Systems of Transition Metal Dichalcogenides : Controlling ...
Valley and spin physics in 2D transition metal dichalcogenides · Wang Yao The University of Hong...
Transcript of Valley and spin physics in 2D transition metal dichalcogenides · Wang Yao The University of Hong...
Wang Yao
The University of Hong Kong
Valley and spin physics in2D transition metal dichalcogenides
Prof. Xiaodong Cui(HKU)
Prof. Xiaodong Xu(U of Washington)
Acknowledgement
Funding
CollaboratorsGroup @ HKU
Zhirui GongHongyi Yu Guibin Liu Pu Gong
Prof. Di Xiao(Carnegie Mellon U)
Outline
Valley physics from inversion symmetry breaking
Spin‐valley coupling in monolayer TMDCs
Interplay of spin, valley & layer in bilayer TMDCs
Exciton Dirac spectra in monolayer TMDCs
Valley index of Bloch electron
Valley index of Bloch electronDegenerate energy extrema of Bloch bands in momentum space
Long lifetime of valley polarization expectedIntervalley scattering suppressed by large k-space separation
In atomically thin 2D crystals: graphene, BN, MoS2 etc.
Valley polarization
Valley index of Bloch electron
Lesson from spintronics
ValleytronicsValley for encoding information
How to distinguish the valleys?
Control of the valley dynamics?
Measurable quantities associated with valley index?
= 0 = 1
Beenakker et al., Nat Phys. 07”Shayegan et al., PRL 06”
Valley vs spin for information processing
Magnetic moment
Hall effect
Spin ValleyIndex of Bloch
electronAssociatedphysical phenomena
Optical selection rule
WY, Xiao & Niu, PRB 08”
Xiao, WY & Niu, PRL 07”
Valley physics from inversion symmetry breaking
Valley can be manipulated in ways similar to spin
Key quantities: Berry curvature & orbital magnetic moment
Hall effect
Valley contrasting properties by ISB
Time-reversal symmetry
Space-inversion symmetry
k k
k k
m m k k
m m k k
Valley contrasting properties
– Necessary condition: inversion symmetry breaking (ISB)– Opposite & m for a time reversal pair of valleys
Both symmetries 0 k 0m k
2
2
Example: graphene with staggered sublattice potential
H = at(�kx σx + ky σy )+∆2σz − λ�
σz − 1
2sz
Massive Dirac fermion:
Berry curvature 1 ( 1)z at valley K (-K)
Valley contrasting Berry curvature
Xiao, WY & Niu, PRL 99, 236809 (2007)
Valley Hall effect
Gapped energy dispersion
gapped Dirac cones
Valley optical selection rule
Magnetic moment 1 ( 1)z at valley K (-K)
magnetic moment of valley pseudospin
WY, Xiao & Niu, PRB 77, 235406 (2008)
Valley selection rule of interband transition
K ‐ KGapped energy dispersion
gapped Dirac cones
Layered structure suitable for extracting monolayer by mechanical exfoliation
Bulk or even‐layers Monolayer
with inversion symmetry
without inversion symmetry
MX2
2D transition metal dichalcogenides
z
x
Top view
x
z Even‐odd oscillation of SHGZeng, et al. Sci Rep 13”
Indirect bandgap Direct bandgap
Splendiani et al., NL 10”Mak et al., PRL 10”
Monolayer group VIB TMDCs
H = at(�kx σx + ky σy )+∆2σz − λ�
σz − 1
2sz
|φci = |dz2 i
|φ⌧v i =1p2(|dx 2 − y2 i + i�|dxy i )Basis:
Hamiltonian:
a ∆ t 2λM oS2 3.193 1.66 1.10 0.15
W S2 3.197 1.79 1.37 0.43
M oSe2 3.313 1.47 0.94 0.18
W Se2 3.310 1.60 1.19 0.46
cos c v
Valley optical selection rule
