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

2

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

3


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

4


B-orbital

(1)

Brillouin zone

wavefunction is smoothly

A-orbital

(Se-orbital)

(Bi-orbital)

5


B-orbital

(1)

Brillouin zone


Brillouin zone

(2)

wavefunction is NOT smoothly

A-orbital

B-orbital

A-orbital

B-orbital

A-orbital

(Se-orbital)

(Bi-orbital)

6


B-orbital

(1)

Brillouin zone


Brillouin zone

(2)


A-orbital

B-orbital

A-orbital

B-orbital

A-orbital

(Se-orbital)

(Bi-orbital)

7


A-orbital

B-orbital

(1)

Brillouin zone


Brillouin zone

(2)


A-orbital

B-orbital

band

inversion

band

inversion

(Se-orbital)

(Bi-orbital)

8

Obey chemical

bond order

Violate chemical

bond order


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

9


(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)

10

Topology in condensed matter physics (Summary)

(1) Robust

EF E

Z2=1 Z2=0

band

inversion

11


(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

12


(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

13

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)

14

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

15

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

16

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

17

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

18

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


3. Conclusion

19

Weyl Fermion

High energy Condensed matter

Graphene Dirac semimetal Dirac Fermion

20

Weyl Fermion


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

21

Weyl Fermion


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

22

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

23

Weyl semimetal

Weyl semimetals:





Weyl points


Berry curvature

(pseudo-spin)

24

Weyl semimetal

Weyl semimetals:





Fermi arc

Weyl points


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

25

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.

26

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.

27

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

28


reduce either strength of SOC

or

lattice constants

=> Weyl phase in WTe2

(insulator) (Weyl) WTe2

gap ~ 1 meV


WTe2

29


We suggested:

Mo doping

(insulator) (Weyl) WTe2 Mo0.2W0.8Te2

gap ~ 1 meV


reduce strength of SOC

as well as

lattice constants

30



Location of WPs (Mo 20%) WPs distance (topological strength)

robust

delicate

31



Location of WPs (Mo 20%) WPs distance (topological strength)

robust

delicate

move

Left-hand Right-hand

move

WPs distance = topological strength

touch gap

32

Schematic of Fermi arc varying energy map

Surface spectral weight simulation


Fermi arc surface state which connects the

direct pair of Weyl nodes.


33


Doping = 0% Doping ~ 1% Doping ~ 20%


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.

34


(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

35


(1) Nature Commun. 7, 13643 (2016)

(2) Phys. Rev. B 94, 085127 (2016)


arc

W1

W2

Theory (cut2)

W2

W1

arc

cut1 cut2 cut3

w1

w2 cut1 cut2 cut3

kx

ky

36


(1) Nature Commun. 7, 13643 (2016)

(2) Phys. Rev. B 94, 085127 (2016)


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.

37

38

Nodal-line semimetal

Normal metal: 2D Fermi surface Topological metal: 1D Nodal-line

FS

Normal metal vs Topological metal

Nodal-line semimetal: PbTaSe2


Q:

Nodal-line semimetals have yet to be found in real materials, even in DFT level. Previous works

39

Our goal:

Searching Nodal-line Fermi surface in real materials. Simplest nodal-line



mirror

reflection

plane

A

B C

A

A B

A

40



+,-: mirror eigenvalues

mirror

plane

41



+,-: mirror eigenvalues

mirror

plane

42



Se-termination

Pb-termination

Theory

NL

g p = ±1

winding number

bulk-boundary correspondece

topo. surface states

integral path of

winding number

43



Ta Pb Ta Pb

ARPES Theory

PbTaSe2


Bulk states

44



Ta Pb Ta Pb

ARPES Theory ARPES

Theory

PbTaSe2 TaSe2


Bulk states

empty

empty

45



Ta Pb Ta Pb

ARPES Theory ARPES

Theory

PbTaSe2 TaSe2

ARPES Theory


Bulk states

Surface states

empty

empty

46

47



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

48

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

49

50

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

51

GGA+SOC

Bulk band structures : VAl3

52

Type-II DP

Slope sign: opposite Slope sign:

the same

Type-II

Type-I

Slope sign: opposite

Slope sign: opposite


Na3Bi or Cd3As2

53

E=E1

E=E1


54

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

55

Surface band structures : VAl3

Na3Bi

X. Su… T-R Chang, et al., Science 347, 294 (2015)

DP

DP

arc arc

56

Topological phase transition

57

Double

Weyl

Cheng Fang et al., Phys. Rev. Lett. 108, 266802 (2012)


58

Each Dirac node consists of

four type-II Weyl nodes with

chiral charge ±1 via

symmetry breaking.


59

Landau level spectrum

60


(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)

62

Thank you !

To see a world in a grain of sand … －William Blake

63

Funding support:

electronic structures in topological semimetals and...

Documents