Electronic structures in topological semimetals and...
Transcript of Electronic structures in topological semimetals and...
Department of physics, National Cheng Kung University, Taiwan
(國立成功大學 物理系)
Tay-Rong Chang (張泰榕)
Electronic structures in topological semimetals and
heterostructure from first-principles
2017/Sep./7 1
their topology is identical
Outline
1. Topology in condensed matter physics
Basic concepts and properties of topological insulator
Example: Bi2Se3
2. New topological phases: Topological semimetal Basic concepts and example: TaAs family
Weyl semimetals: MoxW1-xTe2
Nodal-line semimetals: PbTaSe2
Type-II Dirac semimetal: VAl3
3. Conclusion
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Topology in condensed matter physics
Math => real space Gauss-Bonnet Theorem:
KGauss
ds = 2(1- g)S
òGauss curvature genus
genus g =1 g = 0 g =1
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Topology in condensed matter physics
Math => real space Gauss-Bonnet Theorem:
KGauss
ds = 2(1- g)S
òGauss curvature genus
genus g =1 g = 0 g =1
Phys => momentum space
A
B
B
A
(1) (2) (3)
B
A
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Topology in condensed matter physics
B-orbital
(1)
Brillouin zone
wavefunction is smoothly
A-orbital
(Se-orbital)
(Bi-orbital)
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Topology in condensed matter physics
B-orbital
(1)
Brillouin zone
wavefunction is smoothly
Brillouin zone
(2)
wavefunction is NOT smoothly
A-orbital
B-orbital
A-orbital
B-orbital
A-orbital
(Se-orbital)
(Bi-orbital)
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Topology in condensed matter physics
B-orbital
(1)
Brillouin zone
wavefunction is smoothly
Brillouin zone
(2)
wavefunction is NOT smoothly
A-orbital
B-orbital
A-orbital
B-orbital
A-orbital
(Se-orbital)
(Bi-orbital)
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Topology in condensed matter physics
A-orbital
B-orbital
(1)
Brillouin zone
wavefunction is smoothly
Brillouin zone
(2)
wavefunction is NOT smoothly
A-orbital
B-orbital
band
inversion
band
inversion
(Se-orbital)
(Bi-orbital)
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Obey chemical
bond order
Violate chemical
bond order
Topology in condensed matter physics
Gauss-Bonnet Theorem:
KGauss
ds = 2(1- g)S
ògenus
TKNN theory:
Topological invariant number
Math => real space Phys => momentum space
Berry curvature
wavefunction is smoothly : n = 0 =>
wavefunction is NOT smoothly : n = integer =>
Topological trivial
(normal insulator)
Topological nontrivial
(topological insulator)
Bloch wavefun
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Topology in condensed matter physics
(bulk-edge correspondence)
Surface/Interface
The gapless surface state is the hallmark of topological phase.
