1. science
2. physics

Chun Ning Lau
(Jeanie)
Quantum Transport!
in!
2D Atomic Membranes!
Because most of the ‘low-hanging graphene fruits’ have already been
harvested, researchers have now started paying more attention to other
two-dimensional (2D) atomic crystals6 such as isolated monolayers and
few-layer crystals of hexagonal boron nitride (hBN), molybdenum
disulphide (MoS2), other dichalcogenides and layered oxides. During
the first five years of the graphene boom, there appeared only a few
stack represents an artificial material assembled in a chosen sequence—as
in building with Lego—with blocks defined with one-atomic-plane precision (Fig. 1). Strong covalent bonds provide in-plane stability of 2D
crystals, whereas relatively weak, van-der-Waals-like forces are sufficient
to keep the stack together. The possibility of making multilayer van
der Waals heterostructures has been demonstrated experimentally only
2D Materials and Heterostructures!
Figure 1 | Building van der Waals
heterostructures. If one considers
2D crystals to be analogous to Lego
blocks (right panel), the construction
of a huge variety of layered structures
becomes possible. Conceptually, this
atomic-scale Lego resembles
molecular beam epitaxy but employs
different ‘construction’ rules and a
distinct set of materials.
Graphene
hBN
MoS2
WSe2
Fluorographene
Geim, Nature 2013.
1
School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK. 2Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester M13 9PL, UK.
•  Conductors, e.g. graphene, few-layer graphene
2 5 J U LY 2 0 1 3 | V O L 4 9 9 | N AT U R E | 4 1 9
©2013 Macmillan Publishers Limited. All rights reserved
•  Semiconductors, e.g MoS2, WS2,
•  Superconductors, Nb2Se3
•  Insulators, e.g. hBN
•  Charge density waves, e.g. NbSe
•  Ferromagnets, e.g. VSe2
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Outline!
•  There is still life in graphene….
•  Beyond graphene
•  Few Layer MoS2
•  Few-layer Phosphorene
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Dual-Gated Suspended ABC Trilayer Graphene
4
2
100
G (µS)
G (µS)
400
200
4
2
10
4
0
0
mobility
20,000 –
90,000 cm2/
Vs
40
2
80
0.00
T (K)
0.05
1/T (1/K)
42 mV
4
•  Metal – insulator transition, Tc ~ 35K
•  Thermal activation measurement yields
Δ ~ 41 meV
•  G(Vbias) curves at E⊥=n=0 yield Δ ∼ 42 meV
April 2015
dI/dV (µS)
2x10
0
-40 VV (mV)
bias
bias (V)
NSF US EU Workshop on 2D Layered Materials & Devices
40
Effect of electric and magnetic fields
Differential conductance G vs source drain bias V at n=0"
V (mV)
40
G(µS)
3
10x10
5
0
0
-40
0
B|| (T)
30
•  gap educed symmetrically by |E⊥|!
à  not layer polarized; arises from electronic interactions"
•  gap reduced by parallel magnetic field at 30T"
Y. Lee, D. Tran, K. Myhro, J. V. Jr., N. Gillgren, C. N. Lau, Y. Barlas, J. M. Poumirol, D. Smirnov, and F. Guinea,
Nature Communications, 5, 5656 (2014)
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Proposed Phase Diagram!
U⊥
Quantum Valley Hall
Layer Anti- Canted AntiFerromagnet Ferromagnet
Ferromagnet
B||
Current EU collaboration:
Paco Guinea (CSIC, Spain; Machester)
Frank Koppens (ICFO; Spain)
April 2015
Y. Lee, D. Tran, K. Myhro, J. V. Jr., N. Gillgren, C. N.
Lau, Y. Barlas, J. M. Poumirol, D. Smirnov, and F.
Guinea, Nature Communications, 5, 5656 (2014)
NSF US EU Workshop on 2D Layered Materials & Devices
MoS2
•  gapped, On/Off ratio >106
•  direct-to-indirect band gap
transition as function of
thickness
•  valley physics
But
Mobility <~ 200 – 500 cm2/Vs
Radisavljevic et al, Nat. Nanoetchnol. 2011.
What is the mobility bottlenck?
