜔) ∙ | 𝝓𝒇,𝑬𝒌𝑯𝒊𝒏𝒕 𝝓𝒊,𝒌 𝝍𝒇

𝒌(𝑵−𝟏)|𝝍𝒊

𝒌(𝑵−𝟏) |2 =

Interacting system

E

k

EF

One electron state

Remaining N-1 Electron state

Band dispersion Non-interacting system

E

k

E

k

EF EF

ARPES Spectra Electron band

𝐹(𝑇) ∙ 𝛿(𝐸𝑓−𝐸𝑖−ℏ𝜔) ∙ | 𝝓𝒇,𝑬𝒌𝑯𝒊𝒏𝒕 𝝓𝒊,𝒌 |2

= (Non-interacting system)

3D FS (e.g. FS from bulk state)

kz

kx ky

kz

kx ky

2D FS (e.g. FS from surface state)

How to discriminate bulk & surface?

E1

E2

E3

kx

ky

E1

E2

E3

E1

E2

E3

kx

ky

E1

E2

E3

Ek =ℏ2

2𝑚(𝑘𝑥

2 + 𝑘𝑦2 + 𝑘𝑧

2)

ARPES Analyzer

Electrostatic hemispherical analyzer

Entrance slit

Pre-lens

Photon beam

X-ray tube Gas discharge lamp Synchrotron Laser

kx

ky

E

E(e

V)

Kx(1/Å)

EF

Band dispersion cut

Synchrotron based ARPES station

2D Electron

analyzer

Photon

in

Experiment

Chamber

Sample

ALS Bemline 10

Modern ARPES data taking

Data acquired Experimental setup

2D Electron

analyzer

Photon

in

Experiment

Chamber

Sample

ALS Bemline 10

ARPES on TI Princeton

Stanford

International efforts

Bulk band structure

Realization of TI state in Bi2Te3 Y. L. Chen, et. al., Science 325, 178 (2009)

Crystal Structure Bulk Fermi surface

(n-type)

TI Checklist: 1. There exist Dirac surface states 2. There are odd number of Dirac fermions in a Brillouin Zone

EF

3. The EF is in the gap

0 0.2 -0.2

k y(1

/Å)

0

0.2

-0.2

0

0.2

-0.2

0

0.2

-0.2

Dirac Fermion’s Surface nature

0 0.2 -0.2

Realization of TI state in Bi2Te3

Dirac fermion

TI Checklist: 1. There exist Dirac surface states 2. There are odd number of Dirac fermions in a Brillouin Zone 3. The EF is in the gap

Bulk band gap E2=165meV

Y. L. Chen, et. al., Science 325, 178 (2009)

TI Checklist: 1. There exist Dirac surface states 2. There are odd number of Dirac fermions in a Brillouin Zone 3. The EF is in the gap

Single Dirac fermion in each BZ

Realization of TI state in Bi2Te3

Evolution of the Band

Y. L. Chen, et. al., Science 325, 178 (2009)

TI Checklist: 1. There exist Dirac surface states 2. There are odd number of Dirac fermions in a Brillouin Zone 3. The EF is in the gap

Realization of TI state in Bi2Te3

EF(undoped) BCB bottom

Dirac point position

BVB top

Fermi- Surface

Band Dispersion

Gap Gap Gap Gap

Different charge doping

Y. L. Chen, et. al., Science 325, 178 (2009)

Other single Dirac cone TIs

TlBiSe2

K. Kuroda, et.al., PRL (2010) T. Sato, et.al., PRL (2010) Y. L. Chen, et.al., PRL (2010)

Bi2Se3

Y. Zhang, et.al., Nat. Phys. (2010) Y.L. Chen, et.al., Science (2010) Y. Xia, et.al., Nat. Phys. (2009)

Protection of the time reversal symmetry (TRS)

Massless Dirac fermion is protected by time reversal symmetry (Kramers’ theorem)

Non-magnetic bulk & surface doing

Dirac point

kx

ky

E

ky kx

ky

E

TRS protection – bulk doping Y. L. Chen, et. al., Science 329, 659 (2010)

In gap Dirac point of Bi2Se3

Compare to Bi2Te3

Bulk doping

Non-magnetic impurities

Oxygen Hydrogen Carbon monoxide Carbon dioxide Potassium

… Surface doping

(i) (ii) (iii) (iv) (v)

Photo assisted surface Oxygen doping

TRS protection – surface doping Y. L. Chen, et. al., Science 329, 659 (2010)

Another example

NO2

Surface adsorption

D. Hsieh, et.al., Nature (2009)

What if TRS is broken?

Formation of massive Dirac fermion if TRS is broken

kx

ky

E

ky kx

ky

E

+

Magnetic doing

Dirac Gap

Dirac fermion becomes massive

Magnetic impurities

Braking the Dirac point

Summary of different doping effects

(Bi1-dFed)2Se3

Y. L. Chen, et. al., Science 329, 659 (2010)

Another example

Fe Surface deposition

A. Wray, et.al., Nat. Phys. (2011)

Realize insulating massive Dirac fermion state

Magnetic impurity

+ EF Tuning

Realize new phenomena Provide control for applications

I/M

TI

Why insulating massive Dirac fermion state?

