1. No category

Electronic Proper-es of Atomically Thin Transi-on Metal Dichalcogenides Tony F Heinz Departments of Applied Physics and Photon Science Stanford University and SLAC Na?onal Accelerator Lab 2D Transi-on Metal Dichalcogenides (TMDC) Monolayer TMDC Honeycomb laBce with broken sublaBce symmetry/ broken inversion symmetry S Mo S K K’ 2D Semiconductors
•  Evolution of electronic structure with thickness
•  Many-body effects and excitonic interactions
•  Accessing individual valleys
Photoluminescence from Atomically Thin MoS2 Layers 0.01
Quantum Yield
PL Intensity (a.u.)
1E-3
Strong enhancement In light emission for monolayer 1E-4
1E-5
1lay
2lay
1E-6
1
2
3
4
5
6
Layer Number
1.4
1.6
> 1000 x compared to bulk 1.8
Photon Energy (eV)
2.0
2.2
Mak et al. PRL (2010) Also Feng Wang group: Splendiani et al. Nano Le@. (2010) Op-cal contrast image Photoluminescence image Band Gap Varia-on in MoS2 7
A
6
X3
X 300 Normalized PL
5
B
I
X X
300 3
6lay
5lay
4
4lay
3
Quantum confinement 3lay
2
2lay
X 100 1
1lay
0
Mak, TFH et al. PRL (2010) 1.4
1.6
1.8
Photon Energy (eV)
2.0
2.2
Indirect-­‐Direct Band Gap Transi-on B I A K Γ Blue: Mo orbitals Magenta: S orbitals (Talat Rahman group, UCF) Variety of TMDC Crystals MX2 monolayers Heinz group, Nano LeX 2014 MoS2 MoSe2 WS2 WSe2 MoTe2 1 – 2 eV Direct gaps CVD Growth of Alloys: MoS2x Se2(1-­‐x) a)
b)
1.4
1.9
Intensity (a.u.)
Photoluminiscence Energy (eV)
2.0
Photoluminiscence Energy (eV)
1.9 1.8
1.7
1.6
1.5
S 2p 3/2
Se 3p½
1.8
700
800
Wavelength (nm)
900
152
156
160
164
1.7
1.6
0
0.25
0.5
0.75
Composition (Fraction Sulfu
Heinz group with Bartels group (UC Riverside) [Adv. Mater. (2014)] Metal alloys: MoxW(1-­‐x)S by Suenaga group [Nat. Commun. (2014)] Also: Recently demonstrated exfoliated monolayer MoTe2 with 1.0 eV band gap S 2p ½
Binding Energy / eV
1.5
600
Se 3p3/2
Evolu-on with Layer Thickness Twisted MoS2 Bilayers
Van der Zande et al. Nano LeX. (2014): with Hone, Muller, Reichman groups Twisted MoS2 Bilayers
Direct HR-­‐TEM atom imaging – Muller group, Cornell Twisted MoS2 Bilayers
SHG probe of orienta?on Twisted MoS2 Bilayers PL spectra versus twist angle Twisted MoS2 Bilayers PL spectra versus twist angle Twisted MoS2 Bilayers PL spectra versus twist angle Twisted MoS2 Bilayers Hybridiza?on of electronic states produces new transi?ons and indirect gap behavior Twisted MoS2 Bilayers Nonlinear op?cal proper?es of single layer MoS2 Giant enhancement of second-­‐harmonic genera?on from single layer MoS2 Second-­‐harmonic genera?on from MoS2 Direct band gap? Direct band gap? Strong second-­‐harmonic again for trilayer MoS2 Strong second-­‐harmonic genera?on from odd-­‐layer MoS2 Strong second-­‐harmonic genera?on from odd-­‐layer hexagonal BN Symmetry criterion for second-­‐harmonic genera?on SHG is dipole-allowed only in
non-centrosymmetric media
Inversion symmetry-­‐breaking in single layer MoS2 Symmetry-­‐breaking in single layer MoS2 MoS2 symmetry group
Second-order polarizability tensor elements
Bulk
D6h4 (P63/mmc)
All elements vanish
Even
D3d3 (P3m1)
All elements vanish
Odd
D3h1 (P6m2)
χyyy= -χyxx= -χxxy= -χxyx
In-­‐plane dependence of second-­‐harmonic genera?on Heinz group, Nano Lett. (2014)
Also:
Malard et al (2014)
X. Zhang et al. (2014)