p
s s p
gapless surface state
p
p s
s
inversion point
(gapless point)
electron move
M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)
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Topology in condensed matter physics (Summary)
(1) Robust
EF E
Z2=1 Z2=0
band
inversion
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Topology in condensed matter physics (Summary)
(1) Robust
(2) Topological invariant number (math)
EF
Chern number, Z2 index, mirror Chern number, chiral charge, winding number … etc
E
Z2=1 Z2=0
band
inversion
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Topology in condensed matter physics (Summary)
(1) Robust
(2) Topological invariant number (math)
(3) Gapless surface states (measurable quantity)
EF
Chern number, Z2 index, mirror Chern number, chiral charge, winding number … etc
ss
ex: Bi2Se3
E
Z2=0 Z2=1 (SOC=2) Z2=1 (SOC=1)
band
inversion
gap ss
Z2=1 Z2=0
band
inversion
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Topological insulator: Bi2Se3
ARPES Theory
Surface: gapless surface states
spin-momentum locked
Bulk: insulating gap
topological Z2 invariant
odd/even number
surface states
SS CB
CB SS
Y. Xia et al. Nature Physics 5, 398 (2009)
D. Hsieh et al. Nature 460, 1101 (2009)
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Topological insulator: Bi2Se3
ARPES Theory
Surface: gapless surface states
spin-momentum locked
Bulk: insulating gap
topological Z2 invariant
odd/even number
surface states
Y. Xia et al. Nature Physics 5, 398 (2009)
D. Hsieh et al. Nature 460, 1101 (2009)
CB
CB SS
SS
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Possible application: Ag/Bi2Se3
NPG Asia Materials 8, e332 (2016)
Semiconductor (e.g. Si) Metal (e.g. Pb)
Pb/Si
Ag/Bi2Se3
Rashba parameter
𝛼𝑅 = 0.04
PRL101,266802
𝛼𝑅 = 1.75
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Topological phases
Insulating phase Topological insulator: Bi2Se3, Bi2Te3, LuPtBi …etc
Topological Kondo insulator: SmB6, YbB6 … etc
Weak topological insulator: KHgSb, Bi4Br4 … etc
topological crystalline insulator: SnTe
Topological superconductor: Bi2Se3/NbSe2, CuxBi1-xSe3 …etc
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Topological phases
Insulating phase Topological insulator: Bi2Se3, Bi2Te3, LuPtBi …etc
Topological Kondo insulator: SmB6, YbB6 … etc
Weak topological insulator: KHgSb, Bi4Br4 … etc
topological crystalline insulator: SnTe
Topological superconductor: Bi2Se3/NbSe2, CuxBi1-xSe3 …etc
metallic phase insulating phase
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Outline
1. Topology in condensed matter physics
Basic concepts and properties of topological insulator
Example: Bi2Se3
2. New topological phases: Topological semimetal Basic concepts and example: TaAs family
Weyl semimetals: MoxW1-xTe2
Nodal-line semimetals: PbTaSe2
Type-II Dirac semimetal: VAl3
3. Conclusion
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Weyl Fermion
High energy Condensed matter
Graphene Dirac semimetal Dirac Fermion
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Weyl Fermion
High energy Condensed matter
Graphene Dirac semimetal
Nielsen-Ninomiya theorem: (Nuclear Physics B185 (1981) 20-40)
Equal numbers of 𝜒 =+1 and -1 WFs.
Dirac Fermion
Weyl Fermion
???
m=0
where
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Weyl Fermion
High energy Condensed matter
Graphene Dirac semimetal
Nielsen-Ninomiya theorem: (Nuclear Physics B185 (1981) 20-40)
Equal numbers of 𝜒 =+1 and -1 WFs.
Weyl semimetal
(2015)
Dirac Fermion
Weyl Fermion
TaAs: Theory
S.-M. Huang et al, Nat. commun. 6, 7373 (2015)
H. Weng et al, Phys. Rev. X 5, 011029 (2015)
TaAs: Experiment
S.-Y. Xu et al, Science 349, 613 (2015)
B. Q. Lv et al, Phys. Rev. X 5, 031013 (2015)
L. X. Yang, Nat. phys. 11, 724 (2015)
m=0
where
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Weyl semimetal
Weyl semimetals:
1. Provide the realization of Weyl fermions (analogy with 3D graphene)
2. Extend the classification of topological phases of matter beyond insulators
3. Magnetic monopole in k-space (topological number called “chiral charge”)
4. Host exotic Fermi arc surface states
Weyl points
Experiment Theory Linear band dispersion
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Weyl semimetal
Weyl semimetals:
1. Provide the realization of Weyl fermions (analogy with 3D graphene)
2. Extend the classification of topological phases of matter beyond insulators
3. Magnetic monopole in k-space (topological number called “chiral charge”)
4. Host exotic Fermi arc surface states
Weyl points
Experiment Theory Linear band dispersion
Berry curvature
(pseudo-spin)
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Weyl semimetal
Weyl semimetals:
1. Provide the realization of Weyl fermions (analogy with 3D graphene)
2. Extend the classification of topological phases of matter beyond insulators
3. Magnetic monopole in k-space (topological number called “chiral charge”)
4. Host exotic Fermi arc surface states
Fermi arc
Weyl points
Experiment Theory Linear band dispersion
TaAs
S.-Y. Xu et al,
Science 349, 613 (2015)
NbAs
S-.Y. Xu… T.-R. Chang et al
Nat. Phys. 11, 748 (2015)
TaP
S-.Y. Xu… T.-R. Chang et al
Sci. Adv. 1, e1051092 (2015)
NbP
I. Belopolski … T.-R. Chang et al
PRL 116, 066802 (2016)
NbP (STM/STS)
H. Zheng… T.-R. Chang et al
ACS nano 10, 1378 (2016)
G. Chang… T.-R. Chang et al
PRL 116, 066601 (2016)
Berry curvature
(pseudo-spin)
Normal metal
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Weyl semimetal
Disadvantages of TaAs family (1) 3D structure. Adversely to fabricate thin-film (e. g. MBE).