K ‐ K
k 4cos22cos2
Degree of circular polarization:
Massive Dirac fermions at the band edge
Valley Hall effectBerry curvature: k 3t2
2(2 3k 2a2t2 )3/2
Valley index: 1 1 at K (-K) valley
eV
Xiao, Liu, Feng, Xu & WY, PRL 108, 196802 (2012)
(neglecting SOC)
Optical generation of valley polarization
Cui group @HKU: Zeng, Dai, WY, Xiao & Cui, Nature Nano. 12”
Parallel works: Heinz group @Columbia (Nat. Nano. 12”); PKU‐CAS group (Nat. Comm. 12”)
Optical pump of valley polarization
K ‐ K
Electrically tunable polarized PL in biased bilayer MoS2
Polarized PL under circular polarized excitation in monolayer MoS2
Optical detection of valley polarization
Pump with ‐ light => e‐h pairs in valley K
Valley polarization of e (h) => Faraday rotation
Valley polarization of e‐h pair => polarized photoluminescence
Xu group @ UW: Wu, Ross, Liu et al., Nature Physics 13”
Valley optical selection rule
Controllable inversion symmetry breaking by perpendicular electric field
Absence of Hanle effect: magnetic field do not couple K & –K
Strong Coulomb binding: valley excitons with optical selection rules
σ+ Incident
Energy (eV)
1.60 1.65 1.75
Gat
e (V
)
Photon Energy (eV)
Xo
X+
X-
X -’
60
0
-60
40
20
-40
-20
1.70
σ- Incident
Black: σ+Red: σ-
-5V
Xo
450
300
150
0
-5V
+10VX- Xo
360
240
120
+10V
-60VX+150
75
0 1.60 1.65 1.70 1.75 1.60 1.65 1.70 1.75
-60V
Energy (eV)
Valley polarization of excitons & trions
‐K K‐K K
Detection
eehh
eehhhh
eehhee
σ-σ+
Prof. Xiaodong Xu
Jones, Yu et al., Nature Nano. 13”
monolayer WSe2
Optical generation of valley coherence
Valley optical selection rule
Linear polarized light excite two valleys in linear superposition
Possibility to address valley coherence in macro systems
(Jones, Yu et al., Nature Nanotech 13”)
= +
Linear polarized PL: polarization angle coincide with excitation
Optical injected valley coherence can survive carrier relaxations
DetectionBlack: HRed: V
H Incident
X- Xo
+10V
Xo
-5V
X+-60V
1.60 1.65 1.70 1.75Energy (eV)
σ+ IncidentDetectionBlack: σ +
Red: σ -
-5V
Xo
450
300
150
0
-60VX+
150
75
0 1.60 1.65 1.70 1.75Energy (eV)
+10VX- Xo
360
240
120
PL In
tens
ity (c
ount
s/se
cond
)Excitonic valley coherence in ML WSe2
Valley polarization Valley coherence
Only X0 has linearly polarized PL
PL angle (degre
e)
In cid ent an gle (d egree)
Polarization
120
60
0
180
120600 180
0.4
0.2
0.0
C
Jones, Yu et al., Nature Nano. 13”
‐K K ‐K K
Valley coherence of X‐ broken by exchange w extra electron
Optical orientation of valley pseudospin
|K> + ei2 |-K>
|-K>
|K>
Valley pseudospin of electron‐hole pair (exciton)
(e‐h pair in valley K)
(e‐h pair in valley ‐K)
Outline
Valley physics from inversion symmetry breaking
Spin‐valley coupling in monolayer TMDCs
Interplay of spin, valley & layer in bilayer TMDCs
Exciton Dirac spectra in monolayer TMDCs
Out of plane spin
In plane spin
2D crystal with mirror symmetry
E(, k) E(, k)
Spin orbit coupling has to be out‐of‐plane, i.e. f (k)sz
Spin-valley coupling in monolayer
Time reversal symmetry
f (k) f (k)
mirror sym + time reversal sym + broken inversion sym
Hsoc zsz
Inversion symmetry
f (k) f (k)
Spin-valley coupling in monolayer
2D crystal with mirror symmetry => SOC f (k)sz
