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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


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).


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)


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//


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).


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)


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)


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


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)


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


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


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.


-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

.)


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)


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 :


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%


Tight-Binding model Including nextnearest neighbors coupling :

Electron-hole symmetry is broken Γh2 ≠ Γe

2 Transient THz electric field is emitted


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


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


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


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


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


Thank you for your attention

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