Iván Brihuega-Probing graphene physics at the atomic scale

Madrid, June, 2016ivan.brihuega@uam.es
www.ivanbrihuega.com
Nanoscience and Scanning Probe Microscopy Group
Probing graphene physics at the
atomic scale

UHV-LT-STM
Scanning tunneling microscopy (STM)
Probes nanoscale systems at an atomic level
Resolution: Horizontal (~ 0.1Å), vertical (~ 0.01Å)
Scanning tunneling spectroscopy (STS)
Local electronic structure (LDOS  dI/dV )
Resolución: ~ 1meV (T= 4K)
STM chamber
LHe bath cryostat
Preparation
chamber
Miguel Moreno Ugeda, PhD thesis(2011)
x107
x y
VBIAS
sample sample
tip
Vb
d~10Å
z

Atomic resolution on graphene
MONOLAYER BILAYER
20nm
BL: Triangular “graphite” like
3Å
1-2 ML Graphene on SiC(0001)
ML: “Honeycomb” pattern.
3Å

Vacancy on HOPG
Vacancy on G/Pt(111)
Divacancy
Atomic Hydrogen
Influence of atomic defects

Graphene properties on different surfaces
A.J. Martínez-Galera, et al, Nano Letters 11, 3576 (2011)
a new route to grow graphene on low reactivity metals
Ethylene irradiation
I. Brihuega et al. Phys Rev. Lett. 101, 206802 (2008)
2.5Å
BILAYER
MONOLAYER
2.5Å
P. Mallet et al. Phys. Rev: B 086, 45444, (2012)
Quasiparticle pseudospin
A.J. Martínez-Galera, et al, Scientific Reports 4, 7314 (2014)
Graphene nanopatterning with 2.5 nm precision
Nanopatterning
H. González-Herrero, et al, ACS Nano 10, 5131 (2016)
Tunable transparency

Graphene properties on different surfaces
A.J. Martínez-Galera, et al, Nano Letters 11, 3576 (2011)
a new route to grow graphene on low reactivity metals
Ethylene irradiation
I. Brihuega et al. Phys Rev. Lett. 101, 206802 (2008)
BILAYER
MONOLAYER
P. Mallet et al. Phys. Rev: B 086, 45444, (2012)
Quasiparticle pseudospin
A.J. Martínez-Galera, et al, Scientific Reports 4, 7314 (2014)
Graphene nanopatterning with 2.5 nm precision
Nanopatterning
H. González-Herrero, et al,)
Tunable transparency
Rotating two graphene layers
I. Brihuega, et al. Phys. Rev. Lett. 109, 196802 (2012)

-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
Energy(eV)
Monolayer
ED
Γ ΓKM
DFT calculations: Félix Yndurain
Monolayer
Rotating two graphene layers: electronic decoupling

Bilayer
Monolayer
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
Energy(eV)
Monolayer
Bilayer AB
Γ ΓKM
ED

-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Energy(eV)
Monolayer
Bilayer AB
Rotated Bilayer
Rotational disorder:
Electronic decoupling
(for large enough angles)Bilayer
Monolayer
Layers rotated 28º
M. Sprinkle et al. PRL 103, 226803 (2009)
Nearly ideal graphene band
structure ED  EF
ED
Γ ΓKM
q = 28º
G/SiC(000-1)
…
1st layer
2nd layer
3rd layer
C
Si
4th layer

0 5 10 15 20 25 30
0
2
4
6
8
10
12
14
MoiréPeriod(nm)
q deg)
Moiré pattern hypothesis
P=a/2*sin(q/2)
Rotating two graphene layers: geometry
Generation of Moiré Patterns:
Periodic potential!

