Abstract

A self-consistent theory involving Maxwell’s equations and a density-matrix linear-response theory is solved for an electromagnetically coupled doped graphene micro-ribbon array (GMRA) and a quantum well (QW) electron gas sitting at an interface between a half-space of air and another half-space of a doped semiconductor substrate, which supports a surface-plasmon mode in our system. The coupling between a spatially modulated total electromagnetic (EM) field and the electron dynamics in a Dirac-cone of a graphene ribbon, as well as the coupling of the far-field specular and near-field higher-order diffraction modes, are included in the derived electron optical-response function. Full analytical expressions are obtained with nonlocality for the optical-response functions of a two-dimensional electron gas and a graphene layer with an induced bandgap, and are employed in our numerical calculations beyond the long-wavelength limit (Drude model). Both the near-field transmissivity and reflectivity spectra, as well as their dependence on different configurations of our system and on the array period, ribbon width, graphene chemical potential of QW electron gas and bandgap in graphene, are studied. Moreover, the transmitted E-field intensity distribution is calculated to demonstrate its connection to the mixing of specular and diffraction modes of the total EM field. An externally tunable EM coupling among the surface, conventional electron-gas and massless graphene intraband plasmon excitations is discovered and explained. Furthermore, a comparison is made between the dependence of the graphene-plasmon energy on the ribbon’s width and chemical potential in this paper and the recent experimental observation given by [Nat. Nanotechnol. 6, 630 – 634 (2011)] for a GMRA in the terahertz-frequency range.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012

A. Iurov, G. Gumbs, O. Roslyak, and D. H. Huang, “Anomalous photon-assisted tunneling in graphene,” J. Phys. Condens. Matter 24, 015303 (2012).
[CrossRef]

O. Roslyak, G. Gumbs, and D. H. Huang, “Energy loss spectroscopy of epitaxial versus free-standing multilayer graphene,” Phys. E 44, 1874–1884 (2012).
[CrossRef]

M. A. H. Vozmediano and F. Guinea, “Effect of Coulomb interactions on the physical observables of graphene,” Phys. Scr. T146, 014015 (2012).
[CrossRef]

2011

D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, “Dirac cones reshaped by interaction effects in suspended graphene,” Nat. Phys. 7, 701–704 (2011).
[CrossRef]

D. H. Huang, G. Gumbs, and O. Roslyak, “Field enhanced mobility by nonlinear phonon scattering of Dirac electrons in semiconducting graphene nanoribbons,” Phys. Rev. B 83, 115405 (2011).
[CrossRef]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[CrossRef]

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, 4902–4906 (2011).
[CrossRef]

J. C. W. Song, M. S. Rudner, C. M. Marcus, and L. S. Levitov, “Hot carrier transport and photocurrent response in graphene,” Nano Lett. 11, 4688–4692 (2011).
[CrossRef]

O. Roslyak, G. Gumbs, and D. H. Huang, “Plasma excitations of dressed Dirac electrons in graphene layers,” J. Appl. Phys. 109, 113721 (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]

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

2010

D. S. L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler, and T. Chakraborty, “Properties of graphene: a theoretical perspective,” Adv. Phys. 59, 261–482 (2010).
[CrossRef]

M. Orlita and M. Potemski, “Dirac electronic states in graphene systems: optical spectroscopy studies,” Semicond. Sci. Technol. 25, 063001 (2010).
[CrossRef]

O. Roslyak, A. Iurov, G. Gumbs, and D. H. Huang, “Unimpeded tunneling in graphene nanoribbons,” J. Phys. Condens. Matter 22, 165301 (2010).
[CrossRef]

O. Roslyak, G. Gumbs, and D. H. Huang, “Tunable band structure effects on ballistic transport in graphene nanoribbons,” Phys. Lett. A 374, 4061–4064 (2010).
[CrossRef]

J. Z. Bernád, M. Jääskeläinen, and U. Zülicke, “Effects of a quantum measurement on the electric conductivity: application to graphene,” Phys. Rev. B 81, 073403 (2010).
[CrossRef]

A. Bostwick, F. Speck, T. Seyller, K. Horn, M. Polini, R. Asgari, A. H. MacDonald, and E. Rotenberg, “Observation of plasmarons in quasi-freestanding doped graphene,” Science 328, 999–1002 (2010).
[CrossRef]

