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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 2, Iss. 12 — Dec. 1, 2012
  • pp: 1713–1722
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Probing near Dirac point electron-phonon interaction in graphene

Jingzhi Shang, Suxia Yan, Chunxiao Cong, Howe-Siang Tan, Ting Yu, and Gagik G. Gurzadyan  »View Author Affiliations


Optical Materials Express, Vol. 2, Issue 12, pp. 1713-1722 (2012)
http://dx.doi.org/10.1364/OME.2.001713


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Abstract

Carrier dynamics in graphene films on CaF2 have been measured in the mid infrared region by femtosecond pump-probe spectroscopy. The relaxation kinetics shows two decay times. The fast time component is ~0.2 ps, which is attributed to the mixture of initial few ultrafast intraband and interband decay channels. The slow component is ~1.5 ps, which is primarily assigned to optical phonon-acoustic phonon scattering. The contribution of fast component exhibits an increase trend in the probe photon frequencies from 2600 to 3100 cm−1. At the probe frequency of 2700 cm−1, the accelerated carrier relaxation was detected, which resulted from the interband triple-resonance electron-phonon scattering in graphene. At the probe frequency of 3175 cm−1, a clear instant negative differential transmission signal was observed, which is due to stimulated two-phonon emission involved with G phonons in graphene. This result indicates that graphene can be used as a source of coherent ultrashort sound-wave emission.

© 2012 OSA

1. Introduction

Graphene, two-dimensional carbon, has aroused great attention from both scientific and industrial communities. Their unique properties [1

1. A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009). [CrossRef] [PubMed]

,2

2. K. S. Novoselov, “Nobel lecture: graphene: materials in the flatland,” Rev. Mod. Phys. 83(3), 837–849 (2011). [CrossRef]

] and promising applications [2

2. K. S. Novoselov, “Nobel lecture: graphene: materials in the flatland,” Rev. Mod. Phys. 83(3), 837–849 (2011). [CrossRef]

] strongly rely on the electronic structure with a linear dispersion around Dirac point [3

3. A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009). [CrossRef]

]. In particular, investigation of carrier dynamics in graphene is very important for testing the concepts of fundamental physics and understanding electron-electron (e-e) and electron-phonon (e-p) scattering processes in two-dimensional materials. Nowadays, graphene-based electronic devices have shown many promising applications, however, origins of some electron transport behaviors in these devices are still controversial [2

2. K. S. Novoselov, “Nobel lecture: graphene: materials in the flatland,” Rev. Mod. Phys. 83(3), 837–849 (2011). [CrossRef]

,4

4. S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two-dimensional graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011). [CrossRef]

]. To clarify these electron properties, it is necessary to understand the carrier scattering processes in the low-energy regions near Dirac point. Theoretically, the energy dependences of carrier dynamics have been predicted by considering various possible relaxation channels [5

5. E. H. Hwang, B. Y.-K. Hu, and S. Das Sarma, “Inelastic carrier lifetime in graphene,” Phys. Rev. B 76(11), 115434 (2007). [CrossRef]

8

8. R. Kim, V. Perebeinos, and P. Avouris, “Relaxation of optically excited carriers in graphene,” Phys. Rev. B 84(7), 075449 (2011). [CrossRef]

]. On the other hand, ultrafast laser [9

9. J. Shang, Z. Luo, C. Cong, J. Lin, T. Yu, and G. G. Gurzadyan, “Femtosecond UV-pump/visible-probe measurements of carrier dynamics in stacked graphene films,” Appl. Phys. Lett. 97(16), 163103 (2010). [CrossRef]

28

28. J. H. Strait, H. Wang, S. Shivaraman, V. Shields, M. Spencer, and F. Rana, “Very slow cooling dynamics of photoexcited carriers in graphene observed by optical-pump terahertz-probe spectroscopy,” Nano Lett. 11(11), 4902–4906 (2011). [CrossRef] [PubMed]

] and angle-resolved photoemission spectroscopic studies [29

29. A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phys. 3(1), 36–40 (2007). [CrossRef]

32

32. D. A. Siegel, C.-H. Park, C. Hwang, J. Deslippe, A. V. Fedorov, S. G. Louie, and A. Lanzara, “Many-body interactions in quasi-freestanding graphene,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11365–11369 (2011). [CrossRef] [PubMed]