0 5 10 15 20 25 30
0,0
0,2
0,4
0,6
0,8
1,0
vF
(q)/v
0
F
Rotation angle q (°)
Fermi velocity Renormalization
Rotating two graphene layers : tunning Fermi velocity
JMB Lopes dos Santos et al, Phys. Rev Lett. 99, 256802 (2007)
G. Trambly de Laissardière et al. Nano Letters 10, 804 (2010)
R. Bistritzer et al. PNAS 108, 12233 (2011)
...
60 45 4055 50 35 30
Rotation angle q(º)

KK
q
DEvHs
DOS

K
q
KK
K’K’
K’K’
K’K’
vF(q)/v0
F
0 105
q (degrees)
01
10 3 1.4
Moiré period (nm)
Rotating two graphene layers: Van Hove Singularities
Emergence of Van Hove Singularities
Reciprocal space
K

K
K
q= 9.6º
DEvHs
DOS

K K
q
K
K
K’
K’
K’K’
K’
K’
vF(q)/v0
F
0 105
q (degrees)
01
10 3 1.4
Moiré period (nm)
Rotating two graphene layers: Van Hove Singularities
Emergence of Van Hove Singularities
Reciprocal space

SiC(000-1) experimental sample: many rotational domains
Image size: 320x320nm2Moiré period= 4.0 nm (q=3.6°)
1nm
Moiré period= 2.4 nm (q=5.9°)
1nm
P=a/2*sin(q/2)

q = 9.6°5 nm
q = 9.6°
5 nm
0 2 4 6 8 10
0,0
0,5
1,0
1,5
2,0
VHsseparation(eV)
3.514 7 2.4 1.7 1.4
Moiré size
-1,2 -0,8 -0,4 0,0 0,4 0,8 1,2
0,0
0,2
0,4
0,6
0,8
1,0
.4°(max)
1.4°(min)
3.5°
6.4°
9.6°
dI/dV(au)
Sample bias (V)
Rotating two graphene layers: Robust Van Hove Singularities
Graphene layers on SiC(000-1)
T=6 K

q = 9.6° q = 6.4°5 nm 5 nm
q = 6.4°
5 nm
0 2 4 6 8 10
0,0
0,5
1,0
1,5
2,0
VHsseparation(eV)
3.514 7 2.4 1.7 1.4
Moiré size
-1,2 -0,8 -0,4 0,0 0,4 0,8 1,2
0,0
0,2
0,4
0,6
0,8
1,0
1.4°(max)
1.4°(min)
3.5°
6.4°
9.6°
dI/dV(au)
Sample bias (V)
T=6 K

q = 9.6° q = 6.4° q = 3.5°5 nm 5 nm 5 nm
q = 3.5°
5 nm
-1,2 -0,8 -0,4 0,0 0,4 0,8 1,2
0,0
0,2
0,4
0,6
0,8
1,0
1.4°(max)
1.4°(min)
3.5°
6.4°
9.6°
dI/dV(au)
Sample bias (V)
0 2 4 6 8 10
0,0
0,5
1,0
1,5
2,0
VHsseparation(eV)
3.514 7 2.4 1.7 1.4
Moiré size
T=6 K

q = 1.4°
5 nm
q = 1.4°
5 nm
-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.4°(max)
1.4°(min)
3.5°
6.4°
9.6°
dI/dV(au)
Sample bias (V)
0 2 4 6 8 10
0,0
0,5
1,0
1,5
2,0
VHsseparation(eV)
3.514 7 2.4 1.7 1.4
Moiré size
Rotating two graphene layers: Robust van Hove Singularities
q = 9.6° q = 6.4° q = 3.5°5 nm 5 nm 5 nm
T=6 K

5 nm
0 2 4 6 8 10
0,0
0,5
1,0
1,5
2,0
VHsseparation(eV)
3.514 7 2.4 1.7 1.4
Moiré size
-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.4°(max)
1.4°(min)
3.5°
6.4°
9.6°
dI/dV(au)
Sample bias (V)
q1-10°
Rotating two graphene layers: Robust van Hove Singularities
q = 1.4°
5 nm
q = 9.6° q = 6.4° q = 3.5°5 nm 5 nm 5 nm
T=6 K