Determina?on of orienta?ons of crystallographical axes Piezoelectric Response of MoS2 Heinz group with Hone (Columbia) and Wang (Georgia Tech) Nature 470 (2014). 2D Semiconductors
•  Evolution of electronic structure with thickness
•  Many-body effects and excitonic interactions
•  Accessing individual valleys
Monolayer MoS2 Absorp-on: Excitonic Transi-ons A B CB A VB B Δso 2D Band-­‐ Band transi?ons Exciton Binding Energy? A B CB A VB B Δso Excitons in TMDC monolayers
theoretical predictions
~ 40 meV in bulk
EX = 500 – 1000 meV
free-standing layers
T. Cheiwchanchamnangij et al., Phys. Rev. B., 85, 205302 (2012)
A. Ramasubramaniam, Phys. Rev. B., 86, 115409 (2012)
H.-P. Komsa and A.V. Krasheninnikov, Phys. Rev. B., 86, 241201 (2012)
H. Shi, et al., Phys. Rev. B. 87, 155304 (2013)
A. Molina-Sanchez et al., Phys. Rev. B. 88, 045412 (2013)
D.Y. Qui et al., Phys. Rev. Lett. 111, 216805 (2013)
F. Hüser et al., Phys. Rev. B. 88, 245309 (2013)
G. Berghäuser and E. Malic, Phys. Rev. B. 88, 045318 (2013)
T.C. Berkelbach et al. Phys. Rev. B. 88, 045318 (2013)
A. .Steinhoff et al., Nano. Lett., 14, 3743 (2014)
T. Rahman et al., Phys. Rev. B 90, 085419
quantum
confinement:
x4
EX ~
effective mass
dielectric screening2
36
Optical absorption
Higher-­‐Lying Exciton States in WS2 2.0
2.5
Energy (eV)
3.0
Exciton Rydberg series in 1L WS2
n =1
2
3
4 5
2.5
Energy (eV)
Derivative of RC
2.1
2.3
2D
hydrogen
2.2
2.1
x 0.03
2.0
Eg
2.4
2.2
2.3
Energy (eV)
2.4
1 2 3 4 5
Quantum number n
Exciton binding energy ~ 320 meV
A. Chernikov et al., PRL, 113, 076802 (2014)
38
Non – Hydrogenic Behavior
1s
strong
screening
in the layer
weak screening in
the surroundings
Non – uniform dielectric environment
2s
10
Comparison of theory and experiment
WS2 1L
2.5
Eg
Energy (eV)
2.4
Exciton binding energy (supported samples)
A. Chernikov et al., Phys. Rev. Lett., 113, 076802 (2014)
2.3
EX = 320 (±40) meV
2.2
Experiment
Theory
2.1
1
2
3
4
5
Quantum number n
see also:
K. He et al., Phys. Rev. Lett., 113, 026803 (2014)
M.M. Ugeda et al., Nature Mat., doi:10.1038/nmat4061 (2014)
Z. Ye et al., Nature, doi:10.1038/nature13734 (2014)
G. Wang et al., arXiv:1404.0056 (2014)
B. Zhu et al., arXiv:1403.5108 (2014)
40
1s Excitonic Wavefunc-on in WS2 Exciton wavefunctions
Bohr radius ~ 1 nm
Radial probability
n=1
0
1
2
3
4
Electron – hole separation (nm)
5
n=2
0
1
2
3
4
5
6
Electron – hole separation (nm)
7
8
9
10
42
Linear Op-cal Response: Excitons Heinz group Phys Rev. B (2014) Linear Op-cal Response: Excitons WS2 monolayer Phys Rev. B (2014) Higher Many-­‐Body States
Exciton h+
e-
e-
h+
e-
-­‐ X
e-
h+
e-
h+
Gate tunable charged exciton Trion
Biexciton: Excitonic molecule Mak et al. Nature Materials (2013) You et al., Nature Phys. (in press) Xiaodong Xu Also: Charged Excitons
New stable, tunable exciton states h+
ee-
X-­‐ Trion
____________ 35 meV h+
X e-
MoSe2 Also: Xiaodong Xu Mak, TFH, et al. Nature Materials (2013) Biexciton States
You, TFH et al., Nature Phys. (in press) Biexciton States: Four Body Correlated State
You, TFH et al., Nature Phys. (in press) Observa-on of Strong Excitonic Interac-on in TMDCs scaYering exciton
e-­‐h plasma biexciton trion annihila-on linear Low excitation
density
nonlinear Intermediate excitation density
High excitation density
2D Semiconductors
•  Evolution of electronic structure with thickness
•  Many-body effects and excitonic interactions