] on graphene films have experimentally provided a great deal of information of carrier dynamics. Especially, ultrafast pump-probe technique has been extensively used to study carrier dynamics, i.e. the real-time quasiparticle relaxation, by adjusting the time delay between pump and probe pulses. Previously, most ultrafast pump-probe studies on carrier dynamics in graphene films have been reported in the visible [9

9. J. Shang, Z. Luo, C. Cong, J. Lin, T. Yu, and G. G. Gurzadyan, “Femtosecond UV-pump/visible-probe measurements of carrier dynamics in stacked graphene films,” Appl. Phys. Lett. 97(16), 163103 (2010). [CrossRef]

14

14. M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011). [CrossRef]

], near infrared (NIR: 0.75-3 μm) [11

11. Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. Shen, Q.-H. Xu, D. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011). [CrossRef]

25

25. S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, and M. Helm, “Carrier relaxation in epitaxial graphene photoexcited near the Dirac point,” Phys. Rev. Lett. 107(23), 237401 (2011). [CrossRef] [PubMed]

], mid IR (MIR: 3-50 μm) [24

24. T. Limmer, A. J. Houtepen, A. Niggebaum, R. Tautz, and E. Da Como, “Influence of carrier density on the electronic cooling channels of bilayer graphene,” Appl. Phys. Lett. 99(10), 103104 (2011). [CrossRef]

,25

25. S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, and M. Helm, “Carrier relaxation in epitaxial graphene photoexcited near the Dirac point,” Phys. Rev. Lett. 107(23), 237401 (2011). [CrossRef] [PubMed]

], and far IR (FIR: 50-1000 μm) [25

25. S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, and M. Helm, “Carrier relaxation in epitaxial graphene photoexcited near the Dirac point,” Phys. Rev. Lett. 107(23), 237401 (2011). [CrossRef] [PubMed]

28

28. J. H. Strait, H. Wang, S. Shivaraman, V. Shields, M. Spencer, and F. Rana, “Very slow cooling dynamics of photoexcited carriers in graphene observed by optical-pump terahertz-probe spectroscopy,” Nano Lett. 11(11), 4902–4906 (2011). [CrossRef] [PubMed]

] probe regions. Only few studies [24

24. T. Limmer, A. J. Houtepen, A. Niggebaum, R. Tautz, and E. Da Como, “Influence of carrier density on the electronic cooling channels of bilayer graphene,” Appl. Phys. Lett. 99(10), 103104 (2011). [CrossRef]

,25

25. S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, and M. Helm, “Carrier relaxation in epitaxial graphene photoexcited near the Dirac point,” Phys. Rev. Lett. 107(23), 237401 (2011). [CrossRef] [PubMed]

] on the carrier dynamics of graphene films have been done in the MIR region.

2. Results and discussion

Figure 2
Fig. 2 Carrier dynamics of graphene films on CaF2 by the degenerate MIR pump and probe configuration at 2000 cm−1.
presents the differential transmission (ΔT/T) kinetics as a function of delay time by using the degenerate MIR pump-probe at ν = 2000 cm−1:ΔT = Twith pump-Twithout pump. The positive decay curve was well fitted by two exponential functions convoluted with the instrument response function. The fast and slow components are ~0.2 and ~1.0 ps with the fractional amplitudes of 64% and 36%, respectively. Due to the symmetric linear energy dispersion, the probed electron energy level at 0.124 eV above Dirac energy is half of the probe phonon energy [3

3. A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009). [CrossRef]

,4

4. S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two-dimensional graphene,” Rev. Mod. Phys. 83(2), 407–470 (2011). [CrossRef]

], which is less than the energy of either zone-boundary/edge optical phonon (~0.167 eV) around K (K′) point or zone-center optical phonon (~0.196 eV) around Γ point [34

34. L. M. Malard, M. A. Pimenta, G. Dresselhaus, and M. S. Dresselhaus, “Raman spectroscopy in graphene,” Phys. Rep. 473(5-6), 51–87 (2009). [CrossRef]

36

36. A. Gupta, G. Chen, P. Joshi, S. Tadigadapa, and P. C. Eklund, “Raman scattering from high-frequency phonons in supported n-graphene layer films,” Nano Lett. 6(12), 2667–2673 (2006). [CrossRef] [PubMed]