DEVHs=2ħ·vF·K·sin(q/2)-2tq
K=1.703 Å-1
- Strength of the interlayer interaction =>
- Fermi velocity of a graphene monolayer =>
DEVHs=2ħ·vF·K·sin(q/2)-2tq
K=1.703 Å-1
- Strength of the interlayer interaction => tq = 0.108 eV
- Fermi velocity of a graphene monolayer => vF =1.12 106m/s
I. Brihuega, P. Mallet, H. González-Herrero, G. Trambly de Laissardière, MM. Ugeda, L. Magaud, JM.
Gómez-Rodríguez, F. Ynduráin, JY. Veuillen. Phys. Rev. Lett. 109, 196802 (2012)
-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.4°(max)
1.4°(min)
3.5°
6.4°
9.6°
dI/dV(au)
Sample bias (V)
Rotating two graphene layers : Robust van Hove Singularities
5 nm
q1-10°
0 2 4 6 8 10
0,0
0,5
1,0
1,5
2,0
VHsseparation(eV)
3.514 7 2.4 1.7 1.4
Moiré size

Graphene Nanopatterning with 2.5 nm precision
Cluster superlattice on
graphene/Ir(111) moire
250 x 250 nm2
N'Diaye et al. Phys. Rev. Lett. 97, 215501 (2006).

A.J. Martínez-Galera, I. Brihuega, A. Gutiérrez-Rubio, T. Stauber, J. M. Gómez-Rodríguez, Scientific Reports 4, 7314 (2014
1 2 3
0
5000
10000
15000
20000
Numberofcounts
Conductance (2e
2
/h)
0.0 0.5 1.0
0
1
2
G(2e
2
/h)
Z (nm)
Forward
Backward
+0.1V
+1.0V
+2.2V
2.2V
+3.0V
3.0V
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.2
0.4
0.6
0.8
1.0
ExtractionProbability
Z (nm)

A.J. Martínez-Galera, I. Brihuega, A. Gutiérrez-Rubio, T. Stauber, J. M. Gómez-Rodríguez, Scientific Reports 4, 7314 (2014)
1 2 3
0
5000
10000
15000
20000
Numberofcounts
Conductance (2e
2
/h)
0.0 0.5 1.0
0
1
2
G(2e
2
/h)
Z (nm)
Forward
Backward
+0.1V
+1.0V
+2.2V
2.2V
+3.0V
3.0V
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.2
0.4
0.6
0.8
1.0
Z (nm)
Ir clusters W clusters

Point defects as a source of
graphene magnetism
Vacancy on HOPG
Vacancy on G/Pt(111)
Divacancy
Atomic Hydrogen

Magnetism in graphene: just remove a pz orbital
Atomic Hydrogen
mT = mπ = 1μB
(1.0 mB)
π
σ
O. Yazyev, Rep. Prog. Phys. 73 056501 (2010)
2D honeycomb lattice of carbon atoms
2.46Å
Wave vector
How can we make graphene magnetic?

Atomic Hydrogen on Monolayer Graphene
Relaxed Atomic structure Calculated spin density
• Magnetic moment = 1μB
• spin density located on the
opposite triangular sublattice.
DFT calculations: M. Moaied, J.J Palacios, Felix Yndurain •Spin Polarized – DFT SIESTA code // (DZP) basis set.
0 1 2 3 4 5
-1
0
1
2
3
Desorptionenergy(eV)
Distance of H atom over graphene (Å)
Adsorption Energy  0.9eV
H chemisorbs on Graphene
-0.4 -0.2 0.0 0.2 0.4
DOS(au)
Energy (eV)
Spin Up
Spin Down
Graphene
mT = mπ = 1μB
(1.0 mB)QL
Simulated STM image (Tersoff-Hamann)

Illustration by Julio
Gómez-Herrero
Experimental
approach
UHV-4K-STM
M. M. Ugeda, Doctoral Thesis, 2011.

