Experimental Discovery of

Topological InsulatorsBi-Sb alloys, Bi2Se3, Sb2Te3 and Bi2Te3

Observation of Quantum-Hall-like effects Without magnetic field

M. Zahid HasanJoseph Henry Laboratories of Physics

Department of Physics, Princeton University

1st European Workshop on Topological InsulatorsEcole Normale Supérieure de Lyon, France

December, 2009

Hsieh et.al., NATURE „08Xia et.al., NATURE Phys „09

Hsieh et.al., SCIENCE ‟09

Hsieh et.al., NATURE „09

Roushan et.al., NATURE‟09MZH et.al., PHYSICS‟09

KITP (2007, 2008)

Search & Discovery: PHYSICS TODAY ‟09 (April, August)

A new quantum phase of matter (z2= -1) has been observed (Topological Insulator) which is distinct from the quantum Hall effect phase or any other 2D electron systs.

So far 2 classes of TIs (4 compounds) discovered by us, SC found, FM found

KITP (2007-08) Results were presented at KITP

NATURE (2008) News&Views : Nature (2008)

Phys.Rev. B (09) Editor’s Suggestion & Physics (09)SCIENCE (2009) News&Views : Science (2009)NATURE PHYS (2009) News&Views : Nature Phys. (2009)

PHYSICS TODAY “Search&Discovery” April (2009)

See commentary by F. Wilczek in NATURE (2009)also by B.I. Halperin at CMP Journal Club (2008)

NATURE (2009) Topo Graphene News&Views : Nature (2009)Phys. Rev. Letts (09) Dirac fermions controlledNATURE (2009) Anti-localization of Helical Dirac Fermions

PHYSICS (2009) PRL-ViewPoint on Spin-texture in Warped SS StatesPHYSICS TODAY Insulator’s Metallic Side, NewsPick August (2009)

Our works on Topo Insulators :

Hasan 09

Physics Team

David Hsieh, Dong Qian, Andrew Wray, Matt Xia, MZH

High-purity Materials/Crystal Growth/Characterization

Y.S. Hor, R.J. Cava (Chem), J. Chechelsky, N.P. Ong (Physics), D. Hsieh, Y. Xia, MZH (Physics), N.L. Wang (Beijing), H. Eisaki (Tokyo)

Undergrads/JP-Thesis:

Cathy Kunkel (PU Physics)

Ram Shankar (PU Math)

Matt Severson (PU Engg)

Lindsay Gorman (Harvard)

Alexei Fedorov

(BL-12)

Broken Symmetry Phases of Matter/Forces

?

?

Hasan 09

Superfluidity, Superconductivity : NP ‘72, ‘73, ‘87, ‘96, ’03

Superconductivity without BCS-like paradigm?

New/alternative routes to Higher-Tc superconductivity

Localization, Disorder, Q-Magnetism : NP ‘70, ‘77, ‘94, ’07

Spins without electron’s charge? Spin-liquid TO, Fractionalization?

Quantum Hall Effect : Nobel Prize 1985, 1998

QHE without Magnetic-field? Non-Abelian States?

Majorana fermions? Topological q-computing ?

Fundamental Condensed Matter PhysicsNew Phases of Matter in quantum electron systems

Phase Transition, Condensation : NP 1982, 2001

Phase transitions without T (T=0)? Deconfined Criticality ?

New universality classes?

Hasan 09

Collaborative Spectrometer development

Exotic Superconductors Fermi surface, Spontaneous SB, SC gap, Self-energy

Frustrated Magnetism Spinon dynamics, Quantum Criticality4000

3000

2000

1000

0

-1000

Inte

nsity

605040302010

Two Theta (Degree)

Polarized Neutron Scattering

Phys. Rev.Lett. (subm.) (2009)

Z. Tan Senior-Thesis, P.U. (2005)

Topological Insulators Quantum Spin Hall effect, Topological-Order, Spintronics

Spin-Resolved ARPES, Mott Spectroscopy

Nature (2008), N&V: Nature Phys (2008)

Science (2009), N&V: Science (2009)

Nature Phys (2009), N&V: NatPhys (09)

