Momentum dependence and losses of graphene plasmons.
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Transcript Momentum dependence and losses of graphene plasmons.
Momentum dependence and losses in
graphene plasmons
Graphene Nanophotonics
Benasque, 2013, Mar 03 -- Mar 08
Outline
Damping mechanisms
Plasmons in ribbons
Experimental results
Mid-infrared plasmons in scaled graphene nanostructures
H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. G., P. Avouris, F. Xia
arXiv:1209.1984, Nature Photonics, in press
L. Martín-Moreno, A. Nikitin, F. García-Vidal, M. M. Fogler
Damping mechanisms
Higher order processes, multiple
electron-hole pairs
Lack of momentum conservation
Decay into other excitations:
phonons, …
Elastic scattering
j
e 2 vF k F
i
k j
2 k
k
k+q
k’
vF
elastic mean free path
k
p q i 2 e 2vF k F q
2
Finite systems
vF
D
D
Inhomogeneous electric fields
T. Low, M. M. Fogler, F. G, unpublished
Edges
Local excitations
p(q) 4 q 4
L-1
Inhomogeneous electric fields
F r , t 0 e
q y
Non local conductivity, clean system
2 kF
q vF
Im q, vF2 q
0
q vF
e2
q,
Im q,
2
q
1ms, EF=0.4eV
E
t
p
E
1
A
d q F q
2
2
d q F q q,
1 F
A 2
2
2
vF3 q 3p
2
vF2 q 2p
e2kF
1
D2
Surface polar modes
H e sp
M sp
2
1
M sp ak q ak bq bq
A pq
e 2 e 2 q z 2
F
env q
0
sp
1
1
F
2 env 0 env
2
pl2 q
sp2 *
env 1
2
2
2
2
i i sp sp sp *
4
sp2 *
sp F 2
Si O2 has polar modes
which induce long range
electrostatic potentials.
The dielectric constant of
the system is modified.
Optical phonons
q
k’
k
k+q
Optical phonons at G, ph0.2 eV
Coupling through changes in bond lengths
Weak dispersion
H e ph
t
a u x iu y
a t
23
t a
0
1/
u x iu y 1 t
j u
0 vF a
2
t
D F ph
a M ph
1
Experiments
Y. Yan, T. Low, W. Zhu,Y. Wu, M. Freitag, X. Li, F. G., P. Avouris, and F. Xia, arXiv:1209.1984, Nature Phys., in press
Nanoribbons, antidots , and
nanodisks defined by
electron beam litography.
The samples lie on CVD
graphene on SiO 2 and
diamond like carbon (DLC)
substrates.
Plasmon dispersion
graphene on diamond like carbon (DLC)
q
W W0
W0 28nm
dead layer
asymmetric lineshape
Plasmon dispersion
graphene on SiO2
sp1 806cm1
sp 2 1168cm1
op 1598cm1
Plasmon damping
G
1
G01 a Gpl1 ph
W
Plasmon damping
Comparison between
graphene on SiO 2 and
graphene on DLC
Doping dependence
Conclusions. Open questions
Plasmon dispersion can be accurately measured in
nanoribbons.
Plasmon linewidth can be explained by simple
mechanisms
The main decay channel at high frequencies is decay
into optical phonons and electron-hole pairs
The role of other decay channels is in reasonable
agreement with simple estimates
Coulomb blockade, interplay between plasmons and
dc transport