]. Thus, the intraband optical phonon emission, the dominant energy relaxation process for the visible photon probe regions [9

9. J. Shang, Z. Luo, C. Cong, J. Lin, T. Yu, and G. G. Gurzadyan, “Femtosecond UV-pump/visible-probe measurements of carrier dynamics in stacked graphene films,” Appl. Phys. Lett. 97(16), 163103 (2010). [CrossRef]

13

13. J. Shang, T. Yu, J. Lin, and G. G. Gurzadyan, “Ultrafast electron-optical phonon scattering and quasiparticle lifetime in CVD-grown graphene,” ACS Nano 5(4), 3278–3283 (2011). [CrossRef] [PubMed]

], can be excluded for the observed decay. Here, the fast decay is assigned to the mixture of initial few ultrafast intraband and interband scattering mechanisms [8

8. R. Kim, V. Perebeinos, and P. Avouris, “Relaxation of optically excited carriers in graphene,” Phys. Rev. B 84(7), 075449 (2011). [CrossRef]

,29

29. A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phys. 3(1), 36–40 (2007). [CrossRef]

,38

38. F. Rana, “Electron-hole generation and recombination rates for coulomb scattering in graphene,” Phys. Rev. B 76(15), 155431 (2007). [CrossRef]

44

44. A. L. Walter, A. Bostwick, K.-J. Jeon, F. Speck, M. Ostler, T. Seyller, L. Moreschini, Y. J. Chang, M. Polini, R. Asgari, A. H. MacDonald, K. Horn, and E. Rotenberg, “Effective screening and the plasmaron bands in graphene,” Phys. Rev. B 84(8), 085410 (2011). [CrossRef]

], which include the intraband e-e scattering and interband electron-optical phonon (e-op) scattering and may involve electron-plasmon scattering [8

8. R. Kim, V. Perebeinos, and P. Avouris, “Relaxation of optically excited carriers in graphene,” Phys. Rev. B 84(7), 075449 (2011). [CrossRef]

,29

29. A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phys. 3(1), 36–40 (2007). [CrossRef]

,42

42. F. Rana, J. H. Strait, H. Wang, and C. Manolatou, “Ultrafast carrier recombination and generation rates for plasmon emission and absorption in graphene,” Phys. Rev. B 84(4), 045437 (2011). [CrossRef]

44

44. A. L. Walter, A. Bostwick, K.-J. Jeon, F. Speck, M. Ostler, T. Seyller, L. Moreschini, Y. J. Chang, M. Polini, R. Asgari, A. H. MacDonald, K. Horn, and E. Rotenberg, “Effective screening and the plasmaron bands in graphene,” Phys. Rev. B 84(8), 085410 (2011). [CrossRef]

], interband Auger recombination and impact ionization [38

38. F. Rana, “Electron-hole generation and recombination rates for coulomb scattering in graphene,” Phys. Rev. B 76(15), 155431 (2007). [CrossRef]

,39

39. F. Rana, P. A. George, J. H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11), 115447 (2009). [CrossRef]

,41

41. T. Winzer, A. Knorr, and E. Malic, “Carrier multiplication in graphene,” Nano Lett. 10(12), 4839–4843 (2010). [CrossRef] [PubMed]

,43

43. E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84(20), 205406 (2011). [CrossRef]

].

Figure 3(a)
Fig. 3 (a) Frequency-dependent carrier dynamics of graphene films on CaF2, λexc = 800 nm; (b) the energy dependence of fitting parameters of carrier lifetimes.
shows the ΔT/T spectra at four MIR probe frequencies obtained by the non-degenerate 800 nm pump/MIR probe configuration. It is clear that the carrier relaxation becomes slower at low probe frequencies in the range between 2600 and 3100 cm−1. Performing biexponential fit of the decay curves, the lifetimes and fractional amplitudes versus the electron energy and/or the probe phonon frequency were obtained (Fig. 3(b)). Two time scales were extracted as above: ultrafast processes are 0.2 ± 0.1 ps and the slower ones of 1.5 ± 0.2 ps. The fractional amplitude of the fast/slow component increases/decreases versus the electron energy (half of the probe photon energy). Besides, for the probe photon frequency at 2600 cm−1, the origin of the fast decay is similar to that in Fig. 2. For the other three frequencies, intraband zone-boundary optical phonon emission is allowed, which partially contributes to the ultrafast decay, in contrast to ν = 2000 cm−1, where interband zone-boundary optical phonon emission takes place. Previously, decay of 4 ps for exfoliated bilayer graphene was reported at the probe energy of 0.3 eV [24