(2) Untunable Weyl points. Adversely to explore topological metal-insulator transition.
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Weyl semimetal
Disadvantages of TaAs family (1) 3D structure. Adversely to fabricate thin-film (e. g. MBE).
Our goals
(1) Searching Weyl semimetal with layer structure. (fabricating thin-film)
(2) Searching tunable Weyl semimetal. (exploring topological phase transition)
(2) Untunable Weyl points. Adversely to explore topological metal-insulator transition.
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Weyl semimetal: MoxW1-xTe2
Nature Commun. 7, 10639 (2016)
WTe2
Gap ~ 1 meV
Our goals
(1) Searching Weyl semimetal with layer structure. (fabricating thin-film)
(2) Searching tunable Weyl semimetal. (exploring topological phase transition)
¼ BZ (location of gap min) Band structure along cut
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Weyl semimetal: MoxW1-xTe2
reduce either strength of SOC
or
lattice constants
=> Weyl phase in WTe2
(insulator) (Weyl) WTe2
gap ~ 1 meV
Nature Commun. 7, 10639 (2016)
WTe2
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Weyl semimetal: MoxW1-xTe2
We suggested:
Mo doping
(insulator) (Weyl) WTe2 Mo0.2W0.8Te2
gap ~ 1 meV
Nature Commun. 7, 10639 (2016)
reduce strength of SOC
as well as
lattice constants
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Weyl semimetal: MoxW1-xTe2
Nature Commun. 7, 10639 (2016)
Location of WPs (Mo 20%) WPs distance (topological strength)
robust
delicate
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Weyl semimetal: MoxW1-xTe2
Nature Commun. 7, 10639 (2016)
Location of WPs (Mo 20%) WPs distance (topological strength)
robust
delicate
move
Left-hand Right-hand
move
WPs distance = topological strength
touch gap
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Schematic of Fermi arc varying energy map
Surface spectral weight simulation
Weyl semimetal: MoxW1-xTe2
Fermi arc surface state which connects the
direct pair of Weyl nodes.
Nature Commun. 7, 10639 (2016)
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Weyl semimetal: MoxW1-xTe2
Doping = 0% Doping ~ 1% Doping ~ 20%
Nature Commun. 7, 10639 (2016)
topological strength can be
tuned by varying Mo doping
concentration.
MoxW1-xTe2 is not only a Weyl semimetal with layer structure, but a tunable Weyl semimetal.
This system is a good candidate for investigating topological metal-insulator phase transition.