Wu et al, Nat. Phys. 2013.
and many others
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Suspending MoS2
•  the mobility is even lower, 0.1 -50
cm2/Vs
•  gas annealing à 200 cm2/Vs
•  Removing substrates does not
significantly improve mobility
•  Other mobility bottlenecks:
•  Schottky barriers at contact
F. Wang, M. Gray, P. Stepanov and C.N. Lau,
Nanotechnology, in press (2015)
April 2015
•  impurity scattering
•  defects
NSF US EU Workshop on 2D Layered Materials & Devices
Ionic liquid gating of MoS2
In collaboration with Robert Haddon at UCR
•  Ionic liquids are molten salts with low melting point
•  can induce high carrier density (up to 1014 cm-2)
•  To date all IL gating are performed on substrate-supported devices
•  Suspended devices – enable gating from both surfaces
IL"
S"
SiO2"
D"
IL"gate"
Si"
VILg"
F. Wang, M. Gray, P. Stepanov and C.N. Lau, in preparation (2015)
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Comparing Suspended and non-suspended devices
Performed IL gating of 9 suspended and 9 substrate-supported
samples
•  use DEME-TFSI
• 
all suspended devices are more
conductive by at least 1-2 orders of
magnitude
à IL gating is more effective in freestanding devices
Mechanism:
1.  Higher charge density
2.  Better screening
F. Wang, M. Gray, P. Stepanov and C.N. Lau, in preparation (2015)
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Transport Mechanism
VIlg=0
Schottky emission at MoS2-electrode interfaces
(a)
I (µΑ)
8
(e)
$a V −Φ '
B
I ∝ exp &
)
% k BT
(
-16
-1
Vds (V)
1
a=e
5
e
4πε 0εr d
I (µΑ)
slope yields εr ~ 11
à  dielectric constant of DEME-TFSI ~ 14.5
à  agrees with literature values
-5
-1
Vds (V)
1
Fujimoto, T.; Awaga, K. Phys Chem Chem Phys 15, 8983 (2013).
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Charge Density Induced in Suspended MoS2
Compare ΔVbg and ΔVIL needed to
induce the same change in
conductance
ratio of ionic liquid gate to back gate:
up to 450
à  α up to 4.6x1013 cm-2 V-1
> 2-4x previous values
F. Wang, M. Gray, P. Stepanov and C.N. Lau, in preparation (2015)
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
IL-tuned Metal Insulator Transition
VILg =3V
2V
100
VILg =3V
2V
1.5V
σs (µS)
1.5V
10
1V
1V
0V
1
0V
-0.5V
-0.5V
0.1
120
200
T (K)
0.004
1/T (1/K)
0.008
•  metal insulator transition observed as VILg is tuned
•  At small VILg, transport via thermal activation
$a V −Φ '
B
I ∝ exp &
)
k
T
%
(
B
April 2015
a=e
e
4πε 0εr d
obtained from I-V curves
NSF US EU Workshop on 2D Layered Materials & Devices
Conclusion
•  Mobility not limited by substrate in current generation of devices
•  Bottleneck: Schottky barrier at MoS2-electrode interface
see Cui et al, arXiv 1412.5977 (2014)
à critical: contact engineering
•  Ionic liquid gating of suspended devices
à  ion accumulation on both surfaces
à  higher charge density, enhanced screening
•  Further optimization à Ultra-high density regime for new phases
•  p-doping à spin/valley transport
F. Wang, M. Gray, P. Stepanov and C.N. Lau, in preparation (2015)
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Outline!
•  Few Layer Graphene
•  Few Layer MoS2
•  Fabrication and annealing of suspended MoS2
•  Ionic liquid gating
•  Few-layer Phosphorene
•  Fabrication of air-stable, high mobility devices
•  Observation of quantum oscillation
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
“Curse of 2D Materials”
•  Mobility ~ 105 – 106 cm2/Vs
MoS2,WS2, MoSe2,
WSe2, etc
•  Gapless
•  Mobility ~ 100 cm2/Vs
Graphene
•  Gapped
Black Phosphorus
• 
• 
• 
most stable form of phosphorus
layered structure
bulk mobility up to 60,000 cm2/Vs
peroidictable.com
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Black Phosphorus
•  only other layered element
•  Puckered atoms within layers
•  Anisotropic
•  Thickness dependent band
gap, 0.3 - 2 eV
Tran et al, PRB 2014
April 2015
Asahina & Morita, J. Phys. C, 1986
•  Direct band gap for all
thickness
NSF US EU Workshop on 2D Layered Materials & Devices
Few-Layer Black Phosphorus Transistors
•  ambipolar transport
•  gapped, on/off ration ~105
•  Anisotropic Transport
•  Mobility ~100-1000 cm2/Vs
for thickness ~2 – 20 nm
Li et al, Nature Nanotechnol 2014
Liu et al, ACS Nano 2014
April 2015
•  Best of both worlds!