24. T. Limmer, A. J. Houtepen, A. Niggebaum, R. Tautz, and E. Da Como, “Influence of carrier density on the electronic cooling channels of bilayer graphene,” Appl. Phys. Lett. 99(10), 103104 (2011). [CrossRef]

], which is slightly larger than our results on stacked graphene layers. The difference is attributed to the energy band splitting in bilayer graphene, which slows down the carrier relaxation [47

47. Z. Luo, T. Yu, J. Shang, Y. Wang, S. Lim, L. Liu, G. G. Gurzadyan, Z. Shen, and J. Lin, “Large-scale synthesis of bi-Layer graphene in strongly coupled stacking order,” Adv. Funct. Mater. 21(5), 911–917 (2011). [CrossRef]

].

Figure 4(a)
Fig. 4 (a) Carrier dynamics of graphene films at the probe frequency of 2700 cm−1 measured by the 800 nm pump/MIR probe setup; (b) Raman spectrum of G′ band of graphene films on CaF2; (c) Schematic of double resonance scattering of G′ band; (d) Electron relaxation by intraband (1) and interband (2) intervalley e-op scattering processes; (e) Electron relaxation by triple resonance e-op scattering process in graphene films on CaF2.
presents the carrier dynamics measured at λexc = 800 nm and probed at λpr = 3.7 μm (ν = 2700 cm−1). This probe frequency corresponds to the Gʹ band as shown in Fig. 4(b). Figure 4(c) shows the typical double resonance Raman scattering of G′. The fast decay τ1 is shorter than those probed at both sides (2600 and 2800 cm−1) (Fig. 3(a)), and its contribution to ΔT/T is also larger. In other words, the carrier relaxation at this frequency is faster than those at neighboring frequencies. Different from the conventional intervalley e-op scattering [35

35. R. Saito, M. Hofmann, G. Dresselhaus, A. Jorio, and M. S. Dresselhaus, “Raman spectroscopy of graphene and carbon nanotubes,” Adv. Phys. 60(3), 413–550 (2011). [CrossRef]

,39

39. F. Rana, P. A. George, J. H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11), 115447 (2009). [CrossRef]

,43

43. E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84(20), 205406 (2011). [CrossRef]

] (Fig. 4(d)), the accelerated decay was attributed to the enhanced zone-boundary optical phonon emission (Gʹ band) due to intervalley triply resonant e-op scattering (Fig. 4(e)).

At high intensities of the incident radiation, the pump photons excite large number of electrons from the VB (Epuv) to the CB (Epuv) (Fig. 5(d)). Initial stage of relaxation results in generating of considerable amount of optical phonons. Meanwhile, another intense MIR probe beam produces population inversion of electrons and holes at the probe excited levels Eprc and Eprv, in CB and VB, respectively. Emitted G phonons (in pairs) stimulate electronic transitions from Eprc to Eprv when νpr = c/λpr of the probe beam equals to 3175cm−1, i.e. corresponds to second order of G phonons. We produce population inversion and, as a result, achieve amplification via stimulated emission of phonons. Correspondingly, the band filling effect caused by the intense probe beam weakens at Eprc and Eprv. In the kinetic curve (Fig. 5(a)) it leads to increase of absorption (negative change of transparency) promptly after the excitation pulse.

When the electron population relaxes to the Eprc level, stimulated resonant two-phonon emission is suppressed as shown in Fig. 5(e). Electronic transitions are strongly restricted due to the Pauli blocking between Eprc and Eprv levels. After this, the ΔT/T signal becomes positive, which indicates the induced transmission (bleaching). Subsequently, the decay shows similar behavior as those in Fig. 3(a). Besides, Saito et al. [35

35. R. Saito, M. Hofmann, G. Dresselhaus, A. Jorio, and M. S. Dresselhaus, “Raman spectroscopy of graphene and carbon nanotubes,” Adv. Phys. 60(3), 413–550 (2011). [CrossRef]

] have also theoretically predicted a two-phonon Raman process with a phonon frequency of 3170 cm−1 after photoexcitation, which is consistent with our observation. Stimulated phonon emission has also been observed in Ruby [58