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Weyl semimetal: MoxW1-xTe2
(1) Nature Commun. 7, 13643 (2016)
(2) Phys. Rev. B 94, 085127 (2016)
Experimental results
W2
W1
arc
cut1 cut2 cut3
w1
w2 cut1 cut2 cut3
kx
ky
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Weyl semimetal: MoxW1-xTe2
(1) Nature Commun. 7, 13643 (2016)
(2) Phys. Rev. B 94, 085127 (2016)
Experimental results
arc
W1
W2
Theory (cut2)
W2
W1
arc
cut1 cut2 cut3
w1
w2 cut1 cut2 cut3
kx
ky
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Weyl semimetal: MoxW1-xTe2
(1) Nature Commun. 7, 13643 (2016)
(2) Phys. Rev. B 94, 085127 (2016)
Experimental results
arc
W1
W2
Theory (cut2)
W2
W1
arc
cut1 cut2 cut3
w1
w2 cut1 cut2 cut3
kx
ky
(3)Phys. Rev. Lett. 117, 266804 (2016)
Exp. Theory
Theory
Exp.
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Nodal-line semimetal
Normal metal: 2D Fermi surface Topological metal: 1D Nodal-line
FS
Normal metal vs Topological metal
Nodal-line semimetal: PbTaSe2
Nature Commun. 7, 10556 (2016)
Q:
Nodal-line semimetals have yet to be found in real materials, even in DFT level. Previous works
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Our goal:
Searching Nodal-line Fermi surface in real materials. Simplest nodal-line
Nodal-line semimetal: PbTaSe2
Nature Commun. 7, 10556 (2016)
mirror
reflection
plane
A
B C
A
A B
A
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Nodal-line semimetal: PbTaSe2
Nature Commun. 7, 10556 (2016)
+,-: mirror eigenvalues
mirror
plane
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Nodal-line semimetal: PbTaSe2
Nature Commun. 7, 10556 (2016)
+,-: mirror eigenvalues
mirror
plane
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Nodal-line semimetal: PbTaSe2
Nature Commun. 7, 10556 (2016)
Se-termination
Pb-termination
Theory
NL
g p = ±1
winding number
bulk-boundary correspondece
topo. surface states
integral path of
winding number
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Nodal-line semimetal: PbTaSe2
Nature Commun. 7, 10556 (2016)
Ta Pb Ta Pb
ARPES Theory
PbTaSe2
Experimental results
Bulk states
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Nodal-line semimetal: PbTaSe2
Nature Commun. 7, 10556 (2016)
Ta Pb Ta Pb
ARPES Theory ARPES
Theory
PbTaSe2 TaSe2
Experimental results
Bulk states
empty
empty
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Nodal-line semimetal: PbTaSe2
Nature Commun. 7, 10556 (2016)
Ta Pb Ta Pb
ARPES Theory ARPES
Theory
PbTaSe2 TaSe2
ARPES Theory
Experimental results
Bulk states
Surface states
empty
empty
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Nature Commun. 7, 10556 (2016)
Nodal-line semimetal: PbTaSe2
Ta Pb Ta Pb
ARPES Theory
Nature Communications’ Editor: Nodal-line shape band appearing near
Fermi level hosts unique properties in topological matter, which has yet
to be confirmed in real materials. Here, the authors report the existence
of topological nodal-line states in the non-centrosymmetric single-
crystalline spin-orbit semimetal PbTaSe2.
