Bilayer graphene ARPES band structure

1. ARPES microscopy study on
free standing bilayer graphene
Po-Chun Yeh , Kevin Knox , Wencan Jin , Jerry
Dadap , Philip Kim , Richard M. Osgood
Columbia University
Alexei Barinov, Dudin Pavel
Elettra-Sincrotrone Trieste,Italy

2. Outline
• Goal: To study electronic structure
of free standing graphene
• Brief review of our prior monolayer
graphene studies
• Bilayer
– Theory and related studies
– Sample preparation and apparatus
– Data analysis
– Comments

3. Two Varieties of Graphene
Stormer HL, Kim P
PRL 99, 106802
(2007)
Novoselov KS, Geim AK
22 OCT 2004 VOL 306
SCIENCE
Epitaxial Graphene Exfoliated Graphene
• Large-Area coverage
• Conducting substrate
• Ideal for UHV measurements
• Good PE works
• High-quality crystals
• Insulating substrate
• Ideal for transport
measurements
• Small sample sizeDe Heer, First, Butler, IBM Geim, Novoselov; Kim
PE work: see LBL Group, Georgia Tech Group, IBM, etc.

4. For Monolayer Measurements SPELEEM Needed:
For Roughness Data to Improve ARPES
SPELEEM microscope at ELETTRA
• Combines microscopy, spectroscopy
• High spatial resolution for imaging:
XPEEM (40 nm), LEEM (15 nm)
• 2 μm spot, μLEED, μARPES
• 300 meV energy resolution
• Noninvasive probe
LEEM autocorrelation
2D Roughness Parameters: ξ, w, α
α=0.5
α=0.3
α=0.7
α=0.5
α=0.3
α=0.7
α=0.5
α=0.3
α=0.7
Columbia, ACSNano, 2010Columbia, ACSNano, 2010

5. Suspended vs Supported ARPES
Г
M
K
K'
Supported
Graphene
Suspended
Graphene
Columbia, PRB, 2008Columbia, PRB, 2008
Columbia, PRB, 2011Columbia, PRB, 2011
Our measurements show
β = 0.3 fs-1
eV-1
Lifetime = 1/(β*2*(E-
EF)*vF)
=> marginal Fermi liquid
“Removing Corrugation”
Yields Lifetime:
Marginal Fermi Liquid
High symmetry points
• No SiO2 photoelectrons
• Significantly narrower peaks
• Possible to measure S(k)
Removing SiO2 Interaction
10μm
Slope = β

6. Bilayer Graphene Theory
Bilayer graphene in Bernal stacking
McCann’s Tight-binding calculation:
• Weak A1B2 coupling, γ3 <<VF, negligible
• No doping or external fields
•Small band asymmetry
• Near K point
- L. M. Malard et al., PRB 76, 201401 (2007)
-T. Ohta et al., Science 313, 951 (2006)
-S. Y. Zhou et al., Nature Materials 6, (2007)
-A.B. Kuzmenko et al., PRB 79, 115441 (2009)
-C. Z. Q. Li et al., PRL 102, 037403 (2009)
-E. McCann et al., PRL 96, 086805 (2006).
Interlayer Hopping Energy
Tight-binding approach by McCann
Important works & people
Interlayer
asymmetry, Δ

7. • 300nm thick SiO2 on intrinsic Si substrate
• No substrate doping
• Mechanical exfoliation
• Free standing on 5μm wells
• Shadow mask Au/Cr deposition, no photoresist
• Overnight thermal radiation cleaning
• Well defined layers, single domain
Sample Preparation
(Left) Optical
microscopy image
(Right)Spatially-resolved
photoemission image:
angle integrated mode at
15eV electron kinetic
energy, by
Spectromicroscopy.
1
2
3
4
Monolayer
Bilayer
1
2
3
4
10μm

8. • Study the band structure and the Fermi surface
topography
• Temperature: 110K to 300K
• Beam size: 0.6 - 1μm
• Photon energy: 27eV
• Momentum resolution: 2.7mÅ-1
• Energy resolution: 33meV
SpectroMicroscopy at Elettra :
Microscope + Monochromator
-P. Dudin et al., J. Synchrotron Rad. (2010) 17
Cryostat
Electron
Analyzer
Sample
Counter
Source
Frequency
selection
Schwarzschild
objective
Elettra Sincrotrone,
Trieste, Italy

9. K// (Å-1
)E-EF(eV)
Δ,
γ1
Data Handling
Processing and Fitting
• Coordinate transforms
angles to k//
• Resize the data into a
nonzero matrix
• EDC* Peak fitting to find K
point, Fermi Energy, and π
bands
• Use 2nd
derivative to find
initial values for fitting
• Least square method and
bilayer graphene theory
• Band gap, Fermi velocity,
binding energy γ1, and
lifetime can be established
• 3 samples
• 110 – 300K
• UHV
EDCs
*EDC: Energy Distribution Curve
M’KΓ

10. Fermi Cutoff and Spatial Resolution
EDC*s fit at K point with
Lorentzian function
convoluted with Fermi
function:
T=110K
T=300K

11. Room temperature, 300K
2nd
Derivative2nd
Derivative Peak Fitting
• 2nd
derivative help locates the two bands
• Parabolic – linear feature of bilayer is clear
• Dirac point is close to Fermi level within min energy resolution
• Parabolic region ~ ±0.5 Å-1
M’KΓ

12. Low Temperature, 110K
Peak Fitting2nd
Derivative
• Lowering temperature removes background noise
• Sharper bands
• Interlayer hopping and band gaps are not temperature
dependent, as theory predicted
M’KΓ