Nature(2009a), PRL(09), Nature(2009b)

Quantum Spin-liquid

TL Organics (2006)

K. Kanoda

MERLIN Project

Spin Project

2009

Nature (in rev) (2009), Phys.Rev.Lett.(2009)

PRL N&V: Physics (2009)Phys.Rev.Lett.s (2007a,b,c), PRL/B (2008)

Phys.Rev.Lett.s (2004, 2006 a,b,c)

SC gap in FeAs supercond

MERLIN

Photoemission, Inelastic X-ray Scattering

2004-09

Hasan Group

Topo-insulators in nature

2D Topological Insulators: Ga(Al)As, Hg(Cd)Te

Quantum Hall state (Breaks T-invariance)

Cryogenic, Large Magnetic field, high-purity crystals

Quantum spin Hall state (Preserves T-invariance)

Cryogenic, No Magnetic field, high-purity crystals,

3D Topological Insulator: Bi-Sb, Bi2(Se/Te)3

Strong topological insulator (Preserves T-invariance)

Room Temperature operation, No magnetic field, Dirty crystals

Hasan 09

Physics Today 06

Hasan 09

Bi2(Se/Te)3 classNature Physics 09

Nature 09

PRL 09

also Sb2Te3

Bi-Sb classNature 08

Science 09

Nature 09

Discovery of 2 Classes (4 compounds) of 3D Topological Insulators

(1,000)

(1,111)

Hasan 09

Hall Effect at high magnetic fields

Discrete Energy LevelsElectrons + strong magnetic field

Bulk energy gap

Band Insulator?

Hasan 09

Bulk Insulator but Conduction through the Edge

Conduction through the boundary

Finite Hall Conductivity

Quantum Hall EffectK. von Klitzing et.al., (Nobel Prize, ‘85)

D.C. Tsui et.al.,(Nobel Prize, ‘98)

Quantum Hall State : Topological, TR-breaking

Hall conductance:

sxy = ne2/h

n = Chern no. ( Edge states)

21( ) ( )

2 BZn d u u

i k kk k k

Electron-occupied Bulk bands

Finite n topologically “protected” edge-states

Topological Property

S. Chern : Quantum version (Hilbert space)

of Gauss-Bonnet formula

nh/e2

TKNN invariant

Hasan 09

“Quantum Hall Effect” without Magnetic Field?

Bulk band-structure

Dirac point

Massive Dirac particles

Haldane Model (1988)

Alternating field but net magnetic field is zero

Hall Transport

is determined

by band-structure

Edge > Bulk

Hasan 09

Hall conductance is zero!

(1) Time Reversal Invariant

(2) Bulk gap : Spin-Orbit induced Gap “Landau level”

(3)sxy = n e2/h = 0

n = #edge states = 0

Can there be a new “protection law” for the edge current?“Is there a new topological (collective) state of matter?”

Murakami et.al., (05)

Hasan 09

Do QHE-like topological phases exist in nature

that are time-reversal invariant?

Topological state in 2D (spin Hall state)Kane & Mele (2005), Bernevig, Hughes, Zhang (06),

Murakami (06), Sheng, Haldane et.al.(2006) also others

Distinct new Topo state in 3D (Theta-vac, Axionic state)Moore & Balents (07), Fu, Kane & Mele (07), Roy (09)

Qi, Zhang (08), Franz, Moore, X.G. Wen (08) , Kitaev (08)

Earlier work by Callan, Wilczek, Witten and others (70-80s)

Hasan 09

sxy = ne2/h Transport

Spin-sensitive

Momentum-resolved

Measurements!

Topological quantum number

?

No quantized transport!

{ni}

Topological quantum number

QHE phases

How to experimentally “measure” the topological quantum numbers (ni)

associated with the quantum spin Hall (QSH)or Strong Topological Insulator (STI) phases?

Topo Insulators

Hasan 09

First generation materials:

Graphene

Pb(Sn)Te

Hg(Cd)Te

Bi1-xSbx

Transport measurements

of edge-states

Konig et.al., (Molenkamp).