ARPES Theory
Prediction + Experiment
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Dirac semimetal
Three typical topological semimetal:
Weyl, Nodal-line, and Dirac
MoxW1-xTe2 PbTaSe2
bulk
surface
Dirac semimetal
Finely tuning
chemical composition
Symmetry protected
Na3Bi Cd3As2
Z. Wang et al., Phys. Rev. B 85, 195320 (2012)
Z. Wang et al., Phys. Rev. B 88, 125427 (2013)
M. Neupane…TRC, et al., Nat. Com. 5, 3786 (2014)
X. Su…TRC, et al., Science 347, 294 (2015)
Symmetry is Key
DFT ARPES DFT ARPES
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Lattice parameters
a=3.78
c=8.322
space group: 139
Symmetry operations
(1) C2x, C2y, C2z, C2xy
(2) C4z
(3) Inversion, time-reversal
(4) Mx, My, Mz, Mxy
(5) S4
Crystal structure : VAl3
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GGA+SOC
Bulk band structures : VAl3
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Type-II DP
Slope sign: opposite Slope sign:
the same
Type-II
Type-I
Slope sign: opposite
Slope sign: opposite
Bulk band structures : VAl3
Na3Bi or Cd3As2
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E=E1
E=E1
Bulk band structures : VAl3
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This work
𝑍2 𝑖𝑛𝑑𝑒𝑥: 𝜐2𝐷 = 0
𝐶ℎ𝑒𝑟𝑛 𝑛𝑢𝑚𝑏𝑒𝑟: 𝑁 = 0
𝑀𝑖𝑟𝑟𝑜𝑟 𝐶ℎ𝑒𝑟𝑛 𝑛𝑢𝑚𝑏𝑒𝑟: 𝑛𝑀 = 2
Bohm-Jung Yang & Naoto Nagaosa,
Nat. Commun. 5, 4898 (2014)
Topological invariant number
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Surface band structures : VAl3
Na3Bi
X. Su… T-R Chang, et al., Science 347, 294 (2015)
DP
DP
arc arc
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Topological phase transition
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Double
Weyl
Cheng Fang et al., Phys. Rev. Lett. 108, 266802 (2012)
Topological phase transition
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Each Dirac node consists of
four type-II Weyl nodes with
chiral charge ±1 via
symmetry breaking.
Topological phase transition
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Landau level spectrum
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Type-II Dirac semimetal: VAl3
(1) Type-II Dirac semimetal
(2) Topological invariant number: 𝑀𝑖𝑟𝑟𝑜𝑟 𝐶ℎ𝑒𝑟𝑛 𝑛𝑢𝑚𝑏𝑒𝑟: 𝑛𝑀 = 2
(3) Topological phase transition (via breaking symmetry)
Conclusion: Topological materials
Providing detailed theoretical interpretation for the experimental results.
Prediction for new types of topological materials.
DFT + ab-initio tight-binding: 61
Nature Commun. 7, 10639 (2016) Feb. Nature Commun. 7, 10556 (2016) Feb.
Tunable Weyl semimetal (MoxW1-xTe2) Nodal-line semimetal (PbTaSe2,TlTaSe2)
Type-II Dirac semimetal (VAl3 family)
Phys. Rev. Lett. 119, 026404 (2017) Jul.
Hetrostructures (Ag/Bi2Se3)
NPG Asia Materials 8, e332 (2016) Nov.
Citation: 102 Citation: 164
Citation: 3 Nature Commun. 7, 13643 (2016) Dec. Citation: 17
Phys. Rev. B. 94, 085127(2016) Aug. Citation: 41 Phys. Rev. B. 94, 085127(2016) Aug. Citation: 71
Phys. Rev. Lett. 117, 266804 (2016) Dec. Citation: 9
STM/STS
ARPES
ARPES
DFT
DFT
DFT+ARPES
DFT
Acknowledgements
M. Zhaid Hasan
(Princeton University)
Arun Bansil
(Northeastern U.)
Hsin Lin
(NUS)
ARPES
&
STM
Theory
Horng-Tay Jeng
(NTHU)
Sample
growth
Fangcheng Chou
(CCMS)
Titus Neupert
(U. Zurich)
Shuang Jia
(Peking U.)
Shin-Ming Huang
(NSYSU )
Su-Yang Xu
(MIT)
Guang Bian
(U. Missouri)
Hao Zheng
(Shanghai Jiao Tong U.)
Ilya Belopolski
(Princeton University)
Raman Sankar
(Academia Sinica)
Peng-Jen Chen
(Academia Sinica)
Zheng Liu
(Nanyang Tec. U)
Weiwei Xie
(LSU)
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Thank you !
To see a world in a grain of sand … -William Blake
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