manipulating graphene at the...
TRANSCRIPT
Manipulating Graphene at the Atomic-scale
(I) Atomic-scale Gating
-- Tunable charge centers
(II) Nanoribbon Edge States
-- Controllable edge functionalization
Mike CrommieDept. of Physics, UC Berkeley
Materials Science Division, LBNL
V+
-- - - - - -
+ + + + +
Macroscopic:Electrode
-+ + +
Microscopic:Charged Impurity
-
Klein Tunneling
(I) Atomic-scale Gating
V Ve- e-
Coulomb Impurity
2mc2
Non-relativistic Case (Hydrogen)
2 2 2
22 2
rP L Ze
Em mr r
Veff
++Ze
2Ze
Vr
r
Veff
k
E
Electron
Positron
r
Veff
k
E
Electron band
Hole band
Ultra-relativistic Case for Graphene
Z < Zc (subcritical)
Physics of a Coulomb Impurity
|Z| invariant
r
ZepvE
F
2
Critical Charge: Zc = g
g
2
2mc2
Non-relativistic Case (Hydrogen)
2 2 2
22 2
rP L Ze
Em mr r
Veff
++Ze
2Ze
Vr
r
Veff
k
E
Electron
Positron
r
Veff
k
E
Ultra-relativistic Case for Graphene
Z > Zc (supercritical)
Physics of a Coulomb Impurity
|Z| invariant
r
ZepvE
F
2
Electron band
Hole band
Critical Charge: Zc = g
g
2
Pereira et al., PRL 99, 166802 (2007)
Shytov et al., PRL 99, 246802 (2007)
Subcritical (Z < Zc)
Predicted quasi-bound-states(atomic collapse states)
Predicted Behavior for Dirac Fermions Near Coulomb Potential
Energy
Q > 0
holes electrons
Charge asymmetry
(Solution to Dirac Equation using a Continuum Model)
+Q = + Z |e| > 0
Supercritical (Z > Zc)
Deposit Cobalt Atoms onto Graphene / SiO2 Device
cobalt
V.W. Brar, et al., Nature Physics 7, 43 (2011)
Spectroscopy at Site of Cobalt Atom on Graphene
Gated Cobalt Atom Spectroscopy
E
Atomic Resonances, Gate-induced Charging
EF
LDO
S
Vg
Graphene flake
doped Si bottom gateSiO2
STMtip
Vbcobalt
+
+
E
k
=
E
DOS
cobalt
graphene impurity
V.W. Brar, et al., Nature Physics 7, 43 (2011)
Off-atom Problems: Bi-stability and Inhomogeneity
10nm10nm
Graph. / SiO2 Rough Topography Graph. / SiO2 Charge Inhomogeneity
Charge bi-stability: Co on Graphene
/C60/C60
Teichmann, et al., PRL 101,076103 (2008)
Pradhan, et al., PRL 94,076801 (2005)
Si/GaAs
Previous Impurities in Semiconductors
V.W. Brar, et al., Nat. Phys. 7, 43 (2011)
Dean C. R. et al., Nat Nano 5, 722 (2010)
Doped Si bottom gate
SiO2
BN flake
CVD Graphene
Vb
VG
A New Substrate Solves these Problems (BN)
BN substrate in new STM geometry
Crommie, Zettl
Less Inhomogeneity for Graphene on BN
R. Decker, et al., Nano Letters 11, 2291 (2011)
Similar to: J. Xue, et al., Nature Mat. 10, 282 (2011)
Moiré Patterns
R. Decker, et al., Nano Letters 11, 2291 (2011)
kBN
4 nm4 nm 4 nm 4 nm
a b c d
θ = 21°± 1° θ = 7°± 1° θ = 0°± 1°θ = 4°± 1°
Graph./BN
Vg=50
Vg=35
Vg=25
Vg=15
Vg=10
Vg=5
Vg=-10
Vg=0
Vg=-20
Vg=-30
Vg=-50
Graphene /BN
Gate-dependent STM Spect.
General spectral line-shape: V. W. Brar, et al., PRL 104, 036805 (2010)
Atomic Manipulation on Graphene/BN: Co Trimers
Trimers:no chargebi-stability
Q = +1 |e| State (charged)
Vg = -20V , Vs = +0.3V
Co Trimer
Q = 0 State (uncharged)
Vg = +45V , Vs = +0.3V
Co Trimer
Graphene Graphene
Co Trimer Provides aStable Charged State
Trimers Are Stable, Tunable Charge Centers
STM dI/dV
images
dI/dV Spectra on Graphene around Charged Co Trimer
Co Trimer
Distance dependent spectra around charged Co trimer
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
No
rma
lize
d d
I/d
V (
a.u
.)