Atomic Hydrogen on G/SiC(000-1)
Rotational disorder: Electronic decoupling
(for large enough angles)
Last graphene layer is basically decoupled with ED~EF

-100 -50 0 50 100
0
dI/dV(a.u.)
Voltage (mV)
dI/dV∝LDOS
-200 -100 0 100 200
1
H atom
Graphene
dI/dV(a.u.)
Voltage (mV)
H on G/SiC(000-1) – STS experiments
Spin-split peaks!!
-0.4 -0.2 0.0 0.2 0.4
DOS(au)
Energy (eV)
Spin Up
Spin Down
Graphene
Atomic Hydrogen
mT = mπ = 1μB
 20meV

-100
dI/dV(a.u.)
Experiment
U3
ψ2
)
)
Coulomb splitting
r1
U1
U2r2
r3
A
B
C
H on G/SiC(000-1) – Origin of the spin-split state
-0.4 -0.2 0.0 0.2 0.4
DOS(au)
Energy (eV)
Spin Up
Spin Down
Graphene
Atomic Hydrogen
-100 -50 0 50 100
0
dI/dV(a.u.)
Voltage (mV)
dI/dV∝LDOS
 20meV
Experiment

-100
dI/dV(a.u.)
Experiment
U3
ψ2
)
)
Coulomb splitting
r1
U1
U2r2
r3
A
B
C
-100
dI/dV(a.u.)
Experiment
U3
ψ2
)
)
Coulomb splitting
r1
U1
U2r2
r3
A
B
C
H on G/SiC(000-1) – Origin of the spin-split state
-0.4 -0.2 0.0 0.2 0.4
DOS(au)
Energy (eV)
Spin Up
Spin Down
Graphene
Atomic Hydrogen
-100 -50 0 50 100
0
dI/dV(a.u.)
Voltage (mV)
dI/dV∝LDOS
 20meV
Experiment
U
n↑=1; n=0
20 meV splitting =>
We expect an extended magnetic state

Sublattice localization of the polarized peak
TOPOGRAPHY
DFT
STM
H

-100 -50 0 50 100
LDOS(au)
Voltage (mV)
 atom
TOPOGRAPHY
DFT
STM
+50
0
-50
E[meV]
1.95 V
-0.88 V
LDOS
dI/dV (∝ LDOS) mapping along the profile
H

-100 -50 0 50 100
LDOS(au)
Voltage (mV)
 atom
-100 -50 0 50 100
LDOS(au)
Voltage (mV)
 atom
 atom
+50
0
-50
E[meV]
1.95 V
-0.88 V
LDOS
dI/dV (∝ LDOS) mapping along the profile
-0.4 -0.2 0.0 0.2 0.4
0
PDOS(au)
Energy (eV)
Spin up
Spin Down
TOPOGRAPHY
DFT
STM
H
DFT
 atom
H
Peak height  magnetic moment

+50
0
E[meV]
1.95 V
-0.88 V
LDOS
-50
0 5 10 15
-2.8
-2.4
-2.0
-1.6
Energy[ev]
H-H distance [Å]
AA-Ferromagnetic
Same sublattice
0 5 10 15
-2.8
-2.4
-2.0
-1.6
Energy[ev]
H-H distance [Å]
AA-Ferromagnetic
AB-Non-magnetic
Same sublattice
Different sublattice
H
Non-magnetic
Ferro
Magnetic coupling in graphene sensitive to where
magnetic moments are located in lattice
HH
2.5 3.50
Distance to H [nm]

Manipulating H magnetism
H. González-Herrero, J. M. Gómez-Rodríguez, P. Mallet, M. Moaied, J. J. Palacios, C. Salgado, M.M. Ugeda, J. Y. Veuillen, F. Ynduráin
and I. Brihuega, Science, 352, 437 (2016)

7 H atoms “down”
7 H atoms “up” 7 H atoms “up”

7 H atoms “up” 7 H atoms “up”
x
x
xx
xx
x

7 H atoms “up”
x
x
xx
xx
x

7 H atoms “up”
…
7 H atoms “up”
x
x
xx
xx
x
https://www.youtube.com/watch?v=NmPAAo7_xY0

J.M.Gómez-Rodríguez
…and the most important slide
Félix Ynduráin
Paco Guinea
H. González-Herrero
Juanjo Palacios
M. Moaied
www.ivanbrihuega.com
C. Salgado
M. M. Ugeda
J-Y VeuillenP. MalletL. Magaud
Guy Trambly de Laissardière