z 1 z 1
Spin-valley coupled massive Dirac fermions
• Spin‐valley coupling of hole (~ 0.15 eV in MoX2, ~ 0.4 eV in WX2)
Basis:
Hamiltonian:ra
H = at(�kx σx + ky σy)+∆2σz − λ�
σz − 1
2sz
|φci = |dz2 i
|φ⌧v i =1p2(|dx2 − y2 i + i�|dxy i) (m 2)
(m 0) On-site SOC:
L S LzSz 12
(LS LS )
• Spin‐valley coupling of electron (O(1) - O(10) meV)
K - K
• Spin and valley flip suppressed
• Valley Hall accompanied by spin Hall
Sign difference between MoX2 & WX2
K ‐ K
K ‐ K
WX2
MoX2
Guibin Liu et al., PRB 88, 085433 (2013)
mainly from coupling to remote m=±1 d band
mainly from mix in of porbitals
Spin dependent optical selection rule
Valley optical selection rule
K ‐ K
K ‐ K
AB
Valley & spin optical
selection rule
Selective excitation of valley & spin controlled by light polarization & freq
Xiao, Liu, Feng, Xu & WY, PRL 108, 196802 (2012)
WY, Xiao & Niu, PRB 77, 235406 (2008)
Outline
Valley physics from inversion symmetry breaking
Spin‐valley coupling in monolayer TMDCs
Interplay of spin, valley & layer in bilayer TMDCs
Exciton Dirac spectra in monolayer TMDCs
AB stacked TMDC bilayer & multilayers
• Neighboring layers are 180o rotation of each other
• 180o rotation switch the valleys but leave spin unchanged
AB stackingK -K
Hsocu zsz
Hsocl zsz
Hsoc z zsz
z 1
z 1
z 1 z 1
• Valley and layer dependent spin splitting:
Gong et al., Nat. Comm. 4, 2053 (2013).
AB stacking
K -K
Hopping at K:
Top L Bottom LHopping amplitude~ 0.1 eV
~ 0.15 eV for MoX2~ 0.4 eV for WX2
Top Layer
Bottom Layer
Suppression of interlayer hopping
• Interlayer hopping conserves spin and in‐plane momentum
Energy cost:
w SOC
w/o SOC
WS2 thin films
Suppression of interlayer hopping
Zeng, Liu, et al. Scientific Reports 3, 168 (2013)
w SOC
PL from WS2 :
PL from WSe2 :
IA B
Suppression of interlayer hopping
Zeng, Liu, et al. Scientific Reports 3, 168 (2013)
Prof. Xiaodong Cui
Spin & valley dependent layer polarization
Spin and valley dependent layer polarization:
Band edge carrier near K points:! ! ! ! ! ! ! ! ! ! ! ! !
! ! ! ! ! ! cos 2! , !!!!!cos 2! ≡!
! ! ! !!!
K
-K
Two‐sets of bands localized in opposite layers
~ 85% in MoX2~ 95% in WX2
~ 100%
Gong et al., Nat. Comm. 4, 2053 (2013).
Conduction band at ±K: hopping vanishes in leading order=> even larger ratio of over t,
Spin Hall & Spin circular dichroism
K -K
Bilayer optical selection rule:
Spin circular dichroism in bilayer
-K
K
sin2
cos2
Gong et al., Nat. Comm. 4, 2053 (2013).
E
E
Spin Hall in bilayer
ME effects from spin-layer locking
K
-K
tB0
1
-10
zs
Valley ‐K
Valley K
• Electrically tunable spin Larmor precession
0
-0.4
0.4
0 40 80
Ez
B0 0 40 80tB0
Valley dependent precession frequencies
Spin‐layer locking
Gong et al., Nat. Comm. 4, 2053 (2013).
• Oscillation of layer (electric) polarization in magnetic field
K K
K
K
K
-K
Spin doublet couples to both electric & magnetic fields, in different ways
K
-K
Spin‐layer locking
ME effects from spin-layer locking
Valley conditioned spin rotations
BzEz
Bx
t
Valley dependent spin splitting by E & B fields in z direction
Valley dependent spin resonance by oscillating Bx
K
-K
K -K
K
K
K
K
Faraday geometry
Gong et al., Nat. Comm. 4, 2053 (2013).
