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Chun Ning Lau
(Jeanie)
Quantum Hall Effect in!
Few-layer Atomic Membranes!
Outline!
•  Symmetry-broken Ground State in Few Layer Graphene
•  Transport Properties of Ionic Liquid-Gated Suspended MoS2
Transistors
•  Quantum oscillations in Few-layer Phosphorene
October 2015
Graphene Canada
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
October 2015
Graphene Canada
What to ask a material scientist/experimentalist
Sure, but w
hat’s its
mobility?
October 2015
Graphene Canada
What to ask a material scientist/experimentalist
Sure, but w
hat’s its
mobility?
High Mobility allows exploration of
•  Better electronic devices and transistors
•  Novel phenomena not obscured by disorder
•  integer and fractional quantum Hall effect
•  magnetic focusing
•  electron optics
•  electron correlation
•  spontaneous symmetry breaking
•  ….
•  ultimate possibilities
•  set the stage for technological innovations and revolutions
October 2015
Graphene Canada
Usual Suspects of Mobility Bottleneck!
•  Lattice defects/substitutions/vacancies
•  Phonons
•  intrinsic
•  surface phonons from substrates
•  Impurities
•  intrinsic
•  charged impurities/dangling bonds from substrates
•  Ripples and corrugations
•  intrinsic
•  substrates
Schottky barriers (for semiconducting 2D materials)
elimination (suspended samples)
à substrate engineering
Andrei group
Kim group
atomically flat, no dangling bonds à hexagonal BN
Columbia group, Nat. Nanotechnol. 2012
October 2015
Graphene Canada
There is still life in graphene….
•  Extremely simple and elegant system and Hamiltonian
•  Rich physics
•  massless or massive Dirac fermions
•  possible phases: layer antiferromagnet, ferromagnet, unconventional
superconductivity, quantum spin Hall…
•  Strong interactions in few-layer graphene with competing symmetries
(layer, valley, spin, orbital…)
à rich phase diagram
•  Fantastic quantum Hall platform
•  multicomponent
•  lowest Landau level is 2L-degenerate (L=# layers)
•  extremely tunable (density, Btàspin, B⊥àorbital, E⊥àlayer)
October 2015
Graphene Canada
1, 2, 3…!
B-TLG
(ABA)
E = vF k
October 2015
2k 2
E=
2m *
Graphene Canada
“2+1”
r-TLG
(ABC)
3vF3 k 3
E= 2
t⊥
1, 2, 3…!
s at DP
e
t
a
t
s
f
o
y
it
dens
e
g
r
la
d
ates
n
t
a
s
s
n
d
e
n
k
a
o
r
b
b
t
y
•  Fla
metr
m
y
s
à
s
n
io
t
terac
in
ic
n
o
r
t
c
le
to e
trate
s
b
u
•  Unstable
s
y
b
g
reenin
c
s
e
iz
im
in
to m
s
le
p
m
a
s
d
ende
•  Use susp
B-TLG
(ABA)
E = vF k
October 2015
k
2m *
2 2
E=
Graphene Canada
“2+1”
r-TLG
(ABC)
3vF3 k 3
E= 2
t⊥
Gapped Insulating State in BLG!
dI/dV vs. Electric field and source-drain bias at charge neutrality point
•  intrinsic gapped
ground state ~ 2meV
•  Gap can be closed
by electric field of
either polarity ~ 12
meV/nm.
E⊥ (mV/nm)
•  Layer antiferromagnet
W. Bao, J. Velasco Jr, F. Zhang, L. Jing,
B. Standley, D. Smirnov, M. Bockrath,
A. MacDonald, C.N. Lau, Proc. Nat.
Acad. Sci., 109, 10802 (2012).
J. Velasco Jr., L. Jing, W. Bao, Y. Lee, P.
Kratz, V. Aji, M. Bockrath, C.N. Lau, C.
Varma, R. Stillwell, D. Smirnov, Fan
Zhang, J. Jung, A.H. MacDonald, Nature
Nanotechnol., 7, 156 (2012).
See also results from Yacoby group, Schonenberger
group, van wees group and Morpurgo group.
October 2015
Graphene Canada
Dual-Gated Suspended ABC Trilayer Graphene
4
2
400
G (µS)
G (µS)
100
200
4
2
10
4
0
0
40
mobility
20,000 –
90,000 cm2/
Vs
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
0
•  G(Vbias) curves at E⊥=n=0 yield Δ ∼ 42 meV
October 2015
dI/dV (µS)
2x10
Graphene Canada
-40 VV (mV)
bias
bias (V)
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)
October 2015
Graphene Canada
Proposed Phase Diagram!