Atomic H on Doped graphene
-0.4 -0.2
DOS(au)
Ene
-100 -50 0 50 100
dI/dV(a.u.)
Voltage (mV)
Experiment
Theory
Spin up
Spin down
Graphene
H atom
Graphene
~20 meV
U3
ψ2
)
)
Coulomb splitting
r1
U1
U2r2
r3
A
B
C
D
E
Anderson Impurity model
P. W. Anderson, Physical Review 124, 41 (1961)
-100 -50 0 50 100
dI/dV(a.u.)
Voltage (mV)
2D
E↑ E
MAGNETIC
NON-MAGNETIC
pD/U
x=(EF-Ed)/U
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
E↑=Ed+U(n  1/2)
E =Ed+U(n↑  1/2)
STS on neutral graphene

-0.4 -0.2
DOS(au)
Ene
-100 -50 0 50 100
dI/dV(a.u.)
Voltage (mV)
Experiment
Theory
Spin up
Spin down
Graphene
H atom
Graphene
~20 meV
U3
ψ2
)
)
Coulomb splitting
r1
U1
U2r2
r3
A
B
C
D
E
Anderson Impurity model
P. W. Anderson, Physical Review 124, 41 (1961)
-100 -50 0 50 100
dI/dV(a.u.)
Voltage (mV)
2D
E↑ E
MAGNETIC
NON-MAGNETIC
pD/U
x=(EF-Ed)/U
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
E↑=Ed+U(n  1/2)
E =Ed+U(n↑  1/2)

Peak splitting vs unit cell size
0.00 0.02 0.04 0.06 0.08
0.00
0.05
0.10
0.15
0.20
Splitting[eV]
1/Distance (Å
-1
)
50 25 17 12.5
Distance (Å)
Fit to1/r
Unit cell size matters!

-50 0 50
0
2
4
dI/dV(a.u.)
Voltage (mV)
2 isolated H atoms on the same
terrace, same tip
e-h symmetry
2 isolated H atoms on the same
terrace, 1 isolated H atom dif terrace
small local doping,same tip
1 isolated H atom dif terrace dif tip
-50 0 50
0
2
4
dI/dV(a.u.)
Voltage (mV)

-0,2 0,0 0,2
DOS(au)
Spin Down Monolayer
Spin Down BL Moire (13º)
Spin Down AB Bilayer(on )
Spin Down AB Bilayer(on )
Spin Up ML
Spin Up BL Moire (13º)
Spin Up AB Bilayer(on )
Spin Up AB Bilayer(on )
0
25
50
75
100
125
AB Bilayer(on )
AB Bilayer(on )
BL Moire (13º) Monolayer
Spinsplitting(meV)
4.4nm
4.4nm
A
B
Influence of stacking
-40 -20 0 20 40
2
4
A
B
dI/dV(a.u.)
Voltage (mV)

H on HOPG – Is magnetism preserved?
System is still magnetic in
multilayer graphene/graphite
DFT calculations: M. Moaied and J.J Palacios
Bilayer Multilayer

-0.5 +0.50.0
E (eV)
-0.5 +0.50.0
E (eV)
-0.5 +0.50.0
E (eV)
-0.5 +0.50.0
E (eV)-60 -40 -20 0 20 40 60
0,5
1,0
1,5
AA dimer (3nm)
dI/dV(a.u.)
Voltage (mV)
4.5nm
-60 -40 -20 0 20 40 60
0.5
1.0
1.5
Single H
AA dimer
dI/dV(a.u.)
Voltage (mV)
H-H distance=0.5nm
H-H distance=3nm

