Graphene for THz technology
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1 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 4 Université Grenoble Alpes / CNRS, Institut Néel, France Center for Ultrafast Optical Science, University of Michigan, USA
2 THz technology ü The THz frequency range ~ 0.1 THz ~ 10 THz ~ 3 mm ~ 30 µm ~ 0.4 mev ~ 40 mev ü Interest of THz rays 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 Issue Lack of compact powerful sources and sensitive detectors Source Efficiency Electronic THz Optic Frequency (Hz) Optimizing devices New concepts Advanced materials
3 Graphene for THz technology Ø Gapless material : THz photons can instigate interband transitions S. Boubanga-Tombet et al. Phys. Rev. B 85, (2012) L Prechtel et al. Nature Com. 3, 646 (2012) Ø Electrical gate tunes E f : Strength of transitions can be controlled Gao W. et al, Nano Lett. 14, 1242 (2014) Ø Plasmon resonances at THz frequencies L. Ju et al., Nature Nanotech. 6, 631 (2011) Ø Unequally space Landau level energy : Tunable LL laser Martin Mittendorf,et al., Nature Phys. Nature Physics 11, (2015) ω THz Ø Linear energy dispersion close to the Dirac point : Enhanced nonlinear properties at THz frequencies n=1$ E f n=0$ n=&1$ M.M Glazov et al. Phys. Rep. 535, 101 (2014), S. A. Mikhailov Phys. Rev. B 90, (2014).
4 Nonlinearities in graphene Progress in Photonics Ø THz Generation relying on 3 rd order nonlinearity χ (3) D. Sun et al., Nano Lett. 10, 1293 (2010) ω 1 ω 2 ω THz = 2ω 2 ω 1 P THz = P(ω 2 ) 2 P(ω 1 ) Ø Graphene is centrosymmetric ω 1 ω 2 ω THz = ω 2 ω 1 Second order nonlinearity is a priori cancelled P THz = P(ω 2 )P(ω 1 )
5 Nonlinearities in graphene Progress in Photonics Generation THz relying on 3 rd order nonlinearity D. Sun et al., Nano Lett. 10, 1293 (2010) ω 1 ω 2 ω THz = 2ω 2 ω 1 P THz = P(ω 2 ) 2 P(ω 1 ) 2 nd order effect dependent of q ω 1 (q 1 ) ω 2 (q 2 ) ω THz = ω 2 ω 1 THz generation relying on photon drag effect q //
6 State of the Art q ω 2E F : Resonant photon drag effect Using monochromatic intraband excitation Generation of dc current M. M. Glazov, S. D. Ganichev, Physics Reports, 535 (2014) q ω >> 2E F : Non-resonant photon drag Using broadband interband excitation Generation of 2 nd order nonlinear ac currents and narrowband THz emission P. A. Obraztsov et al., Scientific Reports 4, 4007 (2014). Young-Mi Bahk et al., ACS Nano, 8, 9089 (2014).
7 Photon Drag effect Ø At normal incidence q // =0 Second order nonlinear current j c (2) (t) j c (2) (t) = 0 Ø At oblique incidence q // 0 j c (2) (t) 0
8 Emission of THz radiation Progress in Photonics Using ultrashort optical pulses at oblique incidence (q // 0), j c2 (t) is transient. The short rise and fall times of j c2 (t) generate a THz electromagnetic radiation Current (a.u.) Time (ps) (2) E THz j (2) dj c c (t) dt THz Electric Field (a. u.)