2009

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

D. H. Huang, G. Gumbs, and S. Y. Lin, “Self-consistent theory for near-field distribution and spectrum with quantum wires and a conductive grating in terahertz regime,” J. Appl. Phys. 105, 093715 (2009).
[CrossRef]

A. F. Young and P. Kim, “Quantum interference and Klein tunnelling in graphene,” Nat. Phys. 5, 222–226 (2009).
[CrossRef]

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

2008

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Störmer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
[CrossRef]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[CrossRef]

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, 1308 (2008).
[CrossRef]

T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78, 205403 (2008).
[CrossRef]

D. H. Huang, G. Gumbs, P. M. Alsing, and D. A. Cardimona, “Nonlocal mode mixing and surface-plasmon-polariton-mediated enhancement of diffracted terahertz fields by a conductive grating,” Phys. Rev. B 77, 165404 (2008).
[CrossRef]

B. Y. K. Hu, E. H. Hwang, and S. Das Sarma, “Density of states of disordered graphene,” Phys. Rev. B 78, 165411 (2008).
[CrossRef]

K. S. Gupta and S. Sen, “Bound states in gapped graphene with impurities: effective low-energy description of short-range interactions,” Phys. Rev. B 78, 205429 (2008).
[CrossRef]

2007

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

L. Brey and H. A. Fertig, “Elementary electronic excitations in graphene nanoribbons,” Phys. Rev. B 75, 125434 (2007).
[CrossRef]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[CrossRef]

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

2006

K. Nomura and A. H. MacDonald, “Quantum Hall ferromagnetism in graphene,” Phys. Rev. Lett. 96, 256602 (2006).
[CrossRef]

D. H. Huang, C. Rhodes, P. M. Alsing, and D. A. Cardimona, “Effects of longitudinal field on transmitted near field in doped semi-infinite semiconductors with a surface conducting sheet,” J. Appl. Phys. 100, 113711 (2006).
[CrossRef]

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

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620–625 (2006).
[CrossRef]

B. Baumeier, T. A. Leskova, and A. A. Maradudin, “Transmission of light through a thin metal film with periodically and randomly corrugated surfaces,” J. Opt. A 8, S191–S207 (2006).
[CrossRef]

2005

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Effect of photon-assisted absorption on the thermodynamics of hot electrons interacting with an intense optical field in bulk GaAs,” Phys. Rev. B 71, 045204 (2005).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Coupled energy-drift and force-balance equations for high-field hot-carrier transport,” Phys. Rev. B 71, 195205 (2005).
[CrossRef]

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, 197–200 (2005).
[CrossRef]

Y. Zhang, Y. W. Tan, H. L. Störmer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438, 201–204 (2005).
[CrossRef]

2004

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

D. H. Huang, T. Apostolova, P. M. Alsing, and D. A. Cardimona, “High-field transport of electrons and radiative effects using coupled force-balance and Fokker–Planck equations beyond relaxation-time approximation,” Phys. Rev. B 69, 075214 (2004).
[CrossRef]

2001

D. H. Huang and D. A. Cardimona, “Effects of off-diagonal radiative-decay coupling of electron transitions in resonant double quantum wells,” Phys. Rev. A 64, 013822 (2001).
[CrossRef]

1996

G. Gumbs, D. H. Huang, and D. N. Talwar, “Doublet structure in the absorption coefficient for tunneling-split intersubband transitions in double quantum wells,” Phys. Rev. B 53, 15436–15439 (1996).
[CrossRef]

1967

F. Stern, “Polarizability of a two-dimensional electron gas,” Phys. Rev. Lett 18, 546–548 (1967).
[CrossRef]

Abergel, D. S. L.

D. S. L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler, and T. Chakraborty, “Properties of graphene: a theoretical perspective,” Adv. Phys. 59, 261–482 (2010).
[CrossRef]

Adam, S.

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

Alsing, P. M.

