Abstract

The coupled modes between graphene plasmons and surface phonons of a semiconductor substrate are investigated, which can be efficiently controlled by carrier injection of the substrate. A new physical mechanism on tuning plasmon-phonon coupled modes (PPCMs) is proposed due to the fact that the energy and lifetime of substrate surface phonons depend a lot on the carrier concentration. Specifically, the change of dispersion and lifetime of PPCMs can be controlled by the carrier concentration of the substrate. The energy of PPCMs for a given momentum increases as the carrier concentration of the substrate increases. On the other hand, the momentum of PPCMs for a given energy decreases when the carrier concentration of the substrate increases. The lifetime of PPCMs is always larger than the intrinsic lifetime of graphene plasmons without plasmon-phonon coupling.

© 2015 Optical Society of America

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    [Crossref] [PubMed]

2015 (1)

Z. Li, R. Ye, R. Feng, Y. Kang, X. Zhu, J. M. Tour, and Z. Fang, “Graphene quantum dots doping of MoS2 monolayers,” Adv. Mater. 27, 5235–5240 (2015).
[Crossref] [PubMed]

2014 (4)

Y. Kang, S. Najmaei, Z. Liu, Y. Bao, Y. Wang, X. Zhu, N. J. Halas, P. Nordlander, P. M. Ajayan, and J. Lou, “Plasmonic hot electron induced structural phase transition in a MoS2 monolayer,” Adv. Mater. 26, 6467–6471 (2014).
[Crossref] [PubMed]

S. H. Zhang, W. Xu, F. M. Peeters, and S. M. Badalyan, “Electron energy and temperature relaxation in graphene on a piezoelectric substrate,” Phys. Rev. B 89, 195409 (2014).
[Crossref]

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Bøggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).
[Crossref] [PubMed]

A. Gamucci, D. Spirito, M. Carrega, B. Karmakar, A. Lombardo, M. Bruna, L. Pfeiffer, K. West, A. Ferrari, and M. Polini, “Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures,” Nat. Commun. 5, 5824 (2014).
[Crossref] [PubMed]

2013 (5)

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 2541–2547 (2013).
[Crossref] [PubMed]

J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111, 237405 (2013).
[Crossref]

E. H. Hwang and S. Das Sarma, “Surface polar optical phonon interaction induced many-body effects and hot-electron relaxation in graphene,” Phys. Rev. B 87, 115432 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

2012 (6)

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100, 153111 (2012).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[Crossref]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[Crossref] [PubMed]

M. Carrega, T. Tudorovskiy, A. Principi, M. I. Katsnelson, and M. Polini, “Theory of Coulomb drag for massless Dirac fermions,” New J. Phys. 14, 063033 (2012).
[Crossref]

2011 (5)

S. Kim, I. Jo, J. Nah, Z. Yao, S. Banerjee, and E. Tutuc, “Coulomb drag of massless fermions in graphene,” Phys. Rev. B 83, 161401 (2011).
[Crossref]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407(R) (2011).
[Crossref]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

2010 (2)

E. H. Hwang, R. Sensarma, and S. Das Sarma, “Plasmon-phonon coupling in graphene,” Phys. Rev. B 82, 195406 (2010).
[Crossref]

Y. Liu and R. F. Willis, “Plasmon-phonon strongly coupled mode in epitaxial graphene,” Phys. Rev. B 81, 081406 (2010).
[Crossref]

2009 (1)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

2008 (1)

S. Fratini and F. Guinea, “Substrate-limited electron dynamics in graphene,” Phys. Rev. B 77, 195415 (2008).
[Crossref]

2007 (1)

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[Crossref]

2006 (1)

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. 8, 318 (2006).
[Crossref]

2005 (1)

D. Lockwood, G. Yu, and N. Rowell, “Optical phonon frequencies and damping in AlAs, GaP, GaAs, InP, InAs and InSb studied by oblique incidence infrared spectroscopy,” Solid State Commun. 136, 404–409 (2005).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

1989 (1)

P. M. Solomon, P. J. Price, D. J. Frank, and D. C. La Tulipe, “New phenomena in coupled transport between 2D and 3D electron-gas layers,” Phys. Rev. Lett. 63, 2508–2511 (1989).
[Crossref] [PubMed]