58. W. E. Bron and W. Grill, “Stimulated phonon emission,” Phys. Rev. Lett. 40(22), 1459–1463 (1978). [CrossRef]

61

61. L. G. Tilstra, A. F. M. Arts, and H. W. de Wijn, “Optically excited ruby as a saser: experiment and theory,” Phys. Rev. B 76(2), 024302 (2007). [CrossRef]

] and few other materials [62

62. K. Vahala, M. Herrmann, S. Knünz, V. Batteiger, G. Saathoff, T. W. Hänsch, and T. Udem, “A phonon laser,” Nat. Phys. 5(9), 682–686 (2009). [CrossRef]

65

65. I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010). [CrossRef] [PubMed]

]. Recently, the possibility of population inversion in photoexcited graphene was theoretically confirmed by performing microscopic calculations [66

66. T. Winzer, E. Malic, and A. Knorr, “Microscopic mechanism for transient population inversion and optical gain in graphene,” arXiv:1209.4833v1 (Sep 21, 2012), http://arxiv.org/abs/1209.4833.

]. Population inversion in graphene under femtosecond excitation was also produced by Li et al [67

67. T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012). [CrossRef] [PubMed]

] by observing stimulated emission in NIR. Our observations of stimulated phonon emission in graphene may lead to promising applications, e.g., a stimulated phonon source, saser [61

61. L. G. Tilstra, A. F. M. Arts, and H. W. de Wijn, “Optically excited ruby as a saser: experiment and theory,” Phys. Rev. B 76(2), 024302 (2007). [CrossRef]

] or phonon laser [62

62. K. Vahala, M. Herrmann, S. Knünz, V. Batteiger, G. Saathoff, T. W. Hänsch, and T. Udem, “A phonon laser,” Nat. Phys. 5(9), 682–686 (2009). [CrossRef]

].

3. Methods

4. Conclusion

Ultrafast pump/MIR probe measurements of carrier dynamics have been studied in graphene films on CaF2. Two decay processes were observed. The fast component is ~0.2 ps, which is attributed to the mixture of initial few ultrafast decay channels including interband and/or intraband e-op scattering, plasmon scattering, Auger scattering and impact ionization. The slow component is ~1.5 ps, which is substantially assigned to op-ap scattering. Furthermore, the frequency-dependent carrier relaxation was found, where the contribution of fast component was enhanced with the increase of the frequency of the MIR probe beam. At the probe frequency of 2700 cm−1, the accelerated carrier relaxation was detected in the differential transmission kinetic curve, which resulted from the interband intervalley triple resonance e-op scattering in graphene. More interestingly, at the probe frequency of 3175cm−1, an instant negative differential transmission was observed in the decay kinetics. This signal reflects a stimulated resonant two phonon emission process involved with zone-center G phonons in graphene. Our finding indicates an important potential application of graphene as a source of coherent ultrafast sound-wave emission.

Acknowledgments

We are grateful to Professor Maria-Elisabeth Michel-Beyerle for continuous support. We thank Ms Lin Ma, Dr. Zhiqiang Luo, and Mr. Jiaxu Yan for their suggestions and useful discussions. We thank Prof. Cesare Soci and Mr. Zilong Wang for their help with the steady-state infrared absorption measurement. Yu thanks the support of the Singapore National Research Foundation under NRF Award No. NRF-RF2010-07 and MOE Tier 2 MOE2009-T2-1-037.

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D. Sun, Z.-K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008). [CrossRef] [PubMed]

22.

K.-J. Yee, J.-H. Kim, M. H. Jung, B. H. Hong, and K.-J. Kong, “Ultrafast modulation of optical transitions in monolayer and multilayer graphene,” Carbon 49(14), 4781–4785 (2011). [CrossRef]

23.

D. Sun, C. Divin, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Hot carrier cooling by acoustic phonons in epitaxial graphene by ultrafast pump-probe spectroscopy,” Phys. Status Solidi C 8(4), 1194–1197 (2011). [CrossRef]

24.

T. Limmer, A. J. Houtepen, A. Niggebaum, R. Tautz, and E. Da Como, “Influence of carrier density on the electronic cooling channels of bilayer graphene,” Appl. Phys. Lett. 99(10), 103104 (2011). [CrossRef]

25.

