Optics on Graphene

Gate-Variable Optical Transitions in GrapheneFeng Wang, Yuanbo Zhang, Chuanshan Tian, Caglar Girit, Alex Zettl, Michael Crommie, and Y. Ron Shen, Science 320, 206 (2008).

Direct Observation of a Widely Tunable Bandgap in Bilayer GrapheneYuanbo Zhang, Tsung-Ta Tang, Caglar Girit1, Zhao Hao, Michael C. Martin, Alex Zettl1, Michael F. Crommie, Y. Ron Shen and Feng Wang (2009)

Graphene(A Monolayer of Graphite)

2D Hexagonal lattice

Electrically: High mobility at room temperature, Large current carrying capability

Mechanically: Large Young’s modulus.

Thermally: High thermal conductance.

Properties of Graphene

Quantum Hall effect,

Barry Phase

Ballistic transport,

Klein paradox

Others

Exotic Behaviors

Quantum Hall Effect

Y. Zhang et al, Nature 438, 201(2005)

Optical Studies of Graphene

Optical microscopy contrast; Raman spectroscopy; Landau level spectroscopy.

Other Possibilites

• Spectroscopic probe of electronic structure.

• Interlayer coupling effect.• Electrical gating effect on optical transitions.

• Others

Crystalline Structure of Graphite

Graphene2D Hexagonal lattice

Band Structure of Graphene Monolayer

1 2

int

1 1

2 2

( )

Tight-binding calculation on bands:

, ( )

*( ),

( ) [1 ]

( ) | ( ) |

3

at

p

p

ik a ik a

p

p

H H H k

E f ku uH

u uf k E

f k e e

E k E f k

E

1 2 2 1

2

2cos 2cos 2cos ( )

1 4cos ( 3 / 2) 4cos( 3 / 2)cos(3 / 2)

' near K points

p x x y

p F

k a k a k a a

E k a k a k a

E v k

P.R.Wallace, Phys.Rev.71,622-634(1947)

Band Structure of Monolayer Graphere

Electron Bands of Graphene Monolayer

Band Structure in Extended BZ

Relativistic Dirac fermion.

Band Structure near K Points

eV

Vertical optical transitionVan Hove Singularity

Monolayer Bilayer

Band Structures of Graphene Monolayer and Bilayer near K

EF is adjustable

x

x

Exfoliated Graphene Monolayers and Bilayers

Monolayer Bilayer

Reflecting microscope images.

K. S. Novoselov et al., Science 306, 666 (2004).

20 m

Raman Spectroscopy of Graphene

A.S.Ferrari, et al, PRL 97, 187401 (2006)

(Allowing ID of monolayer and bilayer)

Reflection Spectroscopy on Graphene

Experimental Arrangement

Doped Si

GrapheneGold

290-nm Silica

OPADet

Infrared Reflection Spectroscopyto Deduce Absorption Spectrum

Differential reflection spectroscopy:Difference between bare substrate and graphene on substrate

A

B-R/R (RA-RB)/RA versus

RA: bare substrate reflectivity

RB: substrate + graphene reflectivity20 m

dR/R = -Re[

from substrate

from graphene: interband transitons

free carrier absorptionRe Absorption spectrum

Spectroscopy on Monolayer Graphene

Monolayer Spectrum

x

R/R

E EF

2 2

0

0 0

#electrons/holes

= ( ) / ( v )

v | |

( ) p-doped: 0

can be adjusted by carrier injection through .

FE

F F

F F

g

F g

n

E dE E

E n

n C V V V

E V

2( ) 2 / FE E v

C: capacitance

Experimental Arrangement

Doped Si

GrapheneGold

290-nm Silica

OPADet

Vg

Gate Effect on Monolayer Graphene

2( ) 2 / vFE E

X XX

Small density of states close to Dirac point E = 0 Carrier injection by applying gate voltage can lead to large Fermi energy shift .

EF can be shifted by ~0.5 eV with Vg ~ 50 v;

Shifting threshold of transitions by ~1 eV

R/R

EF

If Vg = Vg0 + Vmod, then should be a maximum at mod

( / )R R

V

2 FE

Vary Optical Transitions by Gating

Laser beam Vary gate voltage Vg.

Measure modulated reflectivity due to Vmod at V

( Analogous to dI/dV measurement in transport)

0

( / )

V

R R

V

Results in Graphene Monolayer

= 350 meV

2 FE 0

2 20

v | |

( )

=( v ) | |

F F

g

F F g

E n

n C V V

E C V V

The maximum determines Vg for the given EF.

Mapping Band Structure near KFor different , the gate voltage Vg determined from maximum is different, following the relation , mod

( / )R R

V

2 2

0( v ) | | F F gE C V V

R/R

EF

Slope of the line allows deduction of slope of the band structure (Dirac cone)

60.83 10 /Fv m s 0 70 vV

2D Plot of Monolayer SpectrumExperiment Theory

R/R) 60V50V

Vg

Strength of Gate Modulation

Bilayer Graphene(Gate-Tunable Bandgap)

Band Structure of Graphene Bilayer

For symmetric layers, = 0

For asymmetric layer,

E. McCann, V.I.Fal’ko, PRL 96, 086805 (2006);

Doubly Gated Bilayer

Asymmetry: D (Db + Dt)/2 0

Carrier injection to shift EF: F D = (Db - Dt)

Sample Preparation

0 ( - ) /b b b b bD V V d

0t ( - ) /t t t tD V V d

0,b tV Effective initial bias

due to impurity doping

Transport Measurement

Maximum resistance appears at EF = 00 0( ) ( - ) / ( - ) / 0b t b b bb tt t tVD D V VD d V d

0D

Lowest peak resistance corresponds to Db = Dt = 0 .0 0, b tV V

Optical Transitions in BilayerI: Direct gap transition (tunable, <250 meV)

II, IV: Transition between conduction/valence bands(~400 meV, dominated by van Hove singularity)

III, V: Transition between conduction and valence bands (~400 meV, relatively weak)

If EF=0, then II and IV do not contribute

Bandstructure Change Induced by0 (from 0 with 0)D D D

Transitions II & IV inactive

Transition I active

x

x

IV

II

Differential Bilayer Spectra (D = 0)(Difference between spectra of D0 and D=0)

I I

Larger bandgap stronger transition I because ot higher density of states

IV

Charge Injection without Change of Bandstructure (D fixed)

xD = 0 D 0

Transition IV becomes activePeak shifts to lower energy as D increases..

Transition III becomes weaker and shifts to higher energy as D increases.

IV

III

Difference Spectra for Different D between D=0.15 v/nm and D=0

Larger D

Bandgap versus D

(dR/R) (dR/R) 60V -(dR/R) -50V

is comparable to R/R in value

Strength of Gate Modulation

SummaryGrahpene exhibits interesting optical behaviors:.

• Gate bias can significantly modify optical transitions over a broad spectral range.

• Single gate bias shifts the Fermi level of monolayer graphene.Spectra provides information on bandstructure, allowing deducti

on of VF (slope of the Dirac cone in the bandstructure).

• Double gate bias tunes the bandgap and shifts the Fermi level of bilayer graphene.

• Widely gate-tunable bandgap of bilayer graphene could be useful in future device applications.

• Strong gating effects on optical properties of graphene could be useful in infrared optoelectronic devices.