1982 (1)

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53, R123–R181 (1982).
[Crossref]

1972 (1)

S. Q. Wang and G. D. Mahan, “Electron scattering from surface excitations,” Phys. Rev. B 6, 4517–4524 (1972).
[Crossref]

1966 (1)

A. Mooradian and G. B. Wright, “Observation of the interaction of plasmons with longitudinal optical phonons in GaAs,” Phys. Rev. Lett. 16, 999–1001 (1966).
[Crossref]

1965 (1)

B. B. Varga, “Coupling of plasmons to polar phonons in degenerate semiconductors,” Phys. Rev. 137, A1896–A1902 (1965).
[Crossref]

Ajayan, P. M.

Y. Kang, S. Najmaei, Z. Liu, Y. Bao, Y. Wang, X. Zhu, N. J. Halas, P. Nordlander, P. M. Ajayan, and J. Lou, “Plasmonic hot electron induced structural phase transition in a MoS2 monolayer,” Adv. Mater. 26, 6467–6471 (2014).
[Crossref] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[Crossref] [PubMed]

Alonso-Gonzalez, P.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 2541–2547 (2013).
[Crossref] [PubMed]

Avouris, P.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

Badalyan, S. M.

S. H. Zhang, W. Xu, F. M. Peeters, and S. M. Badalyan, “Electron energy and temperature relaxation in graphene on a piezoelectric substrate,” Phys. Rev. B 89, 195409 (2014).
[Crossref]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Banerjee, S.

S. Kim, I. Jo, J. Nah, Z. Yao, S. Banerjee, and E. Tutuc, “Coulomb drag of massless fermions in graphene,” Phys. Rev. B 83, 161401 (2011).
[Crossref]

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Bao, Y.

Y. Kang, S. Najmaei, Z. Liu, Y. Bao, Y. Wang, X. Zhu, N. J. Halas, P. Nordlander, P. M. Ajayan, and J. Lou, “Plasmonic hot electron induced structural phase transition in a MoS2 monolayer,” Adv. Mater. 26, 6467–6471 (2014).
[Crossref] [PubMed]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Blakemore, J. S.

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53, R123–R181 (1982).
[Crossref]

Bøggild, P.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Bøggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).
[Crossref] [PubMed]

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 2541–2547 (2013).
[Crossref] [PubMed]

Bruna, M.

A. Gamucci, D. Spirito, M. Carrega, B. Karmakar, A. Lombardo, M. Bruna, L. Pfeiffer, K. West, A. Ferrari, and M. Polini, “Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures,” Nat. Commun. 5, 5824 (2014).
[Crossref] [PubMed]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

Cai, W.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100, 153111 (2012).
[Crossref]

Calle, F.

J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111, 237405 (2013).
[Crossref]

Camara, N.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Carrega, M.

A. Gamucci, D. Spirito, M. Carrega, B. Karmakar, A. Lombardo, M. Bruna, L. Pfeiffer, K. West, A. Ferrari, and M. Polini, “Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures,” Nat. Commun. 5, 5824 (2014).
[Crossref] [PubMed]

M. Carrega, T. Tudorovskiy, A. Principi, M. I. Katsnelson, and M. Polini, “Theory of Coulomb drag for massless Dirac fermions,” New J. Phys. 14, 063033 (2012).
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Castro-Neto, A. H.

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Centeno, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

Chen, J.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Das Sarma, S.

E. H. Hwang and S. Das Sarma, “Surface polar optical phonon interaction induced many-body effects and hot-electron relaxation in graphene,” Phys. Rev. B 87, 115432 (2013).
[Crossref]

E. H. Hwang, R. Sensarma, and S. Das Sarma, “Plasmon-phonon coupling in graphene,” Phys. Rev. B 82, 195406 (2010).
[Crossref]

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[Crossref]

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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Z. Li, R. Ye, R. Feng, Y. Kang, X. Zhu, J. M. Tour, and Z. Fang, “Graphene quantum dots doping of MoS2 monolayers,” Adv. Mater. 27, 5235–5240 (2015).
[Crossref] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[Crossref] [PubMed]

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Feng, R.