S. Winnerl, M. Orlita, P. Plochocka, P. Kossacki, M. Potemski, T. Winzer, E. Malic, A. Knorr, M. Sprinkle, C. Berger, W. A. de Heer, H. Schneider, and M. Helm, “Carrier relaxation in epitaxial graphene photoexcited near the Dirac point,” Phys. Rev. Lett. 107(23), 237401 (2011). [CrossRef] [PubMed]

26.

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008). [CrossRef] [PubMed]

27.

H. Choi, F. Borondics, D. A. Siegel, S. Y. Zhou, M. C. Martin, A. Lanzara, and R. A. Kaindl, “Broadband electromagnetic response and ultrafast dynamics of few-layer epitaxial graphene,” Appl. Phys. Lett. 94(17), 172102 (2009). [CrossRef]

28.

J. H. Strait, H. Wang, S. Shivaraman, V. Shields, M. Spencer, and F. Rana, “Very slow cooling dynamics of photoexcited carriers in graphene observed by optical-pump terahertz-probe spectroscopy,” Nano Lett. 11(11), 4902–4906 (2011). [CrossRef] [PubMed]

29.

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phys. 3(1), 36–40 (2007). [CrossRef]

30.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6(10), 770–775 (2007). [CrossRef] [PubMed]

31.

Y. Liu, L. Zhang, M. K. Brinkley, G. Bian, T. Miller, and T.-C. Chiang, “Phonon-induced gaps in graphene and graphite observed by angle-resolved photoemission,” Phys. Rev. Lett. 105(13), 136804 (2010). [CrossRef] [PubMed]

32.

D. A. Siegel, C.-H. Park, C. Hwang, J. Deslippe, A. V. Fedorov, S. G. Louie, and A. Lanzara, “Many-body interactions in quasi-freestanding graphene,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11365–11369 (2011). [CrossRef] [PubMed]

33.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008). [CrossRef] [PubMed]

34.

L. M. Malard, M. A. Pimenta, G. Dresselhaus, and M. S. Dresselhaus, “Raman spectroscopy in graphene,” Phys. Rep. 473(5-6), 51–87 (2009). [CrossRef]

35.

R. Saito, M. Hofmann, G. Dresselhaus, A. Jorio, and M. S. Dresselhaus, “Raman spectroscopy of graphene and carbon nanotubes,” Adv. Phys. 60(3), 413–550 (2011). [CrossRef]

36.

A. Gupta, G. Chen, P. Joshi, S. Tadigadapa, and P. C. Eklund, “Raman scattering from high-frequency phonons in supported n-graphene layer films,” Nano Lett. 6(12), 2667–2673 (2006). [CrossRef] [PubMed]

37.

Z. Ni, Y. Wang, T. Yu, and Z. Shen, “Raman spectroscopy and imaging of graphene,” Nano Res. 1(4), 273–291 (2008). [CrossRef]

38.

F. Rana, “Electron-hole generation and recombination rates for coulomb scattering in graphene,” Phys. Rev. B 76(15), 155431 (2007). [CrossRef]

39.

F. Rana, P. A. George, J. H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B 79(11), 115447 (2009). [CrossRef]

40.

K. M. Borysenko, J. T. Mullen, E. A. Barry, S. Paul, Y. G. Semenov, J. M. Zavada, M. B. Nardelli, and K. W. Kim, “First-principles analysis of electron-phonon interactions in graphene,” Phys. Rev. B 81(12), 121412 (2010). [CrossRef]

41.

T. Winzer, A. Knorr, and E. Malic, “Carrier multiplication in graphene,” Nano Lett. 10(12), 4839–4843 (2010). [CrossRef] [PubMed]

42.

F. Rana, J. H. Strait, H. Wang, and C. Manolatou, “Ultrafast carrier recombination and generation rates for plasmon emission and absorption in graphene,” Phys. Rev. B 84(4), 045437 (2011). [CrossRef]

43.

E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84(20), 205406 (2011). [CrossRef]

44.

A. L. Walter, A. Bostwick, K.-J. Jeon, F. Speck, M. Ostler, T. Seyller, L. Moreschini, Y. J. Chang, M. Polini, R. Asgari, A. H. MacDonald, K. Horn, and E. Rotenberg, “Effective screening and the plasmaron bands in graphene,” Phys. Rev. B 84(8), 085410 (2011). [CrossRef]

45.