13. Results of Fitting for Exfoliated Gr
Fit the π bands with the tight binding model:
A
300K
A
110K
B C D E
VF
(106
m/s)
1.042
±0.018
1.003
±0.013
* 1.1 1 1 ~ 1.1
Δ/2
(meV)
48.0
±13.4
56.2
±9.4
0 40 -0.05 ~
0.1
Variable
γ1
(eV)
0.6
±0.017
0.611
±0.007
0.378
±0.005
0.404
±0.01
0.41 ~
0.46
0.36 ~
0.45
A. Our ARPES measurement
B. Infrared measurement on SiO2/Si, doped, 10K
C. Infrared measurement on SiO2/Si, doped, 45K
D. ARPES measurement on SiC, doped
E. McCann’s tight binding calculation
References:
B. A.B. Kuzmenko et al., PRB 79, 115441 (2009)
C. Z. Q. Li et al., PRL 102, 037403 (2009)
D. T. Ohta et al., Science 313, 951 (2006)
E. McCann et al., PRL 96, 086805 (2006).
* Not provided.

14. Summary and Direction
Characteristics
 Fermi velocity, VF
 Interlayer asymmetry, Δ
 Interlayer coupling, γ1
– Strain ?
– > 2ML – data looks too clean for this.
– Additional measurements
Zero-to-minimally-doped graphene measured
• Chemical doping experiments needed
• Surface corrugation and width broadening
• Band asymmetry and renormalization

15. Thank you

16. L. M. Malard et al., PRB 76, 201401 (2007)
Raman
From graphite theory paper:
Will optical measurement changes the γ1 ?
γ1 ~0.7eV, VF = 8x105
Cited by A.B. Kuzmenko et al., PRB 79, 115441 (2009), IR study
0.377eV in graphite -D.D. L. Chung, J. Mater. Sci. 37, 1475 (2002)
ARPES Lanzara’s paper: 0.35eV
We shouldn’t be looking
at thin graphite, since the
γ1 decreases when
number of layers
increases.

17. Results of Fitting for Exfoliated Gr
Normal Temperature
• Δ/2 = 48.0±13.4meV
• γ1 = 0.6±0.017eV
• VF = (1.042±0.018)x106
m/s
Low Temperature
• Δ/2 = 56.2±9.4meV
• γ1 = 0.611±0.007eV
• VF = (1.003±0.013)x106
m/s
ARPES results, fit the π bands with McCann’s model:
• Δ = 0
• Δ’ = 15±5meV
• γ1 = 0.378±0.005eV
• γ4 = 0.12eV
• VF = Not provided
IR, exfoliated, n-doped, 10K
SiC, K doped
• Δ = -0.1 – 0.2 meV
• γ1 = 0.41 – 0.46 eV
• VF = 1x106
m/s
• Δ = variable
• γ1 = 0.36 – 0.45eV
• VF = (1 – 1.1)x106
m/s
McCann’s theory
IR, 45K, band asymmetry
• Δ/2 < 40meV
• Δ’ = 18±2meV
• γ1 = 0.404±0.01, 0.450eV
• γ4 = 0.04eV
• VF = 1.1x106
m/s
A.B. Kuzmenko et al., PRB 79, 115441 (2009) Z. Q. Li et al., PRL 102, 037403 (2009)
E. McCann et al., PRL 96, 086805 (2006).T. Ohta et al., Science 313, 951 (2006)

18. Bilayer graphene ARPES studies
T. Ohta et al., Science 313, 951 (2006) S. Y. Zhou et al., Nature Materials 6, (2007)
Graphene on SiC: a very specific case
Rotenberg’s Group Lanzara’s Group

19. Linewidth broadening
• Quasiparticle's lifetime is inversely
proportional to the linewidth(FWHM) in Breit-
Wigner line shape.
• Linewidth are affected by two major effects:
Corrugation broadening and intrinsic
broadening.
• In bilayer graphene, we should expect a mild
corrugation broadening.

20. Corrugation Broadening
• Surface roughness of the graphene sample
provides ripples with phase shift as a wave in
a continuum.
• Electron scattering
• Corrugation parameters: ξ, ω, and α; acquire
from LEEM and LEED measurement.
• Calculation:
A~ Lorentzian, obtainable by fitting MDCs.

21. Intrinsic Broadening
• Changes with different photon energies.
• Since graphene is a 2D crystal, the valence
band initial states are highly localized along z
direction – band structure is kz independent,
thus it will not change with different photon
energy.
• We have only one photon energy 27eV.

22. Sample Preparation
• Mechanical Exfoliation
• 300nm thick SiO2 on intrinsic Si
• Shadow mask Au deposition, no photoresist
Optical microscopy image
1
2
3
4
Monolayer
Bilayer
1
2
3
4
10μm

23. Energy(eV)
degree
GK
K// (Å-1
)
E-EF(eV)
• 3 samples
• Range of temperature: 110 –300K
• UHV
Data Handling
Δ, γ1

24. 1
2
3
4
olayer
er
1
2
10μm
300K 110Kb) c) d)
M’KΓ MKΓ

25. Photoemission
microscopy
Bilayer
Dispersion of trilayer measured
with photon energy 74eV

26. Trilayer @ room temperature
with photon energy 74 eV
 According to the band
structure, the sample is doped
in the fabrication process. We
can see part of the conduction
band and the gap value is
about 350 meV.
 This is the band structure
along Γ-K direction. The
dispersion is strong on one
side with a small tail on the
other side. This is consistent
with our previous theoretical
calculation.