-60 -40 -20 0 20 40 60
0,5
1,0
1,5
Single H
AA dimer0.5nm
AA dimer (3nm)
dI/dV(a.u.)
Voltage (mV)
4.5nm
H-H distance=0.5nm H-H distance=3nm
-60 -40 -20 0 20 40 60
0.5
1.0
1.5
Single H
AA dimer
dI/dV(a.u.)
Voltage (mV)

-300 -200 -100 0 100 200 300
0
2
dI/dV(a.u.)
Voltage (mV)
H atoms on 3rd graphene layer
ED
kF=0.020nm-1=> ED  -0.14eV 4
3rd graphene layer on SiC(000-1) is n-doped:
K1
E
kx
ky
ED
K1
E
kx
ky
EF =ED
Free-standing graphene
EF 2kF
-400 -200 0 200
dI/dV(a.u.)
Voltage (mV)
ED  -0.14eV
G/SiC(000-1)
SiC
C
1st layer
2nd layer
3rd layer
DFT calculations: F Yndurain
0.8e
-
1.0e
-
0.9e
-
0.1e
-
Spin Up
Spin Down
Non-Magnetic
0.7e
-
0.5e
-
0.3e
-
0.2e
-
0.4e
-
0.6e
-
0.0 0.5 1.0
0.0
0.2
0.4
0.6
0.8
1.0

-0.6 -0.4 -0.2 0.0 0.2 0.4
Non doped
Doped with 1e
-
Energy (eV)
DOS(au)
-0.1 0.0 0.1
0.8e
-
0e
-
1.0e
-
0.9e
-
0.1e
-
DOS(au)
Energy (eV)
Spin Up
Spin Down
Non-Magnetic
0.7e
-
0.5e
-
0.3e
-
0.2e
-
0.4e
-
0.6e
-
-0.5 0.0 0.5
DOS(au)
Energy (eV)
AB dimer
Graphene
Theory
H-H distance=1.15nm
-400 -200 0 200 400
AB Dimer
Graphene
dI/dV(a.u.)
Voltage (mV)
-50 0 50
0
2
4
dI/dV(a.u.)
Voltage (mV)
-400 -300 -200 -100 0 100 200 300 400
0.0
0.2
0.4
0.6
0.8
1.0
1.2
dI/dV(a.u.)
Voltage (mV)
-200 -100 0 100 200
0,0
0,2
0,4
0,6
0,8
1,0
dI/dV(a.u.)
Voltage (mV)
Single H atom Non-Magnetic Dimer
STM

Kondo…
“This problem has to be solved properly…”
Misha Katsnelson, ICMM, Madrid, 19.09.2014

0 1 2 3 4 5
0
1
2
3
Distance of H atom over graphene ()
Single H
Atomic H deposition on SiC(000-1) held at RT + 6 minutes at RT => Cool
down to 6K
Atomic H on G/SiC(000-1)
-100 -50 0 50 100
0
2
dI/dV(a.u.)
Voltage (mV)
x

-100 -50 0 50 100
0
2
dI/dV(a.u.)
Voltage (mV)
0 1 2 3 4 5
0
1
2
3
Distance of H atom over graphene ()
Single H
Atomic H deposition on SiC(000-1) held at RT + 6 minutes at RT => Cool down to 6K
Atomic H on G/SiC(000-1)
-100 -50 0 50 100
0
1
2
dI/dV(a.u.)
Voltage (mV)
x
x

1175.top 1178.top 1184.top 1187.top
-200 -100 0 100 200
0.0
0.5
1.0
1.5
2.0
dI/dV(a.u.)
Voltage (mV)
-200 -100 0 100 200
0.0
0.5
1.0
1.5
2.0
dI/dV(a.u.)
Voltage (mV)
H_SiC(000-1)_2013_06_17_RT_HDeposition