Sample Bias (eV)
1.60nm
2.22nm
3.48nm
6.35nm
• LDOS Asymmetry• No Bound-state
Q = +1 |e|
Comparing Experiment to Predictions for Dirac Fermions
THEORYEXPERIMENT
Interband Dielectric Constant: g = 3.0 ± 1.0
D. A. Siegel, et al., PNAS 108, 11365 (2011): g < 6
D. C. Elias, et al., Nat Phys. advance online pub. (2011): g = 2 - 5
J. P. Reed, et al., Science 330, 805 (2010): g = 15
T. Ando, J. of the Phys. Soc. of Japan 75, 074716 (2006): g ≈ 2
E. H. Hwang and S. Das Sarma, PRB 75, 205418 (2007): g ≈ 2
Previous Theory for g : Previous Experiment for g:
Spatial Dependence Reflects Charge Asymmetry
Y. Wang, et al., submitted for publication
Cobalt Trimer:Sub-critical Impurity
Holes
Electrons
g = 3.0 ± 1.0
(II) Nanoribbons: Controlling the Edge
DO
S
E
DO
S
E
……
Armchair
… …
Zigzag
D(e
V)
Zigzag
D(e
V)
Armchair
Spin-polarized
w
Y.-W. Son et al, Phys.Rev. Lett.
97, 216803 (2006)
A. Yamashiro et al, Phys.Rev. B
68, 193410 (2003)
J. Heyd et al, J. Chem. Phys. 118,
8207 (2003)
K. Nakada, et al., PRB 54, 17954
(1996)
M. Fujita, et al., J. Phys. Soc.
Jpn 65, 1920 (1996)
Tunable GapsEdge-statesSpin
GNRsGraphene GNR
Some Previous Nanoribbon Investigations
Ritter and Lyding, Nat. Mat. 8, 235 (2009)
Lithography: Transport Graphene platelet on Si(100)
Jinming Cao et al., Nature 466, 470 (2010)
Armchair GNRs grown on Au
Y. Kobayash et al., PRB 71, 193406 (2005)
Graphite Step edge
Some Previous Edge Investigations
Graphene Edges on SiC & Cu
C. Park, et al., PNAS, doi:10.1073 (2011)
H. Yang, et al., Nano Lett. 10, 943 (2010)
J. Tian, et al., Nano Lett. 11, 3663 (2011)
SiC
Cu
M. Y. Han et al., PRL 98, 206805 (2007)
GNRs from Unzipped Nanotubes
Jiao, et al, Nat. Nanotechnol 5, 321 (2010)
1000 Å
GNR on Au(111)
C. Tao, et al., Nature Physics 7, 616 (2011)
(8, 1) GNR
0.0 Å
5.5 Å
48 Å × 48 Å θ = 5.8°
Different Chiralities Observed
Width = 19.8 nm
C. Tao, et al., Nature Physics 7, 616 (2011)
(1, 1) Armchair
(1, 0) Zigzag
(n, m)
θ
STM Spectroscopy of Nanoribbon Edge State
Au(111)
(8, 1) GNR
0.0 Å
5.5 Å
48 Å × 48 Å
Perpendicular to edge
0 Å
2.2 Å
4.4 Å
6.6 Å
8.8 Å
11.0 Å
13.2 Å
15.4 Å
19.8 Å
24.2 Å
-8.8 Å
Vs (V)
dI/d
V(a
rb.
un
its)
dI/d
V (a. u
.)Vs (V)
Δ0.8
0.00 0.04
0.6
width = 19.8 nm
Gap Width Dependence
ExperimentTheory
C. Tao, et al., Nature Physics 7, 616 (2011)
a b20 nm 20 nmGNR / Au(111) before H2
plasma EtchingGNR / Au(111) after H2 plasma Etching
0 10 20 30
0.0
0.3
0.6
(nm
)
(nm)0 10 20 30
0.0
0.3
0.6
(nm
)
(nm)
Control GNR Edge Through H2 Plasma Etch
Room temperature STM
Crommie, Dai, Louie, Zettl (unpublished)
a
b
dc
d
e
c
e
5 nm
1 nm
5 nm
1 nm
1 nm
Nano-scale Structure of Edge
Zigzag edge
(2, 1) Chiral edge
Armchair edge
Can Find Edge Symmetry, But What is H-Composition?
What is Hydrogen Edge Structure?
Calculate Thermodynamic Stability
of Different Edge Structures
O. Yazyev, S. G. Louie & co-workersPrevious Work:Wassman, Seitsonen, Marco Saitta, Lazzeri, Mauri, PRL 101, 096402 (2008)
Comparing Exp. Edge to Theory w/ Proper H-structure
d
c
e
1 nm
f
g
h
1 nm
1 nm 1 nm
1 nm
1 nm
EXPERIMENT THEORY
Experiment
Theory
Armchair GNR
Edge
Experiment
Theory
Zigzag GNR
Edge
Averaged Linescans
Conclusion
Future:
Atomic Collapse Pseudo-field and SpinSPSTM of GNRs
I) Dirac Fermion Screening of Tunable Charge Impurities
II) Controlling GNR Edges through Chemical Functionalization
Collaborators:
Tunable ChargeCenters
Victor Brar, Regis Decker, Yang Wang, Q. Wu, H. Tsai,
Will Regan, A. Shytov
NanoribbonEdges
Chenggang Tao, Yen-Chia Chen, Liying Jiao, Juanjuan Feng,
Xiaowei Zhang, R. Capaz, Oleg Yazyev
co-PI’s M. F. Crommie, A. Zettl, S. G. Louie, J. M. Tour, H. Dai, L. Levitov
STUDENTS + POSTDOCS + VISITORS
The End