Xia et al, Nature Comm. 2014
NSF US EU Workshop on 2D Layered Materials & Devices
Challenges
Kroenig et al, APL 2014
Island et al, 2D Materials 2014
Instability in air
•  react with water and O2 to form phosphoric acid
•  reaction accelerated by light
April 2015
Favor et al, arxiv 2014
NSF US EU Workshop on 2D Layered Materials & Devices
Encapsulation for stable, high mobility Devices
hexagonal boron nitride (hBN)
from wikipedia
•  atomically flat
•  no dangling bonds à little trapped charges
•  high mobility graphene/hBN devices demonstrated
Columbia group, Nature Nanotechnol. 2012
Encapsulate few-layer phosphorene with hBN?
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Device Fabrication
phosphorene
hBN
top gate
PDMS
hBN
electrode
SiO2
Si/SiO2
•  Dry transfer to form hBN/few-layer
phosphorene/hBN heterostructure
sandwiches
•  etch to expose edges of phosphorene
•  1D metallic contact to 2D layers
Wang et al, Science 2013
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Device Stability
Encapsulated in hBN (our data)
Wood et al, Nano Letters 2014
•  Device left in air for 2 weeks
•  Slight shift in charge neutrality point
•  Only slight decrease in conductance & mobility
N. Gillgren, D. Wickramaratne, Y. Shi, T. Espiritu, J.Yang, J. Hu, J. Wei, X. Liu, Z. Mao, K. Watanabe, T. Taniguchi,
Marc Bockrath, Yafis Barlas, R. K. Lake, C.N. Lau, 2D Materials, 2, 011001 (2014)
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Rxx (Ω)
Rxx (Ω)
Device mobility
•  Ambipolar transport
•  On/off ratio ~ 105
•  linear I-V à ohmic contact
April 2015
•  Metal-insulator transition
•  highly hole-doped: metallic, µ up to 4000
•  towards band edge: insulating, µ ê with T
NSF US EU Workshop on 2D Layered Materials & Devices
Quantum Oscillations
ΔRxx (Ω)
Rxx with smooth background subtracted
•  oscillations periodic in 1/B
•  oscillations periodic in Vg ~n
•  doubling frequency in for B>8T à
Zeeman splitting
a
c
d
N. Gillgren, D. Wickramaratne, Y. Shi, T. Espiritu, J.Yang, J. Hu, J. Wei, X. Liu, Z. Mao, K. Watanabe, T.
Taniguchi, Marc Bockrath, Yafis Barlas, R. K. Lake, C.N. Lau, 2D Materials, 011001 (2015)
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Temperature Dependence Quantum Oscillations
Oscillations’ amplitude
dependence on T
b
•  effective mass of
charge carriers ~0.25
to 0.31 me as Fermi
energy increases
towards band edge
•  agree with DFT
calculations within
50%
N. Gillgren, D. Wickramaratne, Y. Shi, T. Espiritu, J.Yang, J. Hu, J. Wei, X. Liu, Z. Mao, K. Watanabe, T.
Taniguchi, Marc Bockrath, Yafis Barlas, R. K. Lake, C.N. Lau, 2D Materials, 011001 (2014)
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
Conclusion
•  Few layer phosphorene has both high mobility and band gap
•  Stable via hBN encapsulation
Outlook
•  Physics
b
•  strain-dependent band gap
•  large anisotropy (up to factor of 60, electrical and thermal
transport, thermopower)
•  electric field effect
•  quantum Hall effect
•  Electronics and optoelectronics
•  hBN encapsulation of reactive 2D materials
Number
20
see Cao et al, arXiv: 1502.03755
0
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
1
2014 month
12
Acknowledgments!
Graduate Students
Undergraduate Students
Tim Espiritu
Kevin Thilahar
Mason Gray
Ziqi Pi
Yongjin Lee"
Jhao-wun Huang " Fenglin Wang"
Kevin Myhro " Yanmeng Shi" Nathaniel Gillgren"
UCOP
Petr Stepanov"
April 2015
Son Tran "
NSF US EU Workshop on 2D Layered Materials & Devices
Collaborators!
UCR Physics UCR Chem. & CEE
Marc Bockrath
Robert Haddon
Florida Mag Lab
Dmitry Smirnov
Tulane
Zhiqiang Mao
UCR Physics
Yafis Barlas
Tulane
Jiang Wei
Jean-Marie Poumirol
April 2015
NSF US EU Workshop on 2D Layered Materials & Devices
UCR EE
Roger Lake
CSIC
Paco Guinea