Image Surface Monopole

Half Hall conductance sH=e2/2h

Turn off surface conduction

All electric magnetic writing

2D quantum anomalous Hall state

Quantum spin Hall

Quantum anomalous Hall

Y. L. Chen, et. al., Science 329, 659 (2010)

New topological states Search for topological superconductors

Some candidates

CuxBi2Se3 , PdxBi2Te3 TlBiTe2

Hor, et. al., (2010) Fu, Berg, (2010)

Wray, et.al., (2010)

Cu/Pd Bi Se

Bi2Se3

Bi2Se3

(Cu/Pd)x

(Cu/Pd)x

(Cu/Pd)x

Hein/Swiggard, (1970) Yan, et. al., (2010)

Chen, et. al., (2010)

Majorana fermion

Quantum computation

Fu, Kane (2008) Hasan, Kane (2010)

Qi, Zhang (2010)

A candidate for topological superconductors

Band structure of TlBiTe2

Y. L. Chen et. al., Phys. Rev. Lett. 105, 266401 (2010)

Hein & Swiggard Phys. Rev. Lett. 24, 53 (1970)

Superconducting transition

A candidate for topological superconductors Y. L. Chen et. al., Phys. Rev. Lett. 105, 266401 (2010)

Part I: Summary

Electronic structures of Bi2Te3/Bi2Se3 and TlBiSe2/TlBiTe2 families show a

single Dirac cone on the surface

EF can be tuned into the bulk gap upon proper doping; and both p- & n-

dopings can be achieved for possible applications

The topological surface state is robust against impurities when the TRS is

present

Dirac fermions become massive when TRS is broken

Unusual band structure of TlBiTe2 makes it a possible candidate for

topological superconductor

Advanced instrumentation development Future of photoemission spectroscopy

Lower sample temperature (~ 1K)

Improve energy reso lut ion (~ 100meV)

Improve s ignal intensi ty (Brighter l ight source)

f(k,E,s,t)

Spin-resolution Time-resolution

t1 t2 t3

T = 0

Explore new dimensions

More efficient data taking (2D->3D)

Prototype 3D time-of-flight analyzer

(Developed in LBNL)

Explore electron spin

Charge “e”

Spin “S” f(k,E,s)

Spin Energy

Momentum

Heavy nuclei target

e-counter

e-

e- +

Mott scattering

e-

Analyzer Entrance Slit

Analyzer Exit Slit

Mott-detector

hn

Data dimension: 0D Relative efficiency: 10-4

(Compared to regular ARPES)

Spin-resolved electronic structure

D. Hsieh, et. al., Nature 460, 1101 (2009)

ARPES Spin-ARPES

Regular ARPES 3D structure

Spin-ARPES 1D structure

Y. L. Chen, Ph.D Thesis 2008

D. Hsieh, et. al., Science 323, 919 (2009)

Sb

Y. L. Chen, et. al., PRL 105 266401 (2010)

Souma, et. al., arxiv.org/abs/1101.3421 (2011)

TlBiSe2

Y. L. Chen, et. al., Science 325, 178 (2009)

D. Hsieh, et. al., Nature 460, 1101 (2009)

Bi2Te3

Spin-resolved electronic structure

Mott Scattering Exchange Scattering

Heavy nuclei target

e-counter

Magnetic thin film

e-

e-

e-

e-

e-counter

Electron energy: 20~100keV

Electron energy: 2~5eV

Lower Efficiency (10-4) Higher Efficiency

( 1~2 order higher than Mott detector)

More efficient spin-detection is needed

Even more degrees of freedom can be explored

Study on the dynamics of electrons f(k,E,s,t)

Pump Pulse

Probe Pulse

Photoelectron

Sample

Data collection & analysis

An example of time-resolved ARPES

Time-resolution Bi2Te3

Figures courtesy of J. Sobota

What’s next?

New TIs with richer properties

Larger bulk gap, better chemical, physical & electronic properties

Correlated TI systems

Topological Quantum materials

Thin film and nano-scale Topological quantum materials Topological phenomena in low dimension

Better control on properties

Novel topological quantum phases Topological superconductors

Quantum anomalous Hall insulator

Novel topological functional devices, or “topotronics”

ALS BL 10.0.1 (S-K Mo, M. Hashimoto, Z. Hussain)

CAS: X. Dai, Z. Fang

DOE: Funding support

Shen group (Z-X Shen, Z.K. Liu & whole group)

Fisher group (I. R. Fisher, J. Analytis, J-H Chu)

Zhang group (S.C. Zhang, H.J. Zhang, B.H. Yan)

X. L. Qi

BL 5-4 (D.H. Lu, R. Moore)

TIT: T. Sasagawa

Acknowledgement

Thank you!

H. Peng, et. al., Nat. Mat. 9, 225 (2010)

ARPES results supported by transport

A-B effect