-0.10 -0.05 0.00 0.05 0.10
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
E-EF
(eV)
k (Å
-1
)
-0.10 -0.05 0.00 0.05 0.10
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
E-EF
(eV)
k (Å
-1
)
1 2 3
0
5000
10000
15000
20000
Numberofcounts
Conductance (2e
2
/h)
0.0 0.5 1.0
0
1
2
G(2e
2
/h)
Z (nm)
Forward
Backward
+0.1V
+1.0V
+2.2V
2.2V
+3.0V
3.0V
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.2
0.4
0.6
0.8
1.0
Z (nm)a)
b) c) d) e) f)
g) h) i) j) k)
l) m)
Graphene Nanolithography with 2.5 nm precision
A.J. Martínez-Galera, I. Brihuega,
A. Gutiérrez-Rubio, T. Stauber, J.
M. Gómez-Rodríguez

Tunneling on and through graphene: measuring the
local electronic coupling.
BothCu(111)&Graphenecanbeobserved
Same region as above, tip change
G/Cu(111)vsCu(111)
Dispersion relation Pseudospin
-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8
-0,4
-0,3
-0,2
-0,1
0,0
0,1
0,2
0,3
k (nm
-1
)
Energy(eV)
G/Pt(111)G/SiC(000-1)
Gr/Cu(111)
vF = 1.12x106 m/s
ED = -0.34 eV
kF = 0.48 eV
FT from G/Cu(111)
Point defects
Grapheneproperties
H. González-Herrero, A.J. Martínez-Galera, M.M. Ugeda, F.Craes, D. Fernández-Torre, P. Pou, R. Pérez, J.M. Gómez-Rodríguez and I. Brihuega

1175.top
1171.top
x
1179.top
x
1178.top 1184.top
1173.top
x
1187.top
1191.top
H dimer in same sublattice => H dimer in opposite sublattice=> Remove the dimer
Spin polarized peak No peaks at low E
H dimer in opposite sublattice => Remove 1 H atom from dim
No peaks at low E Spin polarized peak
x

0
0.2
0.4
0.6
-0.8 -0.4 0 0.4 0.8
Bottom
Top
dI/dV(arb.units)
Sample bias (V)
0
0.1
0.2
0.3
-1 -0.5 0 0.5 1
dI/dV(arb.units)
Sample bias (V)
0
0.2
0.4
0.6
-0.2 -0.1 0 0.1 0.2
1
1'
2
3
dI/dV(arb.units)
Sample bias (V)
1
1’
2
3
0 2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
VHsseparation(eV)
3.514 7 2.4 1.7 1.4
Moiré size
Rotating two graphene layers: only upmost 2 layers
matter
Left
Right
I. Brihuega, P. Mallet, H. González-Herrero, G. Trambly de Laissardière, MM. Ugeda, L. Magaud, JM. Gómez-Rodríguez, F. Ynduráin, and J-Y. Veuillen to appear

1.65 V
0.05 V
LDOS
High
Low
Moiré period 2.66nm (q  5.30°).

Moiré period  11-12nm; q  1.3º-1.2º

0.20.10-0.1-0.2
0.5
0.4
0.3
0.2
0.1
Bias [V]
CH6[V]
0.10-0.1
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
Bias [V]
CH6[V]
Moiré period  11-12nm; q  1.3º-1.2º
2001000-100-200
300
250
200
150
100
50
0
X[mV]
Z[mV]
Average AA
Average AB

H “dimers” on G/SiC(000-1)
H-H distance=0.28nm
AB dimer
H-H distance=0.49nm
AA dimer
0 5 10 15
-2.8
-2.4
-2.0
-1.6
Energy[ev]
H-H distance [Å]
AA-Ferromagnetic
AB-Non-magnetic
Same sublattice
Experiment
STS
-200 0 200
1
dI/dV(a.u.)
Voltage (mV)
Graphene
Theory (DFT)

STS
-200 0 200
1
dI/dV(a.u.)
Voltage (mV)
Graphene
0 5 10 15
-2.8
-2.4
-2.0
-1.6
Energy[ev]
H-H distance [Å]
AA-Ferromagnetic
AB-Non-magnetic
Same sublattice
Graphene
STS
-200 0 200
1
dI/dV(a.u.)
Voltage (mV)
AB dimer
-0.5 0.0 0.5
AB Dimer
Graphene
DOS(au)
Energy (eV)
DFT
H-H distance=0.28nm
AB dimer
H-H distance=0.49nm
AA dimer
Experiment Theory (DFT)