Z. Li, R. Ye, R. Feng, Y. Kang, X. Zhu, J. M. Tour, and Z. Fang, “Graphene quantum dots doping of MoS2 monolayers,” Adv. Mater. 27, 5235–5240 (2015).
[Crossref] [PubMed]

Ferrari, A.

A. Gamucci, D. Spirito, M. Carrega, B. Karmakar, A. Lombardo, M. Bruna, L. Pfeiffer, K. West, A. Ferrari, and M. Polini, “Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures,” Nat. Commun. 5, 5824 (2014).
[Crossref] [PubMed]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Frank, D. J.

P. M. Solomon, P. J. Price, D. J. Frank, and D. C. La Tulipe, “New phenomena in coupled transport between 2D and 3D electron-gas layers,” Phys. Rev. Lett. 63, 2508–2511 (1989).
[Crossref] [PubMed]

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S. Fratini and F. Guinea, “Substrate-limited electron dynamics in graphene,” Phys. Rev. B 77, 195415 (2008).
[Crossref]

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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

Gamucci, A.

A. Gamucci, D. Spirito, M. Carrega, B. Karmakar, A. Lombardo, M. Bruna, L. Pfeiffer, K. West, A. Ferrari, and M. Polini, “Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures,” Nat. Commun. 5, 5824 (2014).
[Crossref] [PubMed]

García de Abajo, F. J.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

García-Vidal, F. J.

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407(R) (2011).
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Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Godignon, P.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Grigorenko, A.

A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Guinea, F.

J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111, 237405 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

A. Y. Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407(R) (2011).
[Crossref]

S. Fratini and F. Guinea, “Substrate-limited electron dynamics in graphene,” Phys. Rev. B 77, 195415 (2008).
[Crossref]

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. 8, 318 (2006).
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Y. Kang, S. Najmaei, Z. Liu, Y. Bao, Y. Wang, X. Zhu, N. J. Halas, P. Nordlander, P. M. Ajayan, and J. Lou, “Plasmonic hot electron induced structural phase transition in a MoS2 monolayer,” Adv. Mater. 26, 6467–6471 (2014).
[Crossref] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[Crossref] [PubMed]

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Hillenbrand, R.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Horng, J.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Huth, F.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Hwang, E. H.

E. H. Hwang and S. Das Sarma, “Surface polar optical phonon interaction induced many-body effects and hot-electron relaxation in graphene,” Phys. Rev. B 87, 115432 (2013).
[Crossref]

E. H. Hwang, R. Sensarma, and S. Das Sarma, “Plasmon-phonon coupling in graphene,” Phys. Rev. B 82, 195406 (2010).
[Crossref]

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[Crossref]

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M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
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Jang, M. S.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 2541–2547 (2013).
[Crossref] [PubMed]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

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S. Kim, I. Jo, J. Nah, Z. Yao, S. Banerjee, and E. Tutuc, “Coulomb drag of massless fermions in graphene,” Phys. Rev. B 83, 161401 (2011).
[Crossref]

Ju, L.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Kang, Y.

Z. Li, R. Ye, R. Feng, Y. Kang, X. Zhu, J. M. Tour, and Z. Fang, “Graphene quantum dots doping of MoS2 monolayers,” Adv. Mater. 27, 5235–5240 (2015).
[Crossref] [PubMed]

Y. Kang, S. Najmaei, Z. Liu, Y. Bao, Y. Wang, X. Zhu, N. J. Halas, P. Nordlander, P. M. Ajayan, and J. Lou, “Plasmonic hot electron induced structural phase transition in a MoS2 monolayer,” Adv. Mater. 26, 6467–6471 (2014).
[Crossref] [PubMed]

Karmakar, B.

A. Gamucci, D. Spirito, M. Carrega, B. Karmakar, A. Lombardo, M. Bruna, L. Pfeiffer, K. West, A. Ferrari, and M. Polini, “Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures,” Nat. Commun. 5, 5824 (2014).
[Crossref] [PubMed]

Katsnelson, M. I.

M. Carrega, T. Tudorovskiy, A. Principi, M. I. Katsnelson, and M. Polini, “Theory of Coulomb drag for massless Dirac fermions,” New J. Phys. 14, 063033 (2012).
[Crossref]

Keilmann, F.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Kim, S.