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)
October 2015
Graphene Canada
Layer-dependent Gap!
•  Spontaneous and single-particle gaps
•  why stop at 3…
−
Coulomb Energy
−1
α~
~κ n
p
Fermi Energy~k
p−1
2
n=charge density (1010 cm-2)
κ=dielectric constant
Dispersion! α (κ=1)!
Interactioninduced Gap!
Tc!
GaAs/AlGaAs"
E~k2"
(10-50)/√n"
Single Layer
Graphene"
E~k"
2.2"
<0.1meV"
N/A"
Bilayer Graphene"
E~k2"
70/√n"
2-3 meV"
5K"
ABC-stacked Trilayer" E~k3"
1500/n"
40 meV"
36K"
ABC-stacked N-layer" E~kN"
gigantic"
gigantic?"
RT?"
Interaction-induced gap in tetra-layer?
October 2015
Graphene Canada
Outline!
•  Symmetry-broken Ground State in Few Layer Graphene
•  Transport Properties of Ionic Liquid-Gated Suspended MoS2
Transistors
•  Quantum oscillations in Few-layer Phosphorene
October 2015
Graphene Canada
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.
Wu et al, Nat. Phys. 2013.
and many others
October 2015
Graphene Canada
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
•  impurity scattering
•  defects
F. Wang, M. Gray, P. Stepanov and C.N. Lau,
Nanotechnology, in press (2015)
October 2015
Graphene Canada
see recent work from Columbia group
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)
•  use DEME-TFSI (N,N-diethyl-N-(2-methoxyethyl)-N-methylammonium bis(trifluoromethylsulphonyl)-imide)
IL"
S"
SiO2"
D"
IL"gate"
Si"
VILg"
F. Wang, M. Gray, P. Stepanov and C.N. Lau, in preparation (2015)
October 2015
Graphene Canada
Comparing Suspended and non-suspended devices
Performed IL gating of 9 suspended and 9 substrate-supported
samples
•  use DEME-TFSI (N,N-diethyl-N-(2methoxyethyl)-N-methylammonium
bis-(trifluoromethylsulphonyl)-imide)
• 
all suspended devices are more
conductive by 1-4 orders of
magnitude
à IL gating is more effective in freestanding devices
Mechanism:
1.  Higher charge density
2.  Better screening that reduce Schottky
barriers and impurity scattering
F. Wang, M. Gray, P. Stepanov and C.N. Lau, Nano Lett. (2015)
October 2015
Graphene Canada
Transport Mechanism
VIlg=0
Schottky emission at MoS2-electrode interfaces
(a)
I (µΑ)
8
(e)
-16
-1
Vds (V)
$a V −Φ '
B
I ∝ exp &
)
k
T
%
(
B
1
a=e
5
e
4πε 0εr d
I (µΑ)
slope yields εr ~ 11
à dielectric constant of DEME-TFSI ~ 14.5
-5
-1
October 2015
Vds (V)
1
Graphene Canada
IL-tuned Metal Insulator Transition
100
VILg =3V
2V
VILg =3V
2V
1.5V
σs (µS)
1.5V
10
1V
1V
0V
0V
1
-0.5V
-0.5V
0.1
120
200
T (K)
0.004
0.008
1/T (1/K)
•  metal insulator transition observed as VILg is tuned
•  At small VILg, transport via thermal activation
$a V −Φ '
B
I ∝ exp &
)
k
T
%
(
B
October 2015
a=e
e
4πε 0εr d
Graphene Canada
obtained from I-V curves
Ionic liquid gating of Suspended MoS2
•  ratio of ionic liquid gate to
back gate: up to 400
•  >~ coupling efficiency of
substrate-supported devices
•  allow extremely high doping
density
F. Wang, M. Gray, P. Stepanov and C.N. Lau, Nano Lett. (2015)
October 2015
Graphene Canada
Outline!
•  Symmetry-broken Ground State in Few Layer Graphene
•  Transport Properties of Ionic Liquid-Gated Suspended MoS2
Transistors
•  Quantum oscillations in Few-layer Phosphorene
October 2015
Graphene Canada
Black Phosphorus
•  Puckered atoms within layers
•  Anisotropic
•  Thickness dependent band
gap, 0.3 - 2 eV
•  Direct band gap for all
thickness
Tran et al, PRB 2014
October 2015
Asahina & Morita, J. Phys. C, 1986
Graphene Canada
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
Xia et al, Nature Comm. 2014
Liu et al, ACS Nano 2014
October 2015
Graphene Canada
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
October 2015
Graphene Canada
Favor et al, arxiv 2014
Challenges
Mission Impossible?