D. H. Huang, G. Gumbs, P. M. Alsing, and D. A. Cardimona, “Nonlocal mode mixing and surface-plasmon-polariton-mediated enhancement of diffracted terahertz fields by a conductive grating,” Phys. Rev. B 77, 165404 (2008).
[CrossRef]

D. H. Huang, C. Rhodes, P. M. Alsing, and D. A. Cardimona, “Effects of longitudinal field on transmitted near field in doped semi-infinite semiconductors with a surface conducting sheet,” J. Appl. Phys. 100, 113711 (2006).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Effect of photon-assisted absorption on the thermodynamics of hot electrons interacting with an intense optical field in bulk GaAs,” Phys. Rev. B 71, 045204 (2005).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Coupled energy-drift and force-balance equations for high-field hot-carrier transport,” Phys. Rev. B 71, 195205 (2005).
[CrossRef]

D. H. Huang, T. Apostolova, P. M. Alsing, and D. A. Cardimona, “High-field transport of electrons and radiative effects using coupled force-balance and Fokker–Planck equations beyond relaxation-time approximation,” Phys. Rev. B 69, 075214 (2004).
[CrossRef]

Apalkov, V.

D. S. L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler, and T. Chakraborty, “Properties of graphene: a theoretical perspective,” Adv. Phys. 59, 261–482 (2010).
[CrossRef]

Apostolova, T.

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Coupled energy-drift and force-balance equations for high-field hot-carrier transport,” Phys. Rev. B 71, 195205 (2005).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Effect of photon-assisted absorption on the thermodynamics of hot electrons interacting with an intense optical field in bulk GaAs,” Phys. Rev. B 71, 045204 (2005).
[CrossRef]

D. H. Huang, T. Apostolova, P. M. Alsing, and D. A. Cardimona, “High-field transport of electrons and radiative effects using coupled force-balance and Fokker–Planck equations beyond relaxation-time approximation,” Phys. Rev. B 69, 075214 (2004).
[CrossRef]

Asgari, R.

A. Bostwick, F. Speck, T. Seyller, K. Horn, M. Polini, R. Asgari, A. H. MacDonald, and E. Rotenberg, “Observation of plasmarons in quasi-freestanding doped graphene,” Science 328, 999–1002 (2010).
[CrossRef]

Bao, Q.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[CrossRef]

Basov, D. N.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Störmer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Baumeier, B.

B. Baumeier, T. A. Leskova, and A. A. Maradudin, “Transmission of light through a thin metal film with periodically and randomly corrugated surfaces,” J. Opt. A 8, S191–S207 (2006).
[CrossRef]

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]

Berashevich, J.

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J. Z. Bernád, M. Jääskeläinen, and U. Zülicke, “Effects of a quantum measurement on the electric conductivity: application to graphene,” Phys. Rev. B 81, 073403 (2010).
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D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, “Dirac cones reshaped by interaction effects in suspended graphene,” Nat. Phys. 7, 701–704 (2011).
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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, 1308 (2008).
[CrossRef]

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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, 1308 (2008).
[CrossRef]

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A. Bostwick, F. Speck, T. Seyller, K. Horn, M. Polini, R. Asgari, A. H. MacDonald, and E. Rotenberg, “Observation of plasmarons in quasi-freestanding doped graphene,” Science 328, 999–1002 (2010).
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L. Brey and H. A. Fertig, “Elementary electronic excitations in graphene nanoribbons,” Phys. Rev. B 75, 125434 (2007).
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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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D. H. Huang, G. Gumbs, P. M. Alsing, and D. A. Cardimona, “Nonlocal mode mixing and surface-plasmon-polariton-mediated enhancement of diffracted terahertz fields by a conductive grating,” Phys. Rev. B 77, 165404 (2008).
[CrossRef]

D. H. Huang, C. Rhodes, P. M. Alsing, and D. A. Cardimona, “Effects of longitudinal field on transmitted near field in doped semi-infinite semiconductors with a surface conducting sheet,” J. Appl. Phys. 100, 113711 (2006).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Effect of photon-assisted absorption on the thermodynamics of hot electrons interacting with an intense optical field in bulk GaAs,” Phys. Rev. B 71, 045204 (2005).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Coupled energy-drift and force-balance equations for high-field hot-carrier transport,” Phys. Rev. B 71, 195205 (2005).
[CrossRef]

D. H. Huang, T. Apostolova, P. M. Alsing, and D. A. Cardimona, “High-field transport of electrons and radiative effects using coupled force-balance and Fokker–Planck equations beyond relaxation-time approximation,” Phys. Rev. B 69, 075214 (2004).
[CrossRef]

