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Graphene for THz technology
J. Mangeney1, J. Maysonnave1, S. Huppert1, F. Wang1, S.
Maero1, C. Berger2,3, W. de Heer2, T.B. Norris4, L.A. De
Vaulchier1, S. Dhillon1, J. Tignon1 and R. Ferreira1
1 Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS (UMR 8551), Université P. et M. Curie, Université D. Diderot, France
2 School of Physics, Georgia Institute of Technology, Atlanta, USA 3 Université Grenoble Alpes / CNRS, Institut Néel, France
4 Center for Ultrafast Optical Science, University of Michigan, USA
Progress in Photonics Fri, 16th Oct 2015 Firenze
THz technology
§ Excite vibration and rotation modes of molecules § Many substances such as polymers, paper, packing material are transparent § Non-ionizing rays § Bandwith of futur electronic circuits
ü Interest of THz rays
ü Issue
~ 0.1 THz → ~ 10 THz ~ 3 mm → ~ 30 µm
~ 0.4 meV→ ~ 40 meV
ü The THz frequency range
Lack of compact powerful sources and sensitive detectors
Source Efficiency
Frequency (Hz) 109 1010 1011 1012 1013 1014
THz Electronic Optic
§ Optimizing devices § New concepts § Advanced materials
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Graphene for THz technology
Ø Unequally space Landau level energy : Tunable LL laser
Ø Plasmon resonances at THz frequencies
Ø Gapless material : THz photons can instigate interband transitions
Ø Electrical gate tunes Ef : Strength of transitions can be controlled
S. Boubanga-Tombet et al. Phys. Rev. B 85, 035443 (2012) L Prechtel et al. Nature Com. 3, 646 (2012)
Gao W. et al, Nano Lett. 14, 1242 (2014)
L. Ju et al., Nature Nanotech. 6, 631 (2011)
Martin Mittendorf ,et al., Nature Phys. Nature Physics 11, 75–81 (2015)
Ø Linear energy dispersion close to the Dirac point : Enhanced nonlinear properties at THz frequencies
Ef
ωTHz
n=0$n=1$
n=&1$
M.M Glazov et al. Phys. Rep. 535, 101 (2014), S. A. Mikhailov Phys. Rev. B 90, 241301 (2014).
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Nonlinearities in graphene ω1
ω2
ωTHz = 2ω2 −ω1
PTHz = P(ω2 )2P(ω1)
χ (3)
ω1
ω2
ωTHz =ω2 −ω1
PTHz = P(ω2 )P(ω1)
Ø Graphene is centrosymmetric
Second order nonlinearity is a priori cancelled
Ø THz Generation relying on 3rd order nonlinearity D. Sun et al., Nano Lett. 10, 1293 (2010)
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Nonlinearities in graphene
ω1
ω2
ωTHz = 2ω2 −ω1
PTHz = P(ω2 )2P(ω1)
ω1(q1)
ω2 (q2 ) ωTHz =ω2 −ω1§ 2nd order effect dependent of q
THz generation relying on photon drag effect
§ Generation THz relying on 3rd order nonlinearity
D. Sun et al., Nano Lett. 10, 1293 (2010)
q//
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State of the Art
P. A. Obraztsov et al., Scientific Reports 4, 4007 (2014).
ω ≤ 2EFq
M. M. Glazov, S. D. Ganichev, Physics Reports, 535 (2014)
Generation of dc current
ω >> 2EFq Using broadband interband excitation
Generation of 2nd order nonlinear ac currents and narrowband THz emission
Using monochromatic intraband excitation : Resonant photon drag effect
: Non-resonant photon drag
Young-Mi Bahk et al. , ACS Nano, 8, 9089 (2014).
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Photon Drag effect Ø At normal incidence q//=0
jc(2)(t) = 0
Ø At oblique incidence q//≠0
jc(2)(t) ≠ 0
Second order nonlinear current jc(2)(t)
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Emission of THz radiation Using ultrashort optical pulses at oblique incidence (q// ≠ 0), jc2(t) is transient.
The short rise and fall times of jc2(t) generate a THz electromagnetic radiation
0.0 0.5 1.0 1.5-0.5
0.0
0.5
1.0
Cur
rent
(a. u
.)
Time (ps)
0.0
0.5
1.0
THz
Ele
ctric
Fie
ld (
a. u
.)
ETHz ∝djc(2)
dt
0.0 0.5 1.0 1.5-0.5
0.0
0.5
1.0
Cur
rent
(a.u
.)
Time (ps)
0.0
0.5
1.0
jc(2)(t)
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Outline
I. Experimental investigation of the emitted THz radiation
II. Microscopic tight-binding model of transient photon drag effect
III. Physical insights obtained by the confrontation between experimental results with theoretical predictions
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SiC substrate Multilayer graphene
W. de Heer, C. Berger, Georgia Tech, Atlanta
…
Ef=8 meV Ef=300 meV Ef=8 meV
37 independent layers
From magneto-spectroscopy measurements
-> Thermal desorption of Si from the C-terminated face of single-crystal 4H-SiC(0001)
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THz emission spectroscopy
Delay Line
Lock-In multi-layer graphène
waveplate λ/2
Ti:Sa Laser
100 fs
800 nm
Electro-optic Detection
ZnTe 1 mm
Non resonant photoexcitation
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Coherent THz emission
391 392 393 394 395
-30
0
30
60
Delay (ps)
Ele
ctric
fiel
d (
mV
/cm
)
1 2 30
2
4
6
Frequency (THz)
Spe
ctra
l Am
plitu
de (
a. u
.)
