2D Materials with Strong Spin-orbit Coupling: Topological and - - PowerPoint PPT Presentation

2D Materials with Strong Spin-orbit Coupling: Topological and Electronic Transport Properties

Artem Pulkin

California Institute of Technology (Caltech), Pasadena, CA 91125, US Institute of Physics, Ecole Polytechnique F´ ed´ erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland pulkin@caltech.edu

November 1, 2017

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 1 / 32

1

Topological insulators Spin-orbit coupling

2

Two-dimensional transition metal dichalcogenides Quantum spin Hall phase in 2D TMDs Edges and topological edge modes Structural phase boundaries Line defects and transport of electronic spin

3

Summary

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 1 / 32

Topological insulators

Timeline

1975-1981 (Nobel prize 1985) Quantum Hall effect 2005 Quantum spin Hall (QSH) effect, topological order 2006 First realization in HgTe quantum wells Materials?

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 2 / 32

The QSH effect in 2D

Kane-Mele model H =

• spin
• NN

tNN · c†c +

• NNN

iνtNNN · c†c

• Tight-binding model of graphene

E k E k

NNN

Spin-orbit coupling

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 3 / 32

Spin-orbit coupling

Increases with atomic number Z: ∆SO ∼ Z 2 n3l(l + 1) Valence shells in carbon: ∆SO < meV Too small for spectroscopic and transport measurements Compare: HgTe quatnum wells: 10-100 meV (Bernevig et al. Science 314, 1757 (2006))

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 4 / 32

Are there any 2D materials with a large spin-orbit coupling?

Two-dimensional transition metal dichalcogenides

TMD = MX2, M = {Mo, W}, X = {S, Se, Te} 2H phase

= = = , K K' Γ

stable phase (except for WTe2), semiconductor in a hexagonal lattice; large spin-orbit splitting in the valence band (150 meV in MoS2, up to 460 meV in WSe2): spin-polarized states; spin-valley coupling

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 5 / 32

2D TMDs

• M. Chhowalla, et al., Nat Chem 5, 263275 (2013)

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 6 / 32

Applications

Transistors

Radisavljevic et al., Nat Nano 6 no. 3 147-150 (2011)

Solar cells

Bernardi el al., Nano Lett. 13 no. 8 3664-3670 (2013)

LEDs

Amani et al., Science 350 no. 6264 1065-1068 (2015)

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 7 / 32

Is it possible to drive 2D TMDs into the QSH phase?

QSH effect in 2D TMDs

1T’ phase same material in a metastable structure hexagonal symmetry breaking → rectangular unit cell formation of dimerization chains

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 8 / 32

Electronic properties of the 1T’ structural phase

0.3 0.0 0.3 Energy (eV) MoS2 48 meV MoSe2 35 meV MoTe2 0.5 0.0 0.5 ky (2

b )

0.3 0.0 0.3 Energy (eV) WS2 0.5 0.0 0.5 ky (2

b )

WSe2 29 meV 0.5 0.0 0.5 ky (2

b )

WTe2

spin-degenerate bands (inversion + time reversal symmetries) semimetals or semiconductors with a 10 meV-order band gap topological band inversion

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 9 / 32

QSH phase in 1T’ 2D TMDs

band inversion at Γ → quantum spin Hall (QSH) topological phase Qian et al., Science 346, 1344-1347 (2014) Choe et al., Phys. Rev. B 93, 125109 (2016)

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 10 / 32

Is the QSH phase in 1T’ TMDs robust against lattice deformations?

Electronic structure in equilibrium

At the density functional theory level (GGA): MoS2, MoSe2, WSe2 have a band gap; WS2, MoSe2, WTe2 are semimetals;

ky kx WS2 ky kx MoTe2 ky kx WTe2

Hole, electron pockets in semimetallic 1T’ TMDs

Close to semiconducting phase transition phase?