This device will self-destruct in 1 hour
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
Favron et al, arxiv 2014
October 2015
Graphene Canada
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
Columbia group, Science 2013
October 2015
Graphene Canada
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, in press (2014)
October 2015
Graphene Canada
Rxx (Ω)
Rxx (Ω)
Device mobility
•  Ambipolar transport
•  On/off ratio ~ 105
•  linear I-V à ohmic contact
October 2015
•  Metal-insulator transition
•  highly hole-doped: metallic, µ up to 4000
•  towards band edge: insulating, µ ê with T
Graphene Canada
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, in press (2015)
October 2015
Graphene Canada
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, in press (2014)
October 2015
Graphene Canada
Fast Moving Field
More than 120 preprints on arxiv
Number
20
b
0
1
October 2015
2014 month
12
Graphene Canada
Report of Quantum Hall Effect!
Li et al, arxiv 2015
October 2015
Graphene Canada
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 60x, electrical and thermal transport,
thermopower)
•  electric field effect
•  pressure-induced superconductivity?
•  (anisotropic?) quantum Hall effect
•  ….
•  Electronics and optoelectronics
•  hBN encapsulation of reactive 2D materials
October 2015
see Cao etGraphene
al, arXiv:
1502.03755
Canada
Number
20
0
1
2014 month
12
ostructures
2D Materials: Gap vs Mobility!
Energy Gap vs Mobility
2.5
aphene
ructure
Courtesy: FAME center
Calculated
Experiment
jayan,
Theme3)
KWKim,
me4
SnS [25]
SnS [26]
2
SnS [7]
2
2
2
MoS [15]
2
MoS2
MoS [29]
2
1.5
ation
aphene
SnSe [28]
2
MoS2 (Columbia group)
MoS [1]
2
2
2
MoS [30]
2
MoSe [16]
2
SnSe [27]
2
2
PtS [13]
2
MoSe [2]
2
WSe [5]
HfS [11]
2
WSe [19]
2
WSe [21]
2
WSe [20]
2
2
ZrS [9]
2
MoTe [17]
MoTe [3]
2
2
o
WTe [6]
2
ono 0.97
ulk
0.5
HfSe [12]
2
Phosphorene
ZrSe [10]
2
m2/Vs
Graphene
0
-1
10
T
f = 10
WS [4]
SnSe [8]
2
2
1
T
2
WS [24]
WS [23]
2
WS [18]
Eg (eV)
pe
WS [22]
?
MoS [14]
10
0
10
1
10
2
10
3
10
4
Mobility [cm2/(V*s)]
6
• Potentially high mobility, high on/off ratio
October 2015
Graphene Canada
What to ask a material scientist, part II
Yes, but doe
s it
scale?
6
8
6
10
2
2
mobility (cm /Vs)
4
Mobility
value
5
8
6
10
4
2
4
10
2005
2
4
2008
6
2010
0
10
-1
size (m)
10
-2
10
Size of
graphene
sheets
Basic research
à technology
-3
10
-4
10
October 2015
-5
10
2004
Graphene Canada
'07
'09 '10
Year
Acknowledgments!
Former Graduate Students
Graduate Students
Feng Miao (Now @ Nanjing Univ.)"
Gang Liu (Now @ USC) "
Wenzhong Bao (Now @ Univ. Maryland)"
Jairo Velasco (Now @ Berkeley)"
Hang Zhang (Now @ Caltech)"
Yongjin Lee"
Jhao-wun Huang " Fenglin Wang"
Undergraduate Students
Kevin Myhro " Yanmeng Shi" Nathaniel Gillgren"
Petr Stepanov"
October 2015
Tim Espiritu
Kevin Thilahar
Mason Gray
Ziqi Pi
UCOP
Son Tran "
Graphene Canada
Collaborators!
Florida Mag Lab UCR Physics
Dmitry Smirnov Marc Bockrath
Tulane
Zhiqiang Mao
Tulane
Jiang Wei
Jean-Marie Poumirol
CSIC
Paco Guinea
October 2015
UCR Physics
Yafis Barlas
UT Austin
UCR EE
Allan MacDonald
Roger Lake Fan Zhang,Jeil Jung
Graphene Canada