D. H. Huang and D. A. Cardimona, “Effects of off-diagonal radiative-decay coupling of electron transitions in resonant double quantum wells,” Phys. Rev. A 64, 013822 (2001).
[CrossRef]

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D. S. L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler, and T. Chakraborty, “Properties of graphene: a theoretical perspective,” Adv. Phys. 59, 261–482 (2010).
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J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
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F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
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S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, “Electronic transport in two-dimensional graphene,” Rev. Mod. Phys. 83, 407–470 (2011).
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B. Y. K. Hu, E. H. Hwang, and S. Das Sarma, “Density of states of disordered graphene,” Phys. Rev. B 78, 165411 (2008).
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E. H. Wang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
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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, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
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D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, “Dirac cones reshaped by interaction effects in suspended graphene,” Nat. Phys. 7, 701–704 (2011).
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T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78, 205403 (2008).
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L. Brey and H. A. Fertig, “Elementary electronic excitations in graphene nanoribbons,” Phys. Rev. B 75, 125434 (2007).
[CrossRef]

Firsov, A. A.

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, 197–200 (2005).
[CrossRef]

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

Geim, A. K.

D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, “Dirac cones reshaped by interaction effects in suspended graphene,” Nat. Phys. 7, 701–704 (2011).
[CrossRef]

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

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, 1308 (2008).
[CrossRef]

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620–625 (2006).
[CrossRef]

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, 197–200 (2005).
[CrossRef]

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

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]

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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).
[CrossRef]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
[CrossRef]

Gorbachev, R. V.

D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, “Dirac cones reshaped by interaction effects in suspended graphene,” Nat. Phys. 7, 701–704 (2011).
[CrossRef]

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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, 1308 (2008).
[CrossRef]

Grigorieva, I. V.

D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, “Dirac cones reshaped by interaction effects in suspended graphene,” Nat. Phys. 7, 701–704 (2011).
[CrossRef]

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, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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M. A. H. Vozmediano and F. Guinea, “Effect of Coulomb interactions on the physical observables of graphene,” Phys. Scr. T146, 014015 (2012).
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D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, “Dirac cones reshaped by interaction effects in suspended graphene,” Nat. Phys. 7, 701–704 (2011).
[CrossRef]

A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
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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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A. Iurov, G. Gumbs, O. Roslyak, and D. H. Huang, “Anomalous photon-assisted tunneling in graphene,” J. Phys. Condens. Matter 24, 015303 (2012).
[CrossRef]

O. Roslyak, G. Gumbs, and D. H. Huang, “Energy loss spectroscopy of epitaxial versus free-standing multilayer graphene,” Phys. E 44, 1874–1884 (2012).
[CrossRef]

D. H. Huang, G. Gumbs, and O. Roslyak, “Field enhanced mobility by nonlinear phonon scattering of Dirac electrons in semiconducting graphene nanoribbons,” Phys. Rev. B 83, 115405 (2011).
[CrossRef]

O. Roslyak, G. Gumbs, and D. H. Huang, “Plasma excitations of dressed Dirac electrons in graphene layers,” J. Appl. Phys. 109, 113721 (2011).
[CrossRef]

O. Roslyak, A. Iurov, G. Gumbs, and D. H. Huang, “Unimpeded tunneling in graphene nanoribbons,” J. Phys. Condens. Matter 22, 165301 (2010).
[CrossRef]

O. Roslyak, G. Gumbs, and D. H. Huang, “Tunable band structure effects on ballistic transport in graphene nanoribbons,” Phys. Lett. A 374, 4061–4064 (2010).
[CrossRef]

D. H. Huang, G. Gumbs, and S. Y. Lin, “Self-consistent theory for near-field distribution and spectrum with quantum wires and a conductive grating in terahertz regime,” J. Appl. Phys. 105, 093715 (2009).
[CrossRef]

D. H. Huang, G. Gumbs, P. M. Alsing, and D. A. Cardimona, “Nonlocal mode mixing and surface-plasmon-polariton-mediated enhancement of diffracted terahertz fields by a conductive grating,” Phys. Rev. B 77, 165404 (2008).
[CrossRef]

