topological phases in transition metal dichalcogenides
TRANSCRIPT
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Junwei Liu
Massachusetts Institute of Technology
Topological Phases in
Transition Metal Dichalcogenides
May 18 2017, IMA
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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.
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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
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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
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Topology + time reversal symmetry TI
Time reversal symmetry 𝐸𝑛↑ 𝑘 = 𝐸𝑛↓ −𝑘 (Kramers theorem)
Breaking 𝑺𝒛conservation
Still gapless
Breaking 𝑺𝒛conservation
gapped
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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.
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2D TIs and VdW heterostructure
7 / 26A. K. Geim & I. V. Grigorieva Nature 499, 419-425 (2013)
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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)
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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)
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Transition metal dichalcogenide (TMD)
Stable Structure of MoS2 Stable Structure of WTe2
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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
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Topological nontrivial MoS2 in 1T’ structure
X. Qian*, J. Liu*, et. al Science 346, 1344 (2014)12 / 26
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Robust again strain
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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 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 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
)
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
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Structural stability of monolayer TMD
X. Qian*, J. Liu*, et. al Science 346, 1344 (2014)15 / 26
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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
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Transport experiments
17 / 26
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Non-local measurements and effect of B fields
Z. Fei, et al Nat. Phys. (2017)18 / 26
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ARPES experiments
S. Tang et al arXiv:1703.03151 19 / 26
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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
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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
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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
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Electric tunable - on/off states
23 / 26
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More channels – higher conductance
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Topological field transistor
Large band gap (50 meV) ~ high temperature
Linearly increasing conductance ~ 102 Τ𝑒2 ℎ
Easy to control ~ electric field tunable
X. Qian*, J. Liu*, et. al Science 346, 1344 (2014)25 / 26
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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)
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Crystal Structure of Ternary TM Chalcogenides
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QSH phase in monolayer TTMC
28 / 26