《石墨烯光学介绍》PPT课件

Quantum Hall Effect
Y. Zhang et al, Nature 438,
Optical Studies of Graphene
Optical microscopy contrast; Raman spectroscopy; Landau level spectroscopy.
Optics on Graphene
Gate-Variable Optical Transitions in Graphene
Feng Wang, Yuanbo Zhang, Chuanshan Tian, Caglar Girit, Alex Zettl, Michael Crommie, and Y. Ron Shen, Science 320, 206 (2008).
Measure modulated reflectivity due to Vmod at V
(d R / R)
V
V0
( Analogous to dI/dV measurement in transport)
Results in Graphene Monolayer
= 350 meV
2EF
If dEF=0, then II and IV do not contribute
Bandstructure Change Induced by
D 0 (from D 0 with d D 0)
x
IV
I
x
I
Transitions II & IV inactive
Transition I active
Mechanically:
Large Young’s modulus.
Thermally:
High thermal conductance.
Exotic Behaviors
Quantum Hall effect, Barry Phase Ballistic transport, Klein paradox Others
/
(
vF )2
(E) 2E / vF2
EF vF | n |
n C(Vg V0 )
p-doped: V0 0
C:
capacitance
EF can be adjusted by carrier injection through Vg .
Experimental Arrangement
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)
Det
OPA
Gold
Graphene
290-nm Silica
Doped Si
Infrared Reflection Spectroscopy to Deduce Absorption Spectrum
Differential reflection spectroscopy: Difference between bare substrate and graphene on substrate
Band Structure of Graphene Bilayer
For symmetric layers, D = 0 For asymmetric layer, D 0
E. McCann, V.I.Fal’ko, PRL 96, 086805
Doubly Gated Bilayer
Asymmetry: D D (Db + Dt)/2 0 Carrier injection to shift EF: dF dD = (Db - Dt)
H
u1 u2
Ep, f *(k
),
f (k Ep
)
u1 u2
f (k ) [1 eik a1 eik a2 ]
E (k ) Ep | f (k ) |
Ep 3 2 cos k a1 2 cos k a2 2 cos k (a2 a1)
Ep 1 4 cos2( 3kxa / 2) 4 cos( 3kxa / 2) cos(3kya / 2)
EF vF | n |
n C(Vg V0 )
EF2 =( vF )2 C | Vg V0 |
The maximum determines Vg for the given EF.
Mapping Band Structure near K
For different w, the gate voltage Vg determined
dD = 0 x
IV
dD 0
III
Transition IV becomes active Peak shifts to lower energy as D
increases..
Ep vF k '
near K points
P.R.Wallace, Phys.Rev.71,622-
Band Structure of Monolayer Graphere
p-Electron Bands of Graphene Monolayer
Band Structure in Extended BZ
Other Possibilites
• Spectroscopic probe of electronic structure. • Interlayer coupling effect. • Electrical gating effect on optical transitions. • Others
Crystalline Structure of Graphite
Graphene
2D Hexagonal lattice
Band Structure of Graphene Monolayer
H Hat Hint (k )
Tight-binding calculation on bands:
Band Structure near K Points
~10 eV
Relativistic Dirac fermion.
Band Structures of Graphene Monolayer and Bilayer near K
Monolayer
Bilayer
K
x K
x
Vertical optical transition
Graphene
(A Monolayer of Graphite)
2D Hexagonal lattice
Properties of Graphene
Electrically:
High mobility at room temperature, Large current carrying capability
20 m
A
B
RA: bare substrate reflectivity RB: substrate + graphene
reflectivity
-dR/R (RA-RB)/RA versus w
dR/R = -Re[h(w)s(w)]
h(w) from substrate
s(w) from graphene: transitons
d D (Db Dt ) b (Vb -Vb0 ) / db t (Vt -Vt0 ) / dt 0
Lowest peak resistance corresponds to Db = DVtb0=, 0Vt0
.
Optical Transitions in Bilayer
I: Direct gap transition (tunable, <250 meV)
Det
OPA
Gold
Graphene
290-nm
Vg
Silica
Doped Si
Gate Effect on Monolayer Graphene
dR/R
X
XX
2EF
(E) 2E / v2F
Small density of states close to Dirac point E = 0 Carrier injection by applying gate vsEvohF;litfcatagne. bceanshliefatdedtobyla~r0g.e5 FeeVrmwiitehneVrgg~y 50
from maximu(dmR / R)
is different, following
the relationVmod
EF2 ( vF )2C |Vg,V0|
dR/R
2EF
Slope of the line allows deduction of slope of the band
structure (Dirac cvoFne)0.83106 m / s
Differential Bilayer Spectra (dD = 0)
(Difference between spectra of D0 and
I
D=0) I
IV
Larger bandgap stronger
transition I
because ot higher
Charge Injection without Change of Bandstructure (D fixed)
Raman Spectroscopy of Graphene