Topological Phases in Transition Metal Dichalcogenides

Junwei Liu

Massachusetts Institute of Technology

Topological Phases in

Transition Metal Dichalcogenides

May 18 2017, IMA

CrystalTranslational symmetry

MagnetRotational symmetry

SuperconductorGauge symmetry

Symmetry breaking phases

• In condensed matter physics, searching for new states of

matter and studying the corresponding phase transition are

the most important and fundamental issues.

• Landau theory tells us that continuous phase transition

always accompanies symmetry breaking, i.e. different phases

can be distinguished/characterized by different symmetries.

2 / 26

Topological phases

• Topological invariant (Chern Number)

)(2

1kFdn S

von Klitzing, (1980)

Thouless et al, (1982)

• The bulk is insulating, and the edge is conducting and robust against any perturbations.

• No symmetry was broken in different plateaus and it cannot be described by Landau theory.

The 1985, 1998 and 2016 Nobel Prize in Physics

h

enxy

2

• Quantized conductance

3 / 26

Topology+ 𝑺𝒛conservation “quantum spin Hall”

Nontrivial topology of gapped bulk

states means there are some gapless

edge states.

• With 𝑺𝒛 conservation

Spin Chern number

𝒏𝑺 = 𝒏↑ − 𝒏↓ /𝟐

"𝐐𝐒𝐇" = 𝑸𝑯↑ +𝑸𝑯↓

• Topological invariant,

Chern number 𝒏 for

quantum Hall (QH)

effect and quantum

anomalous Hall effect

4 / 26

Topology + time reversal symmetry TI

Time reversal symmetry 𝐸𝑛↑ 𝑘 = 𝐸𝑛↓ −𝑘 (Kramers theorem)

Breaking 𝑺𝒛conservation

Still gapless

Breaking 𝑺𝒛conservation

gapped

5 / 26

2D and 3D topological insulator

Kane & Hasan, RMP (2010); Qi & Zhang, RMP (2011)

• Time reversal symmetry is preserved and the total Chern

number is zero.

• The new topological invariant Z2 is one but not zero.

• There are topologically (time reversal symmetry) protected

edge/surface states.

Only 2D TIs can give

quantized conductance.

6 / 26

2D TIs and VdW heterostructure

7 / 26A. K. Geim & I. V. Grigorieva Nature 499, 419-425 (2013)

Existing experimental 2D TIs

M. König, et al, Science 318, 766 (2007)

• Limited material choices: only HgTe/CdTe and InAs/GaSb

quantum well after 10 years seeking

• Small band gap (< 10 meV)

• Hard to fabricate

• Not fully quantized

• Not tunable M. Hasan & C. Kane, RMP 82, 3045 (2010)

XL Qi & SC Zhang, RMP 83, 1057 (2011)

Yoichi Ando, JPSJ 82, 102001 (2013)

L. Du et al, PRL 114, 096802 (2015)

8 / 26

WTe2 type of 2D topological insulators

Potential application

Experimental observations

Our theoretical predictions

References[1] X. Qian*, J. Liu*, L. Fu, J. Li, Science 346, 1344 (2014)

[2] J. Liu, H. Wang, C. Fang, L. Fu, X. Qian, Nano Lett.

17, 467-475 (2017)

9 / 26

Transition metal dichalcogenide (TMD)

Stable Structure of MoS2 Stable Structure of WTe2

10 / 26

Band structure of MoS2/WTe2 in 1H structure

1H MoS2 1H WTe2

Kumar, A. & Ahluwalia, P.K. Eur. Phys. J. B 85, 186 (2012)11 / 26

Topological nontrivial MoS2 in 1T’ structure

X. Qian*, J. Liu*, et. al Science 346, 1344 (2014)12 / 26

Robust again strain

13 / 26

Sandwich structure with BN

13

Fig. S10.

Effect of van der Waals heterostacking with hexagonal BN monolayers on electronic structure,

projected density of states, fundamental band gap (Eg), and Z2 invariant of 1T’-WTe2 under 4%

biaxial strain. The supercell was constructed by 2x2 1T’-WTe2 and 3 3×3!BN monolayers

under 4% biaxial strain to minimize the lattice mismatch for first-principles calculations. (A)

biaxially-strained monolayer 1T’-WTe2. (B) strained 1T’-WTe2 stacked on hexagonal BN

monolayer. (C) strained 1T’-WTe2 sandwiched by two hexagonal BN layers. It clearly shows

that BN monolayers have negligible effect on the electronic structure of 1T’-WTe2 in a wide

energy range around the Fermi level, demonstrating hexagonal BN sheets as ideal dielectric

layers for the experimental realization of van der Waals heterostructure-based topological field

effect transistor.