K. Kang, D. Abdula, D. G. Cahill, and M. Shim, “Lifetimes of optical phonons in graphene and graphite by time-resolved incoherent anti-Stokes Raman scattering,” Phys. Rev. B 81(16), 165405 (2010). [CrossRef]

46.

W.-K. Tse and S. Das Sarma, “Energy relaxation of hot Dirac fermions in graphene,” Phys. Rev. B 79(23), 235406 (2009). [CrossRef]

47.

Z. Luo, T. Yu, J. Shang, Y. Wang, S. Lim, L. Liu, G. G. Gurzadyan, Z. Shen, and J. Lin, “Large-scale synthesis of bi-Layer graphene in strongly coupled stacking order,” Adv. Funct. Mater. 21(5), 911–917 (2011). [CrossRef]

48.

C. Thomsen and S. Reich, “Double resonant raman scattering in graphite,” Phys. Rev. Lett. 85(24), 5214–5217 (2000). [CrossRef] [PubMed]

49.

I. Kupčic, “Triple-resonant two-phonon Raman scattering in graphene,” J. Raman Spectrosc. 43(1), 1–5 (2012). [CrossRef]

50.

J. Kürti, V. Zolyomi, A. Gruneis, and H. Kuzmany, “Double resonant Raman phenomena enhanced by Van Hove singularities in single-wall carbon nanotubes,” Phys. Rev. B 65(16), 165433 (2002). [CrossRef]

51.

S. Wu, L. Jing, Q. Li, Q. W. Shi, J. Chen, H. Su, X. Wang, and J. Yang, “Average density of states in disordered graphene systems,” Phys. Rev. B 77(19), 195411 (2008). [CrossRef]

52.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef] [PubMed]

53.

J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J. H. Smet, K. von Klitzing, and A. Yacoby, “Observation of electron–hole puddles in graphene using a scanning single-electron transistor,” Nat. Phys. 4(2), 144–148 (2008). [CrossRef]

54.

Y. Zhang, V. W. Brar, C. Girit, A. Zettl, and M. F. Crommie, “Origin of spatial charge inhomogeneity in graphene,” Nat. Phys. 5(10), 722–726 (2009). [CrossRef]

55.

K. Ziegler, B. Dóra, and P. Thalmeier, “Density of states in disordered graphene,” Phys. Rev. B 79(23), 235431 (2009). [CrossRef]

56.

R. Xiao, F. Tasnadi, K. Koepernik, J. W. F. Venderbos, M. Richter, and M. Taut, “Density functional investigation of rhombohedral stacks of graphene: topological surface states, nonlinear dielectric response, and bulk limit,” Phys. Rev. B 84(16), 165404 (2011). [CrossRef]

57.

B. A. Ruzicka, S. Wang, J. Liu, K.-P. Loh, J. Z. Wu, and H. Zhao, “Spatially resolved pump-probe study of single-layer graphene produced by chemical vapor deposition,” Opt. Mater. Express 2(6), 708–716 (2012). [CrossRef]

58.

W. E. Bron and W. Grill, “Stimulated phonon emission,” Phys. Rev. Lett. 40(22), 1459–1463 (1978). [CrossRef]

59.

P. Hu, “Stimulated emission of 29-cm−1 phonons in ruby,” Phys. Rev. Lett. 44(6), 417–420 (1980). [CrossRef]

60.

L. G. Tilstra, A. F. M. Arts, and H. W. de Wijn, “Coherence of phonon avalanches in ruby,” Phys. Rev. B 68(14), 144302 (2003). [CrossRef]

61.

L. G. Tilstra, A. F. M. Arts, and H. W. de Wijn, “Optically excited ruby as a saser: experiment and theory,” Phys. Rev. B 76(2), 024302 (2007). [CrossRef]

62.

K. Vahala, M. Herrmann, S. Knünz, V. Batteiger, G. Saathoff, T. W. Hänsch, and T. Udem, “A phonon laser,” Nat. Phys. 5(9), 682–686 (2009). [CrossRef]

63.

P. M. Walker, A. J. Kent, M. Henini, B. A. Glavin, V. A. Kochelap, and T. L. Linnik, “Terahertz acoustic oscillations by stimulated phonon emission in an optically pumped superlattice,” Phys. Rev. B 79(24), 245313 (2009). [CrossRef]

64.