S. Kim, I. Jo, J. Nah, Z. Yao, S. Banerjee, and E. Tutuc, “Coulomb drag of massless fermions in graphene,” Phys. Rev. B 83, 161401 (2011).
[Crossref]

Koppens, F. H.

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[Crossref] [PubMed]

Koppens, F. H. L.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

La Tulipe, D. C.

P. M. Solomon, P. J. Price, D. J. Frank, and D. C. La Tulipe, “New phenomena in coupled transport between 2D and 3D electron-gas layers,” Phys. Rev. Lett. 63, 2508–2511 (1989).
[Crossref] [PubMed]

Larsen, M. B.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Bøggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Li, X.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

Li, Z.

Z. Li, R. Ye, R. Feng, Y. Kang, X. Zhu, J. M. Tour, and Z. Fang, “Graphene quantum dots doping of MoS2 monolayers,” Adv. Mater. 27, 5235–5240 (2015).
[Crossref] [PubMed]

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100, 153111 (2012).
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Y. Liu and R. F. Willis, “Plasmon-phonon strongly coupled mode in epitaxial graphene,” Phys. Rev. B 81, 081406 (2010).
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Y. Kang, S. Najmaei, Z. Liu, Y. Bao, Y. Wang, X. Zhu, N. J. Halas, P. Nordlander, P. M. Ajayan, and J. Lou, “Plasmonic hot electron induced structural phase transition in a MoS2 monolayer,” Adv. Mater. 26, 6467–6471 (2014).
[Crossref] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
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Lombardo, A.

A. Gamucci, D. Spirito, M. Carrega, B. Karmakar, A. Lombardo, M. Bruna, L. Pfeiffer, K. West, A. Ferrari, and M. Polini, “Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures,” Nat. Commun. 5, 5824 (2014).
[Crossref] [PubMed]

Lopez, J. J.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 2541–2547 (2013).
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J. Schiefele, J. Pedrós, F. Sols, F. Calle, and F. Guinea, “Coupling light into graphene plasmons through surface acoustic waves,” Phys. Rev. Lett. 111, 237405 (2013).
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Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
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Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
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Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
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Z. Li, R. Ye, R. Feng, Y. Kang, X. Zhu, J. M. Tour, and Z. Fang, “Graphene quantum dots doping of MoS2 monolayers,” Adv. Mater. 27, 5235–5240 (2015).
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M. Carrega, T. Tudorovskiy, A. Principi, M. I. Katsnelson, and M. Polini, “Theory of Coulomb drag for massless Dirac fermions,” New J. Phys. 14, 063033 (2012).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
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P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100, 153111 (2012).
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X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Bøggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).
[Crossref] [PubMed]

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Y. Kang, S. Najmaei, Z. Liu, Y. Bao, Y. Wang, X. Zhu, N. J. Halas, P. Nordlander, P. M. Ajayan, and J. Lou, “Plasmonic hot electron induced structural phase transition in a MoS2 monolayer,” Adv. Mater. 26, 6467–6471 (2014).
[Crossref] [PubMed]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[Crossref] [PubMed]

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A. Gamucci, D. Spirito, M. Carrega, B. Karmakar, A. Lombardo, M. Bruna, L. Pfeiffer, K. West, A. Ferrari, and M. Polini, “Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures,” Nat. Commun. 5, 5824 (2014).
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A. Mooradian and G. B. Wright, “Observation of the interaction of plasmons with longitudinal optical phonons in GaAs,” Phys. Rev. Lett. 16, 999–1001 (1966).
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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

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B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. 8, 318 (2006).
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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
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X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Bøggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).
[Crossref] [PubMed]

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P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100, 153111 (2012).
[Crossref]

Xu, W.

S. H. Zhang, W. Xu, F. M. Peeters, and S. M. Badalyan, “Electron energy and temperature relaxation in graphene on a piezoelectric substrate,” Phys. Rev. B 89, 195409 (2014).
[Crossref]

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H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

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X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Bøggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).
[Crossref] [PubMed]

Yao, Z.

S. Kim, I. Jo, J. Nah, Z. Yao, S. Banerjee, and E. Tutuc, “Coulomb drag of massless fermions in graphene,” Phys. Rev. B 83, 161401 (2011).
[Crossref]

Ye, R.

