ARPES microscopy study on free standing bilayer graphene

Po-Chun Yeh , Kevin Knox , Wencan Jin , Jerry Dadap , Philip Kim , Richard M. Osgood

Columbia UniversityAlexei Barinov, Dudin Pavel

Elettra-Sincrotrone Trieste,Italy

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

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 size

De Heer, First, Butler, IBM Geim, Novoselov; Kim

PE work: see LBL Group, Georgia Tech Group, IBM, etc.

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

=0.5

=0.3

=0.7

=0.5

=0.3

=0.7

=0.5

=0.3

=0.7

Columbia, ACSNano, 2010Columbia, ACSNano, 2010

Suspended vs Supported ARPES

ГM

K

K'

Supported Graphene

Suspended Graphene

Columbia, PRB, 2008Columbia, PRB, 2008Columbia, PRB, 2011Columbia, PRB, 2011

Our measurements show β = 0.3 fs-1eV-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

Bilayer Graphene TheoryBilayer 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

• 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

23

4

10μm

• 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

K// (Å-1)E

-EF (

eV)

Δ, γ1

Data HandlingProcessing 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’K

Fermi Cutoff and Spatial Resolution

EDC*s fit at K point with Lorentzian function

convoluted with Fermi function:

T=110K

T=300K

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’K

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’K

Results of Fitting for Exfoliated GrFit the π bands with the tight binding model:

A300K

A110K

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 measurementB. Infrared measurement on SiO2/Si, doped, 10KC. Infrared measurement on SiO2/Si, doped, 45KD. ARPES measurement on SiC, dopedE. 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.

Summary and DirectionCharacteristics

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

Thank you

L. M. Malard et al., PRB 76, 201401 (2007)

RamanFrom 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.

Results of Fitting for Exfoliated GrNormal 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)x106m/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 = 1x106m/s

• Δ = variable

• γ1 = 0.36 – 0.45eV

• VF = (1 – 1.1)x106m/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 = 1.1x106m/sA.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)

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

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.

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.

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.

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

23

4

10μm

Ene

rgy

(eV

)

degree

GK

K// (Å-1)

E-E

F (eV

)

• 3 samples

• Range of temperature: 110 –300K

• UHV

Data Handling

Δ, γ1

1

2

3

4

Monolayer

Bilayer

1

2

10μm

300K 110Kb) c) d)

M’K M’K

Photoemission microscopy

Bilayer

Dispersion of trilayer measured with photon energy 74eV

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.