Electrically & magnetically driven ESR
K K
K K
K K
K K
Bx
Ez
t +_
Bz
t
K -K
Electrically driven ESR and magnetically driven ESR
Valley dependent interference of electric & magnetic fields
Voigt geometry
K
-K
Spin‐layer locking
E
v
c
⇑
Lower LayerUpper Layer
ɷ1ɷ2 c v‐ɷ1 ɷ2‐ =
σ+
σ-
Nor
mal
ized
PL
150V
60V
90V
120V
Energy (eV)1.61.651.71.75
ɷ1ɷ2
Evidence of spin-layer locking in bilayer PL
~ 100%
~ 95%
Prof. Xiaodong Xu
Jones, Yu, et al., Nat. Phy. 10, 130, 14”
PL from trion in BL WSe2
Electrically induced Zeeman splitting
K
150V
Energy (eV)1.6 1.65 1.7 1.75
Excitation: V
Black: VRed: H
ɷ1ɷ2150V
Energy (eV)1.6 1.65 1.7 1.75
Energy (eV)1.6 1.7 1.75
Jones, Yu, et al., Nat. Phy. 10, 130, 14”
VV
XIntralayerXInterlayer
X- Xo
+10V
1.60 1.65 1.70 1.75Energy (eV)
Monolayer WSe2
Interlayer & intralayer trionBilayer WSe2
Intralayer X‐: valley coherence suppressed, similar to monolayer
Interlayer X‐: valley coherence preserved, no exchange with excess electron
bottom layer has lower energy for excess electron
Outline
Valley physics from inversion symmetry breaking
Spin‐valley coupling in monolayer TMDCs
Interplay of spin, valley & layer in bilayer TMDCs
Exciton Dirac spectra in monolayer TMDCs
Tightly bound valley excitons in monolayer
1.60 1.65 1.75
Gat
e (V
)
Photon Energy (eV)
Xo
X+
X-
X -’
60
0
-60
40
20
-40
-20
1.70
Ultra strong coulomb binding
X0 binding energy: 0.5 – 1 eVBohr radius: ~ 1 nm
Large effective mass & reduced screening in 2D
Valley configurations
K -K
K -K
=
=
σ+
Valley‐orbit coupling
Trion binding 30 meVK -K
V(k)
strong e‐h exchange
Valley-orbit coupling of exciton
Effective valley‐orbit coupling
~ 10-2K
light cone
longitudinal branch
transverse branch
~ 2 meV
ωu
ωd
ω0~ 10-3K
probability for e-h to overlap~ aB
2
Coulomb in 2D
linear in k
strong coupling: VOC splitting >> radiative decay
chirality of 2
vanish at k = 0
rotation symmetry
Hongyi Yu et al. arXiv 1401.0667
Effect of tensile strain
-0.01 0 0.01
-0.01
0.01
0
kx / K
k y /Klight cone
2K J0
J
strain breaks rotational symmetry
I = 2 VOCin-plane
Zeeman field
one I = 2 cone
two I = 1 cones
light cone
2J0
20JcK
Linearly dispersed Dirac saddle point
Yu et al. arXiv 1401.0667
Gapped Dirac cone of trion
K -K K -K K -K K -K
exchangeexchange
Negatively charged trions
• Indexed by polarization of emitting photon + spin of extra electron (s)
• Exchange coupling with the extra electron
• An effective out-of-plane Zeeman field conditioned on the extra spin
valley pseudospin of recombining e-h pair ()
K -K K -K K -K K -K
exchangeexchange
E
10
Trion brightness
qX-1 0.991.01 -1 -1.01-0.99
0
-5
5
Ener
gy (m
eV)
Berry curvature (10
4Å2)
0
-2
2
≈≈
/ K
Gapped Dirac cone of trion
Trion valley Hall
Summary
Valley dependent Hall current, magnetic moment, optical selection rule from inversion symmetry breaking
A pair of time reversal symmetric valleys may play similar roles like spin in electronic applications
Strong spin‐valley coupling in monolayer TDMCs: valley control enables spin control
Coupling of layer pseudospin to valley & spin in bilayers: magnetoelectric effects, valley conditioned spin control
e‐h exchange of the tightly bound excitons: strong valley‐orbit coupling, strain tunable Dirac spectra