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 11 / 32

Band gap under strain in 1T’ 2D TMDs

5.5 5.6 5.7 5.8 5.9 6.0 3.1 3.2 3.3 b (Å)

semimetal semiconductor MoS2 PBE 57 meV QSH

a

5.7 5.8 5.9 6.0 6.1 6.2 3.2 3.3 3.4

semimetal semiconductor MoSe2 PBE 92 meV

b

5.5 5.6 5.7 5.8 5.9 6.0 a (Å) 3.1 3.2 3.3 b (Å)

semimetal semiconductor WS2 PBE 63 meV QSH trivial

c

5.7 5.8 5.9 6.0 6.1 6.2 a (Å) 3.2 3.3 3.4

semimetal semiconductor WSe2 PBE 120 meV

d

15 30 45 60 75 90 105 120 Eg, meV

Pulkin & Yazyev Journal of Electron Spectroscopy and Related Phenomena 219 72-76 (2017)

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 12 / 32

Conclusions

1T’-TMDs posess a topological band inversion at the Gamma point; MoS2, MoSe2, WSe2 also have a positive band gap → topological insulators; The size of the band gap is sensitive to lattice deformations; Both semiconductor-to-semimetal and topological phase transitions can be induced by strain

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 13 / 32

How do topological edge states in 1T’ TMDs look like?

Recall: Kane-Mele model

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 14 / 32

Edges in 1T’ TMDs

The “zigzag” edge 1,2 = neutral m1,m2 = metal-rich c1,c2 = chalcogen-rich

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 15 / 32

Edges in 1T’ TMDs

m2 is always preferred for metal-rich conditions; 2 is usually preferred for chemically balanced conditions; c1, c2 are equally preferred for calcogen-rich conditions

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 15 / 32

Electronic properties of edges in 1T’ TMDs

Energetically preferred terminations are considered; Method: DFT + Green’s function (NEGF)

• 1

1 Energy (eV) 1

Balanced

MoS2

2

MoSe2

2

MoTe2

2

WS2

2

WSe2

2

WTe2

• 1

1 Energy (eV) m2

M-rich

m2 m2 m2 m2 m2 1 ky ( /b)

• 1

1 Energy (eV) c2

C-rich

1 ky ( /b) c1 1 ky ( /b) c1 1 ky ( /b) c2 1 ky ( /b) c2 1 ky ( /b) c1

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 16 / 32

Is topological protection of the ballistic transport regime possible?

Topologically protected transport

Protected Unprotected topological protection = protection against back-scattering

0A single spin channel is shown Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 17 / 32

Ballistic transport along 1T’-WSe2 edges

• 0.1

0.0 0.1 Energy (eV) WSe2 (2) Y Y

• 0.1

0.0 0.1 Energy (eV) WSe2 (c2)

non-uniform dispersion of edge modes; protected transport is possible in a narrow energy region and only at specific edges of 1T’-WSe2

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 18 / 32

What is available experimentally?

Experimental observations of the 1T’ phase in 2D WSe2

✓ Defect-free bulk

Images are courtesy of Miguel M. Ugeda, nanoGUNE, San Sebastian, Spain

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 19 / 32

Experimental observations of the 1T’ phase in 2D WSe2

✓ Defect-free bulk ? Regular periodic edges

Images are courtesy of Miguel M. Ugeda, nanoGUNE, San Sebastian, Spain

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 19 / 32

Experimental observations of the 1T’ phase in 2D WSe2

✓ Defect-free bulk ? Regular periodic edges ! Structural phase boundaries

Images are courtesy of Miguel M. Ugeda, nanoGUNE, San Sebastian, Spain

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 19 / 32

Structural phase boundary is topologically non-trivial

1T’-WSe2 interface states

2H 1T'

Images are courtesy of Miguel M. Ugeda, nanoGUNE, San Sebastian, Spain

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 20 / 32

Can theory confirm the presence of interface modes? Are these modes “topological”?