SCIENCE (2007)

No SS in

Gap too small

2D(spin Hall state)

3D(Theta-vac state)

Arpes/spin-ARPES

measurements of edge-

states

Hsieh et.al., (Hasan).

NATURE (2008)

SCIENCE (2009)

NATURE (2009)

Second generation : “hydrogen atom” materials

Bi2Se3

Sb

Sb2Te3 PRL(09), see KITP talk (2008)

Topo. Metal : SCIENCE (2009)

“Hydrogen Atom” of Topological InsulatorXia, Qian et.al., arXiv:0812.2078v1

NATURE PHYSICS (2009)

Bi2X3NATURE, PRL (2009)

Hasan 09

How to isolate Bulk(3D) vs. Surface(2D) states ?

Hasan 09

Bulk band shows a gap ..Insulating samples

Hasan 09

Momentum distribution of gapless boundary electron modes

kx

ky

kx

ky

Hasan 09

Signatures of Topology : Nature of the edge states

# crossing between TRIM odd even

Z2 class -1 +1

Protected bulk crossing yes no

Z2 invariant characterizes the presence or absence of Kramers degeneracy

associated with a boundary (Fu-Kane model)

Hasan 09

Hasan 09

Hasan 09

Which one is the “Knot” band?

Originates from conduction band

Which band threads the gap : Guarantees metalicity

Hasan 09

EF

Z2

Topology

Hasan 09

Spin-textures of the edge-states

Hasan 09

Spin Chirality & Berry’s Phase

= -1

Hasan 09

Bi2Se3

Can we make an insulating version of Sb?

We determined the topology

in Sb [Hsieh et.al., SCIENCE 09]

Discovery of the Bi2Se3 class

Xia et.al., NATURE PHYS 09

News&Views NATURE PHYS 09

“TOPOLOGICAL INSULATORS : A large-gap family found”

Nature Physics Cover, June 2009

Helical Dirac fermions

Hsieh, Xia et.al. (MZH), http://aps.arxiv.org/abs/0904.1260

(NATURE 09)

One to One Spin-LinearMomentum Locking : half Fermi gas with a Berry’s phase

Hasan 09

Boundary Fermi pocket encloses odd number of Dirac points

• Berry’s phase around the Fermi pocket

• Opposite to Anderson Localization (weak-”anti-localization”)• Should exhibit Half-integer charge QHE

Surface states form a “Topological 2D novel Metal” phase !

Xu and Moore 06

Absence of Backscattering: No “U” turn

Spin-ARPES Data

Hasan 09

• Berry’s phase around the Fermi pocket

Opposite to Anderson Localization (weak-”anti-localization”)

Absence of Backscattering: No “U” turn

Spin-ARPES Data

Spin-ARPES Data

STM Data, Yazdani group (Princeton)

Hasan 09

“TOPOLOGICAL Graphene”

Hasan 09

Topological Order at Room Temperature(QH-like topological effect at 300k, no magnetic field)

Half Fermi gasDirac nodal Topo Insulator

Topological Fermions

Hasan 09

Topological Insulator Properties :

Boundary Fermi pocket encloses odd number of Dirac points

Surface states form a “Topological 2D Metal” phase :This topological state is fundamentally different from conventional 2D electron matter (2DEG) and the integer QHE state as in GaAs/GaAlAs heterostructures.

• Berry’s phase around the Fermi pocket

• Should exhibit Half-integer charge QHE

• Opposite to Anderson Localization (weak-”anti-localization”)

EF

Spin-textured Dirac cone Mirror Chern number Hasan 09

Graphene

Topo Insulator

Hasan 09

Deposit a magnetic submonolayer on TI

Strong Topological Insulator

See our preprint for details : Xia, Hasan et.al., arXiv:0812.2078v1 (2008)

Fe (iron)

Hasan 09

Topological Quantum Computing

Kitaev, Preskill (CalTech)

Das Sarma (Maryland)

Freedman (Microsoft-Q)

Nayak (Microsoft-Q)

Fendley (Virginia)

Kane (UPenn)

Others..