-200 0 200
1
dI/dV(a.u.)
Voltage (mV)
STS
AA dimer
STS
-200 0 200
1
dI/dV(a.u.)
Voltage (mV)
AB dimer
0 5 10 15
-2.8
-2.4
-2.0
-1.6
Energy[ev]
H-H distance [Å]
AA-Ferromagnetic
AB-Non-magnetic
Same sublattice
-0.5 0.0 0.5
AB Dimer
Graphene
DOS(au)
Energy (eV)
DFT
Graphene
AB dimer
H-H distance=0.28nm
AB dimer
H-H distance=0.49nm
AA dimer
AA Dimer
Spin up
Spin down
-0.5 0.0 0.5
AB Dimer
Graphene
DOS(au)
Energy (eV)
DFT

-200 0 200
1
dI/dV(a.u.)
Voltage (mV)
STS
AA dimer
STS
-200 0 200
1
dI/dV(a.u.)
Voltage (mV)
AB dimer
0 5 10 15
-2.8
-2.4
-2.0
-1.6
Energy[ev]
H-H distance [Å]
AA-Ferromagnetic
AB-Non-magnetic
Same sublattice
-0.5 0.0 0.5
AB Dimer
Graphene
DOS(au)
Energy (eV)
DFT
Graphene
AB dimer
H-H distance=0.28nm
AB dimer
H-H distance=0.49nm
AA dimer
AA Dimer
Spin up
Spin down
-0.5 0.0 0.5
AB Dimer
Graphene
DOS(au)
Energy (eV)
DFT
H-H distance=0.57nm
AB dimer
-200 -100 0 100 200
1
2
dI/dV(a.u.)
Voltage (mV)
STS
Same sublattice => peak is polarized
Different sublattices => no peaks
AB dimer
Graphene

-200 -100 0 100 200
0.5
1.0
1.5
2.0
Voltage (mV)
dI/dV(a.u.)
A-B dimer
“Magnetism OFF”X
X
Removing single H

-200 -100 0 100 200
0.5
1.0
1.5
2.0
Voltage (mV)
dI/dV(a.u.)
Isolated H
“Magnetism ON”
Removing single H

-200 -100 0 100 200
0.5
1.0
1.5
2.0
dI/dV(a.u.)
Voltage (mV)
A-A dimer
“Magnetism ON”
Lateral motion

A-B dimer
“Magnetism OFF”
-200 -100 0 100 200
0.5
1.0
1.5
2.0
dI/dV(a.u.)
Voltage (mV)
Lateral motion

A-B dimer at 1.15 nm
“Magnetism OFF!”
x
H-H distance=1.15nm
x
0 5 10 15
-2.8
-2.4
-2.0
-1.6
Energy[ev]
H-H distance [Å]
AA-Ferromagnetic
AB-Non-magnetic
Same sublattice
-400 -200 0 200 400
AB Dimer
Graphene
dI/dV(a.u.)
Voltage (mV)
-0.5 0.0 0.5
DOS(au)
Energy (eV)
AB dimer
Graphene
Theory (DFT)
A-B dimer

0 5 10 15
-2.8
-2.4
-2.0
-1.6
Energy[ev]
H-H distance [Å]
AA-Ferromagnetic
AB-Non-magnetic
Same sublattice
-400 -200 0 200 400
AB Dimer
Graphene
dI/dV(a.u.)
Voltage (mV)
-0.5 0.0 0.5
DOS(au)
Energy (eV)
AB dimer
Graphene
Theory (DFT)
Isolated H
“Magnetism ON”
Exchange energy for 2H at 1.5 nm is -35meV
Eex = [(2H in AA with spin 2)-(2H in AA forced to spin 0)]
Isolated H

Iván Brihuega-Probing graphene physics at the atomic scale

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