Atomic structures of phase boundaries in WSe2

Construct model: choose the zigzag edge of the 2H phase (2x); choose the zigzag edge of the 1T’ phase (4x, half discarded); concatenate

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 21 / 32

Electronic structure of phase boundaries in WSe2

Method: DFT + NEGF

• 1

1 E (eV) 1 Y K K' Y

• 1

1 E (eV) 5 2 Y K K' Y 6 3 Y K K' Y 7 4 Y K K' Y 8

1, 3 and 6, 8 are similar Multiple spectroscopic signatures No topological protection of transport

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 22 / 32

Conclusions

Edge modes of real topological materials require ab-initio description; DFT+NEGF calculations reveal multiple spin-polarized modes spanning a large energy region in 1T’-TMDs; The dispersion of edge modes is consistent with the QSH phase; Specific 1T’-WSe2 edges are suitable for ballistic charge carrier transport protected against back-scattering; Regular topological phase boundary is accessible experimentally!

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 23 / 32

Topological edge states carry spin-polarized current in a non-magnetic media → applications for spintronics and quantum computing. Other examples in 2D?

Idea

2H phase

= = = , K K' Γ

Discriminate valleys in some physical process → spin-valley coupling → induce spin polarization

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 24 / 32

Example: optical excitation of charge carriers in semiconducting 2D MoS2

Cao et al. Nat Commun 3 887 (2012)

Also: Mak et al. Nat Nano 7 no. 8 494-498 (2012); Zeng et al., Nat Nano 7 no. 8 490-493 (2012)

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 25 / 32

Is it possible to achieve valley polarization in an all-electric manner?

Idea: valley-polarized transport across a line defect

• D. Gunlycke and C.T. White PRL 106, 136806 (2011), graphene

Symmetry: Tν (θ) = T−ν (−θ) = T−ν (θ) , Polarization: P(θ) = Tν=1 − Tν=−1 Tν=1 + Tν=−1 ≈ sin θ Tν - transmission probability; ν = ±1 - valley; θ - group velocity angle In TMDs valley ν and spin σ are coupled!

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 26 / 32

Results of simulations: line defects in 2H-MoS2

Pulkin & Yazyev, Phys. Rev. B 93 041419(R) (2016) valley and spin filtering with strong energy dependence spin-orbit transport gap for holes in IDB1

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 27 / 32

Poor/no transport across inversion domain boundaries: why?

Ballistic transport

MoS MoS

2 2

periodic Line defect semi-infinite

Take into account:

conservation of energy ( = ballistic transport); conservation of pseudo-momentum ( = periodic line defect); conservation of spin ( = planar non-magnetic defects)

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 28 / 32

Ballistic transport

MoS MoS

2 2

periodic Line defect semi-infinite

Project the bands onto 1D Brillouin zone (BZ) of the defect (size 2π/d)

d - periodicity of the defect a - TMD lattice constant (3-4 ˚ A)

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 28 / 32

Transport gap Et

Spin match (no gap) e.g. sulfur vacancy line Spin mismatch (transport gap) e.g. inversion domain boundary

K K K’ K’ K K’ K’ K

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 29 / 32

Transport gap Et: criterion

Other line defects with a transport gap?

Defect periodicity vector

d = nLa1,L + mLa2,L = nRa1,R + mRa2,R d = (1, 0) |d| = a = 0.3 nm d = (1, 0)L = (−1, 0)R |d| = a = 0.3 nm d = (3, 5)L = (5, 3)R |d| = 7a = 2.2 nm

Komsa et. al. PRB 88, 035301 (2013); Zhou et. al. Nano Lett. 13, 2615-2622 (2013) Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 30 / 32

Transport gap Et: criterion

Spin match (no gap) e.g. sulfur vacancy line Spin mismatch (transport gap) e.g. inversion domain boundary

K K K’ K’ K K’ K’ K

(nL − mL) mod 3 = (nR − mR) mod 3 = 0 0 = (nL − mL) mod 3 = (nR − mR) mod 3 = 0

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 31 / 32

Summary

2D TMDs are prospective materials for modern electronics, spintronics and topological electronic structure community; There is a large experimental effort towards confirming the QSH phase in 1T’-TMDs; Line defects found in these materials can be employed for spin-selective transport both along or across the defect, with or without relying on topological arguments; In either case, the spin polarization of charge carrier current exists without net magnetization and macroscopic magnetic fields: fewer spin relaxation channels and the increased spin lifetime in the material

Artem Pulkin (Caltech, EPFL) Transport in 2D materials November 1, 2017 32 / 32

Thank you