R. P. Beardsley, A. V. Akimov, M. Henini, and A. J. Kent, “Coherent terahertz sound amplification and spectral line narrowing in a stark ladder superlattice,” Phys. Rev. Lett. 104(8), 085501 (2010). [CrossRef] [PubMed]

65.

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010). [CrossRef] [PubMed]

66.

T. Winzer, E. Malic, and A. Knorr, “Microscopic mechanism for transient population inversion and optical gain in graphene,” arXiv:1209.4833v1 (Sep 21, 2012), http://arxiv.org/abs/1209.4833.

67.

T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringides, J. Schmalian, and J. Wang, “Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene,” Phys. Rev. Lett. 108(16), 167401 (2012). [CrossRef] [PubMed]

68.

S. Yan, M. T. Seidel, Z. Zhang, W. K. Leong, and H.-S. Tan, “Ultrafast vibrational relaxation dynamics of carbonyl stretching modes in Os3(CO)12.,” J. Chem. Phys. 135(2), 024501 (2011). [CrossRef] [PubMed]

69.

S. Ullrich, T. Schultz, M. Z. Zgierski, and A. Stolow, “Electronic relaxation dynamics in DNA and RNA bases studied by time-resolved photoelectron spectroscopy,” Phys. Chem. Chem. Phys. 6(10), 2796–2801 (2004). [CrossRef]

OCIS Codes
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors
(160.4236) Materials : Nanomaterials

ToC Category:
Nanomaterials

History
Original Manuscript: September 13, 2012
Revised Manuscript: October 18, 2012
Manuscript Accepted: October 21, 2012
Published: November 5, 2012

Citation
Jingzhi Shang, Suxia Yan, Chunxiao Cong, Howe-Siang Tan, Ting Yu, and Gagik G. Gurzadyan, "Probing near Dirac point electron-phonon interaction in graphene," Opt. Mater. Express 2, 1713-1722 (2012)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-2-12-1713


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References

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  28. J. H. Strait, H. Wang, S. Shivaraman, V. Shields, M. Spencer, and F. Rana, “Very slow cooling dynamics of photoexcited carriers in graphene observed by optical-pump terahertz-probe spectroscopy,” Nano Lett.11(11), 4902–4906 (2011). [CrossRef] [PubMed]
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  39. F. Rana, P. A. George, J. H. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, and M. Spencer, “Carrier recombination and generation rates for intravalley and intervalley phonon scattering in graphene,” Phys. Rev. B79(11), 115447 (2009). [CrossRef]
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  42. F. Rana, J. H. Strait, H. Wang, and C. Manolatou, “Ultrafast carrier recombination and generation rates for plasmon emission and absorption in graphene,” Phys. Rev. B84(4), 045437 (2011). [CrossRef]
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  46. W.-K. Tse and S. Das Sarma, “Energy relaxation of hot Dirac fermions in graphene,” Phys. Rev. B79(23), 235406 (2009). [CrossRef]
  47. Z. Luo, T. Yu, J. Shang, Y. Wang, S. Lim, L. Liu, G. G. Gurzadyan, Z. Shen, and J. Lin, “Large-scale synthesis of bi-Layer graphene in strongly coupled stacking order,” Adv. Funct. Mater.21(5), 911–917 (2011). [CrossRef]
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  49. I. Kupčic, “Triple-resonant two-phonon Raman scattering in graphene,” J. Raman Spectrosc.43(1), 1–5 (2012). [CrossRef]
  50. J. Kürti, V. Zolyomi, A. Gruneis, and H. Kuzmany, “Double resonant Raman phenomena enhanced by Van Hove singularities in single-wall carbon nanotubes,” Phys. Rev. B65(16), 165433 (2002). [CrossRef]
  51. S. Wu, L. Jing, Q. Li, Q. W. Shi, J. Chen, H. Su, X. Wang, and J. Yang, “Average density of states in disordered graphene systems,” Phys. Rev. B77(19), 195411 (2008). [CrossRef]
  52. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005). [CrossRef] [PubMed]
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  55. K. Ziegler, B. Dóra, and P. Thalmeier, “Density of states in disordered graphene,” Phys. Rev. B79(23), 235431 (2009). [CrossRef]
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