9 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
10 Multilayer graphene 37 independent layers SiC substrate W. de Heer, C. Berger, Georgia Tech, Atlanta -> Thermal desorption of Si from the C- terminated face of single-crystal 4H-SiC(0001) From magneto-spectroscopy measurements E f =300 mev E f =8 mev E f =8 mev
11 THz emission spectroscopy Progress in Photonics multi-layer graphène Lock-In Electro-optic Detection ZnTe 1 mm Ti:Sa Laser waveplate λ/2 100 fs 800 nm Delay Line Non resonant photoexcitation
12 Coherent THz emission Room temperature, φ=25, s-polarized pump excitation Electric field (mv/cm) Delay (ps) Spectral Amplitude (a. u.) Frequency (THz) J. Maysonnave et al., Nano Lett. 14, 5797, 2014
13 Second-order nonlinearity Progress in Photonics E THz = 70 mv/cm Electric Field (a.u) E THz E opt Optical Fluence (µj/cm²) Optical-to-THz conversion efficiency = 1.5x10-11 Conversion efficiency par length unit reaches ~10-5 /cm.
14 q // dependence of THz emission + φ q // Electric field (a.u.) Time (ps) Ø At normal incidence, no signal is detected. Progress in Photonics Electric Field (a.u.) Time (ps) Ø The oscillations show reverse polarity for opposite incidence angles - φ q // Relative amplitude (a.u.) Incidence Angle φ ( ) 0
15 Microscopic Model The effect of the optical pulse is described by the hamiltonien : with A(r,t) = A 0 f L (t)e i(q.r ω Lt) + cc H = H 0 + H 1 and The density matrix evolution in the standard perturbation formalism : (0) S. Huppert, R. Ferreira (Theory group, LPA) j (2) (t) e m 0 k, λ ˆp k, λ k, λ ˆρ (2) (t) k, λ k,λ H 1 = e m 0 A(r,t). ˆp i ˆρ = " # H 0, ˆρ (0) $ % t = 0 i (1) ˆρ = " # H 0, ˆρ (1) $ % t + " # H 1, ˆρ (0) $ % i Γ (1) 1 ˆρ i (2) ˆρ = " # H 1, ˆρ (1) $ % t + " # H 0, ˆρ (2) $ % i Γ (2) 2 ˆρ The second-order transient current is calculated : = j c (2) (t)+ j v (2) (t)
16 Tight-Binding model Ø Including nearest neighbors coupling : 8 j c (2) electrons Current (a.u) Time (ps) Transient electron and hole currents compensate exactely No THz electric field is emitted
17 Tight-Binding model Including nextnearest neighbors coupling : ε k t ' γ k 2 ± tγ k nearest neighbors coupling only including next-nearest neighbors Electron-hole symmetry is broken! Dissymmetry between electron and hole dispersion relation ~ 2%
18 Tight-Binding model Including nextnearest neighbors coupling : Electron-hole symmetry is broken Γ h 2 Γe 2 Transient THz electric field is emitted
19 Experiment vs modeling Progress in Photonics 60 Electric Field (mv/cm) Spectral Amplitude (a.u) Time (ps) Frequency (THz) Good agreement between experimental results and theoretical predictions J. Maysonnave et al., Nano Lett. 14, 5797, 2014
20 Experiment vs modeling Progress in Photonics Relative amplitude (a.u.) Incidence Angle φ ( ) q // = q sin θ u x The dynamical photon drag model well reproduces the experimental features
21 Polarization dependence Progress in Photonics Amplitude Spectra (a.u.) TeraHertz (THz) p s E θ Amplitude Spectra (a.u.) Frequency (THz) p s 1/ Γ e =170 fs and 1/ 2 Γh 2 =174 fs 2% of variation between Γ e 2 and Γh 2 Insight in the dynamics of the non-equilibrium populations during the first 100 fs after interband excitation
22 Polarization of THz emission φ z θ y x Electric Field along x direction (a.u) θ = 45 θ = 135 Electric Field along y direction (a.u) θ = 45 θ = Time (ps) Time (ps) The symmetries of graphene are reflected in the polarization dependence of photon drag signal
23 Conclusion Graphene emits THz radiation through difference frequency generation. Unique probe of physical properties of graphene: - the next-nearest-neighbor coupling - distinct dynamics of electron and hole Perspectives Ultrabroadband emission Resonant excitation Spectral Amplitude (u.a) Frequency (THz)
24 Thank you for your attention
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