Z. Li, R. Ye, R. Feng, Y. Kang, X. Zhu, J. M. Tour, and Z. Fang, “Graphene quantum dots doping of MoS2 monolayers,” Adv. Mater. 27, 5235–5240 (2015).
[Crossref] [PubMed]

Yu, G.

D. Lockwood, G. Yu, and N. Rowell, “Optical phonon frequencies and damping in AlAs, GaP, GaAs, InP, InAs and InSb studied by oblique incidence infrared spectroscopy,” Solid State Commun. 136, 404–409 (2005).
[Crossref]

Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref] [PubMed]

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. C. Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11, 4701–4705 (2011).
[Crossref] [PubMed]

Zhang, S. H.

S. H. Zhang, W. Xu, F. M. Peeters, and S. M. Badalyan, “Electron energy and temperature relaxation in graphene on a piezoelectric substrate,” Phys. Rev. B 89, 195409 (2014).
[Crossref]

Zhang, X.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100, 153111 (2012).
[Crossref]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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Figures (6)

Fig. 1
Fig. 1 The sketch of graphene placed on doped GaAs. The carrier concentration of GaAs can be tuned by field effect or photon excitation. The dots in substrate indicate the free electrons injected into GaAs.
Fig. 2
Fig. 2 (a) The dispersion of plasmon-phonon coupled modes (PPCMs) for graphene laid on GaAs substrate with various carrier concentrations. The labelled modes A and B describe the coupled higher and lower energy branches, respectively. The black arrows mean the increasing of the carrier concentration in GaAs. The carrier concentrations are 0, 2 × 1016, 1 × 1017, 2 × 1017, 5 × 1017, 1 × 1018, 2 × 1018 and 5 × 1018 cm−3, respectively. The shadow triangle area indicates the Landau intraband loss. The parameters of graphene are assumed to be EF = 0.2 eV, and relaxation time τe = 0.2 ps (correspond to a DC mobility of 10000 cm2/Vs) in the whole paper. (b) Plasmon lifetime of the two branches A and B with different carrier concentrations. The free electron scattering of substrate is not included in the calculation.
Fig. 3
Fig. 3 (a) The energy and lifetime of surface phonons in doping GaAs, The thick (thin) line indicates the high (low) energy branch, and the dashed lines indicate their lifetime. (b) The surface phonon strength of these branches in Fig. 3(a).
Fig. 4
Fig. 4 The plasmon lifetime of the coupled plasmon-phonon modes with the free electron scattering of the substrate GaAs. It is notable that the curve n = 0 is the same as it in Fig. 2(b).
Fig. 5
Fig. 5 (a) Carrier concentration dependent plasmon momentum and lifetime for given photon energies. The thick line (ħω = 0.06 eV) is chosen from branch A, and the thin line (ħω = 0.03 eV) from branch B. The dashed lines show the corresponding lifetime of the branches. (b) Concentration dependent energy for a given momentum 5 μm−1, the thick and thin lines indicate the branch A and B, respectively.
Fig. 6
Fig. 6 Carrier concentration dependent surface phonon energy in different semiconductors, GaAs, AlAs, InAs, GaP and InP.

Equations (6)

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q = ε eff ω pl 2 2 α c E F ,
ε ( ω ) = ε + ( ε 0 ε ) ω TO 2 ω TO 2 ω 2 i ω Γ ε ω p 2 ω 2 + i ω δ p ,
ε / ε k 0 2 q 2 + 1 / k 0 2 q 2 = 4 π σ ( ω ) / ω ,
V eff = v c / ε rpa v c ε + M ( k ) 2 ε 2 D ( q , ω ) 1 1 v c ( v c ε + M ( k ) 2 ε 2 D ( q , ω ) ) v c ( q ) Π s 0 ( q , ω )
ε rpa ε eff = 1 ω pl 2 ( q ) ( ω + i δ e ) 2 2 ε eff g 2 ω so 2 ( ω + i δ so ) 2 ( 1 2 ε eff g 2 ) ω so 2 ε 1 + ε ω p 2 ( ω + i δ p ) 2
S m = ε / ε 0 ( ε / ε 0 1 ) x m 3 ( ε / ε 0 ) x m 4 + y 2 ( 1 x m 2 ) 2 ,

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