•  Accessing individual valleys
Valley degree of Freedom TRS K K’ Di Xiao, Wang Yao, Xiaodong Xu, PRL 2012 Valley degree of Freedom Accessed by Circularly Polarized Light K K’ Di Xiao, Wang Yao, Xiaodong Xu, PRL 2012 Valley dependent op-cal selec-on rules Broken inversion symmetry Finite intercellular angular momentum Coupled valley-­‐spin excitonic absorp5on B
A
Plus: Intracellular angular momentum (orbital) Electron spin 1.  How exact are the selec5on rules? 2.  How long can the carriers be retained in one valley? K
K’
Also: H. Zeng et al., Nature Nanotech T. Cao et al., Nature Comm. G. Sallen et al, PR B Op-cally induced valley-­‐spin polariza-on in MoS2 monolayers I+ − I−
ρ≡
I+ + I−
K K’ Highly selecHve pumping Complete retenHon at one valley Mak, TFH et al. Nature Nano. Coupled Valley-­‐Spin in Monolayer MoS2 H SO
K 1    
= 2 Si ∇V ( r ) × p
2c
(
)
K’ Zhu et al. PRB 2011 D. Xiao et al. PRL 2012 Open ques-ons •  How to tune and manipulate the individual valley? Valley Degeneracy Break TRS with a magne5c field K K’ •  Valleys are degenerate by Hme reversal symmetry •  Electric field •  Strain •  Doping Neutral exciton (X0) PL magne-c shi] σ− σ+ K’ K Zeeman shi] of the X0 PL peak X0 Experimental slope (0.01 meV/T) − + 0.12 meV/T Predicted slope − + 0.12 meV/T Yilei Li, TFH, … Jonathan Ludwig, Dmitry Smirnov, Zhiqiang Li (NHMFL), PRL (2014) Valley polariza-on by valley spli`ng B EF K K’ Varia-on in Rela-ve Strength of X0 and X-­‐ Emission -­‐> Produced valley polariza5on (popula5on difference) Valley Control of Transport Electrical bias h+
e-
e-
h+
ee-
Helicity-­‐dependent photo-­‐Hall current Kin Fai Mak, McEuen, Park Cornell Valley Hall Effect Science (2014) Valley Occupa-on and Excitonic Correla-on (a)$
XD#
XD#
XK#
X$K#
XK#X$K#
XK#XD#
X$K#XD#
XD#XD#
XK#XK#
(c)$
XK#X$K#
EXX#$#EX#
(b)$
XK#
X$K#
EX#
K$
(K$
Summary: Monolayer TMDs 1.  New band structure and light emission for atomically thin layers Direct-­‐gap material with strong light emission in monolayer New materials, syntheses 2. Strong many-­‐body effects and excitonic interac-ons Excitonic Rydberg series with nonlocal screening WS2 binding energy ~ 320 meV Tunable charged excitons, biexcitons, … 3. Accessing the valley degree of freedom Selec-ve excita-on of valleys by circularly polarized light Tuning valleys and crea-ng steady-­‐state popula-on by breaking -me-­‐reversal symmetry with magne-c field 4. Crea-ng new materials: 2D heterostructures Tunable electronic structure as a func-on of twist angle Rapid charge transfer and separa-on in heterostructures •  Columbia University –  Heinz group: Burak Aslan, Alexey Chernikov, Heather Hill,Yilei Li, Holger Lange, Kin Fai Mak, Yi Rao, Albert Rigosi, Cyrielle Roquelet, Claudia Ruppert, Dezheng Sun, Yumeng You, Xiaoxiao Zhang, Arend van der Zande –  Louis Brus group –  Jim Hone group – Changgu Lee, Gwan Hyoung Lee –  Philip Kim group –  David Reichman group: Tim Berkelbach •  Brookhaven Na?onal Lab: Mark Hybertsen •  Penn State University: Jie Shan, Kin Fai Mak groups •  Cornell University: David Muller group •  U Central Florida: Talat Rahman group •  UC Riverside: Ludwig Bartels group •  NHMFL, Tallahassee: Dmitry Smirnov and Zhiqiang Li groups NSF, AFOSR, DOE
Keck, von Humbot Foudations
Collaborators And specially thanks to