Room temperature, φ=25°, s-polarized pump excitation
J. Maysonnave et al., Nano Lett. 14 , 5797, 2014
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Second-order nonlinearity
0 5 10 15 20 25 30 35
1
2
Ele
ctric
Fie
ld (
a.u)
Optical Fluence (µJ/cm²)
ETHz ∝Eopt2
ETHz= 70 mV/cm
Optical-to-THz conversion efficiency = 1.5x10-11 Conversion efficiency par length unit reaches ~10-5/cm.
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-20 -10 0 10 20-200
0
200
q// dependence of THz emission
-51 -50 -49
Time (ps)
Ele
ctric
Fie
ld (
a.u.
)
Ø At normal incidence, no signal is detected. Ø The oscillations show reverse polarity for opposite incidence angles
q//
+ φ
q//
- φ -81 -80 -79
Ele
ctric
fiel
d (a
.u.)
Time (ps)
0
Incidence Angle φ (°) Rel
ativ
e am
plitu
de
(a.u
.)
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Microscopic Model The effect of the optical pulse is described by the hamiltonien :
The density matrix evolution in the standard perturbation formalism :
with
and
The second-order transient current is calculated :
j(2)(t) ≈ em0
k,λ p̂ k,λ k,λ ρ̂ (2)(t) k,λk,λ∑ = jc
(2)(t)+ jv(2)(t)
H = H0 +H1A(r, t) =A0 fL (t)e
i(q.r−ωLt ) + cc
H1 =em0
A(r, t).p̂
i∂ρ̂∂t
(0)
= H0, ρ̂(0)"# $%= 0
i∂ρ̂∂t
(1)
= H0, ρ̂(1)"# $%+ H1, ρ̂
(0)"# $%− iΓ1ρ̂(1)
i∂ρ̂∂t
(2)
= H1, ρ̂(1)"# $%+ H0, ρ̂
(2)"# $%− iΓ2ρ̂(2)
S. Huppert, R. Ferreira (Theory group, LPA)
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Tight-Binding model
Transient electron and hole currents compensate exactely No THz electric field is emitted
-0.5 0.0 0.5 1.0-8
-4
0
4
8 jc(2) electrons
Cur
rent
(a.u
)
Time (ps)
Ø Including nearest neighbors coupling :
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Tight-Binding model Including nextnearest neighbors coupling :
Electron-hole symmetry is broken !
including next-nearest neighbors nearest neighbors coupling only εk ≈ t ' γk
2± tγk
Dissymmetry between electron and hole dispersion relation ~ 2%
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Tight-Binding model Including nextnearest neighbors coupling :
Electron-hole symmetry is broken Γh2 ≠ Γe
2 Transient THz electric field is emitted
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Experiment vs modeling
-1 0 1 2
-30
0
30
60
1 2 3
-30
0
30
60
Ele
ctric
Fie
ld (m
V/c
m)
Time (ps) Frequency (THz) S
pect
ral A
mpl
itude
(a.u
)
Good agreement between experimental results and theoretical predictions
J. Maysonnave et al., Nano Lett. 14 , 5797, 2014
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Experiment vs modeling
q// = q sin θ ux
-20 -10 0 10 20-200
0
200
Incidence Angle φ (°)
Rel
ativ
e am
plitu
de
(a.u
.)
The dynamical photon drag model well reproduces the experimental features
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Polarization dependence
0 1 2 3 Am
plitu
de S
pect
ra (a
.u.) p
s
Frequency (THz)
0 1 2 3
Am
plitu
de S
pect
ra (a
.u.)
TeraHertz (THz)
p s
E θ
1/Γe2 =170 fs 1/Γh
2 =174 fs2% of variation between Γe
2 and Γh2
Insight in the dynamics of the non-equilibrium populations during the first 100 fs after interband excitation
and
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Polarization of THz emission
-1 0 1
-1 0 1
θ = 45° θ = 135°
Ele
ctric
Fie
ld a
long
y d
irect
ion
(a.u
) θ = 45° θ = 135°
Ele
ctric
Fie
ld a
long
x d
irect
ion
(a.u
)
Time (ps) Time (ps)
The symmetries of graphene are reflected in the polarization dependence of photon drag signal
φ
θ
y
z x
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Conclusion
1 2 3 4 5 6 7 8
Spec
tral A
mplitu
de (u
.a)
Frequency (THz)
• Ultrabroadband emission
• Resonant excitation
• Graphene emits THz radiation through difference frequency generation. • Unique probe of physical properties of graphene:
Perspectives
- the next-nearest-neighbor coupling - distinct dynamics of electron and hole