W Te - B N ( =4% )2BA W Te ( =4% )2 C B N - W Te - B N ( =4% )2

Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

En

erg

y (

eV

)

Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

2 1 0 1 2 3

2 1 0 1 2 3

De

nsity o

f sta

tes (

arb

.)

WTe2

E EF (eV)

Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

De

nsity o

f sta

tes (

arb

.)

h BNWTe2

2 1 0 1 2 3

E EF (eV)

h BNWTe2

De

nsity o

f sta

tes (

arb

.)

2 1 0 1 2 3

E EF (eV)

E g = 0.093 eV, Z2 = 1 E g = 0.089 eV, Z2 = 1 E g = 0.095 eV, Z2 = 1

13

Fig. S10.










effect transistor.


Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

En

erg

y (

eV

)

Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

2 1 0 1 2 3

2 1 0 1 2 3

De

nsity o

f sta

tes (

arb

.)

WTe2

E EF (eV)

Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

De

nsity o

f sta

tes (

arb

.)

h BNWTe2

2 1 0 1 2 3

E EF (eV)

h BNWTe2

De

nsity o

f sta

tes (

arb

.)

2 1 0 1 2 3

E EF (eV)

E g = 0.093 eV, Z2 = 1 E g = 0.089 eV, Z2 = 1 E g = 0.095 eV, Z2 = 1

13

Fig. S10.










effect transistor.


Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

En

erg

y (

eV

)

Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

2 1 0 1 2 3

2 1 0 1 2 3

De

nsity o

f sta

tes (

arb

.)

WTe2

E EF (eV)

Y R X R2

1.5

1

0.5

0

0.5

1

1.5

2

En

erg

y (

eV

)

D

en

sity o

f sta

tes (

arb

.)

h BNWTe2

2 1 0 1 2 3

E EF (eV)

h BNWTe2

De

nsity o

f sta

tes (

arb

.)

2 1 0 1 2 3

E EF (eV)

E g = 0.093 eV, Z2 = 1 E g = 0.089 eV, Z2 = 1 E g = 0.095 eV, Z2 = 114 / 26

Structural stability of monolayer TMD


Some experimental progresses

• Many groups have successfully grown the materials in 1T’.

• Some measurements indicate that thin films are narrow-gap

semiconductor (~60 meV).16 / 26

Transport experiments

17 / 26

Non-local measurements and effect of B fields

Z. Fei, et al Nat. Phys. (2017)18 / 26

ARPES experiments

S. Tang et al arXiv:1703.03151 19 / 26

L. Peng et al

arXiv:1703.05658

Z. Jia et al

arXiv:1703.04042

STM experiments for different groups

How to use it?

S. Tang et al

arXiv:1703.03151 20 / 26

Inspiration from bilayer graphene

If the states around the

Fermi level come from

different atomic layers,

the band gap is very

sensitive to the external

perpendicular electric

field.

Edward McCann, Phys. Rev. B 74, 161403(R) (2006)21 / 26

Detailed properties of band structure of MoS2

• Conduction band is from

𝑝 orbitals of S atoms in

1st and 3rd atomic layers.

Mo

S

S

• Valence band is from 𝑑orbitals of Mo atoms in

2nd atomic layer.

X. Qian*, J. Liu*, et. al Science 346, 1344 (2014)

• Band structure should

be sensitive to external

perpendicular electric

field, thus topological

phases should be

tunable.

Electric

Field

22 / 26

Electric tunable - on/off states

23 / 26

More channels – higher conductance

24 / 26

Topological field transistor

Large band gap (50 meV) ~ high temperature

Linearly increasing conductance ~ 102 Τ𝑒2 ℎ

Easy to control ~ electric field tunable


Acknowledgements

DMR-1231319

References

[1] X. Qian*, J. Liu*, L. Fu, J. Li, Science 346, 1344

(2014)

[2] J. Liu*, H. Wang*, C. Fang, L. Fu, X. Qian, Nano

Lett. 17, 467-475 (2017)

26 / 26

Xiaofeng Qian

(TAMU)

Collaborators：

Prof. Xiaofeng Qian (TAMU)

Prof. Liang Fu(MIT)

Prof. Ju Li (MIT)

Prof. Chen Fang (IOP)

Hua Wang (TAMU)

Liang Fu

(MIT)

Ju Li

(MIT)

Crystal Structure of Ternary TM Chalcogenides

27 / 26

QSH phase in monolayer TTMC

28 / 26

Documents

Topological Phases in Transition Metal Dichalcogenides