Topological Quantum Computation (Kitaev 2003)

- 2 separated Majoranas = 2 degenerate states (1 qubit)

- 2N separated Majoranas = N qubits

- Quantum information immune to local decoherence

- Adiabatic “braiding” of vortices performs

unitary operations on N qubits

STI/Superconduct interface

s wave superconductor

Topological insulator

2D interface state with energy gap and exotic topological order

Resembles 2D spinless px+ipysuperconductor but does not violate time reversal symmetry

† † *†( v )H i s

proximity inducedsuperconductivity

Dirac surface states(no spin degeneracy)

( ) ir e Majorana bound state at a vortex :

- bound state solution to BdG equation at exactly zero energy

- c0 = c0† (electron=hole) Majorana fermion = “1/2 a state”

- Also predicted in n=5/2 FQHE, Sr2RuO4, cold atoms, etc

Topological Quantum Computation : (Kitaev 2003)

- 2 separated Majoranas = 2 degenerate states (1 qubit)

- 2N separated Majoranas = N qubits

- Quantum information immune to local decoherence

- Adiabatic “braiding” of vortices performs unitary operations on N qubits

Kane-Fu proposal

Cartoon from Moore

Manipulation of Majorana Fermions for Computing

S-TI-S Tri-Junction

f1f2

0

Create, Transport and Fuse Majorana fermions along line junctions

Majorana boundstate present attri-junction

The challenges :

• Find suitable topological insulator

• Find suitable superconductor which makes good interface

• Optimize proximity induced gap and discrete Andreev bound states• Control the superconducting phases with Josephson junctions• Measure current difference when Majoranas are fused ………

Kane 2008

Bi2(Ca)Se3+d

3D Topological

Insulators

Making BULK insulators

Tuning to the topological insulator regime in Bi1-xSbx

Bulk INSULATOR

Superconductivity in Doped Topo Insulators(Hor et.al., 2009)

sxy = ne2/h

Topological quantum number

No quantized transport!

{ni}

Topological quantum number

Quantum Hall effect

How to experimentally “measure” the topological quantum numbers (ni) associated with the quantum

spin Hall or Strong Topological Insulator (STI) phases?

Topological Insulators

Spin-textured Dirac

Chiral degenerate fermions

Helical Dirac fermions

Hasan 09

Topological Insulators are expected to exhibit :(short list)

- Half-integer charge quantum Hall effect- Opposite to Anderson localization (weak anti-localization)- Superconducting proximity: Majorana Fermions :

Fu, Kane et.al., Beenakkar et.al.,- Magnetoelectric/Axion effects: Moore,Franz,Vanderbilt et.

- Topo exciton (BEC)condensates: Moore, Franz et.al,- Magnetic proximity effect, Monopole: Qi, Zhang et.al,- Helical-metal in Dislocations: Ran,Vishwanath et.al., - Topological (fault-tolerant) quant.computing Kitaev, Kane,

Hasan 09

beyond LCLS/SLAC

New Photon sources also for Fundamental PhysicsBESAC :

Topological Insulators

among the highlighted topics

Results from

Nature 08

Science 09

A new quantum phase of matter (z2= -1) has been observed (Topological Insulator) which is distinct from the quantum Hall effect phase or any other 2D electron systs.

So far 2 classes of TIs (4 compounds) discovered by us, SC found, FM found

KITP (2007-08) Results were presented at KITP

NATURE (2008) News&Views : Nature (2008)

Phys.Rev. B (09) Editor’s Suggestion & Physics (09)SCIENCE (2009) News&Views : Science (2009)NATURE PHYS (2009) News&Views : Nature Phys. (2009)

PHYSICS TODAY “Search&Discovery” April (2009)

See commentary by F. Wilczek in NATURE (2009)also by B.I. Halperin at CMP Journal Club (2008)

NATURE (2009) Topo Graphene News&Views : Nature (2009)Phys. Rev. Letts (09) Dirac fermions controlledNATURE (2009) Anti-localization of Helical Dirac Fermions

PHYSICS (2009) PRL-ViewPoint on Spin-texture in Warped SS StatesPHYSICS TODAY Insulator’s Metallic Side, NewsPick August (2009)

Our works on Topo Insulators :

Hasan 09