G. Gumbs, D. H. Huang, and D. N. Talwar, “Doublet structure in the absorption coefficient for tunneling-split intersubband transitions in double quantum wells,” Phys. Rev. B 53, 15436–15439 (1996).
[CrossRef]

G. Gumbs and D. H. Huang, Properties of Interacting Low-Dimensional Systems (Wiley, 2011), Chaps. 4 and 5.

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K. S. Gupta and S. Sen, “Bound states in gapped graphene with impurities: effective low-energy description of short-range interactions,” Phys. Rev. B 78, 205429 (2008).
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Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[CrossRef]

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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).
[CrossRef]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Störmer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

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K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[CrossRef]

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Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Störmer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

Horn, K.

A. Bostwick, F. Speck, T. Seyller, K. Horn, M. Polini, R. Asgari, A. H. MacDonald, and E. Rotenberg, “Observation of plasmarons in quasi-freestanding doped graphene,” Science 328, 999–1002 (2010).
[CrossRef]

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]

Hu, B. Y. K.

B. Y. K. Hu, E. H. Hwang, and S. Das Sarma, “Density of states of disordered graphene,” Phys. Rev. B 78, 165411 (2008).
[CrossRef]

Huang, D. H.

O. Roslyak, G. Gumbs, and D. H. Huang, “Energy loss spectroscopy of epitaxial versus free-standing multilayer graphene,” Phys. E 44, 1874–1884 (2012).
[CrossRef]

A. Iurov, G. Gumbs, O. Roslyak, and D. H. Huang, “Anomalous photon-assisted tunneling in graphene,” J. Phys. Condens. Matter 24, 015303 (2012).
[CrossRef]

O. Roslyak, G. Gumbs, and D. H. Huang, “Plasma excitations of dressed Dirac electrons in graphene layers,” J. Appl. Phys. 109, 113721 (2011).
[CrossRef]

D. H. Huang, G. Gumbs, and O. Roslyak, “Field enhanced mobility by nonlinear phonon scattering of Dirac electrons in semiconducting graphene nanoribbons,” Phys. Rev. B 83, 115405 (2011).
[CrossRef]

O. Roslyak, G. Gumbs, and D. H. Huang, “Tunable band structure effects on ballistic transport in graphene nanoribbons,” Phys. Lett. A 374, 4061–4064 (2010).
[CrossRef]

O. Roslyak, A. Iurov, G. Gumbs, and D. H. Huang, “Unimpeded tunneling in graphene nanoribbons,” J. Phys. Condens. Matter 22, 165301 (2010).
[CrossRef]

D. H. Huang, G. Gumbs, and S. Y. Lin, “Self-consistent theory for near-field distribution and spectrum with quantum wires and a conductive grating in terahertz regime,” J. Appl. Phys. 105, 093715 (2009).
[CrossRef]

D. H. Huang, G. Gumbs, P. M. Alsing, and D. A. Cardimona, “Nonlocal mode mixing and surface-plasmon-polariton-mediated enhancement of diffracted terahertz fields by a conductive grating,” Phys. Rev. B 77, 165404 (2008).
[CrossRef]

D. H. Huang, C. Rhodes, P. M. Alsing, and D. A. Cardimona, “Effects of longitudinal field on transmitted near field in doped semi-infinite semiconductors with a surface conducting sheet,” J. Appl. Phys. 100, 113711 (2006).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Coupled energy-drift and force-balance equations for high-field hot-carrier transport,” Phys. Rev. B 71, 195205 (2005).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Effect of photon-assisted absorption on the thermodynamics of hot electrons interacting with an intense optical field in bulk GaAs,” Phys. Rev. B 71, 045204 (2005).
[CrossRef]

D. H. Huang, T. Apostolova, P. M. Alsing, and D. A. Cardimona, “High-field transport of electrons and radiative effects using coupled force-balance and Fokker–Planck equations beyond relaxation-time approximation,” Phys. Rev. B 69, 075214 (2004).
[CrossRef]

D. H. Huang and D. A. Cardimona, “Effects of off-diagonal radiative-decay coupling of electron transitions in resonant double quantum wells,” Phys. Rev. A 64, 013822 (2001).
[CrossRef]

G. Gumbs, D. H. Huang, and D. N. Talwar, “Doublet structure in the absorption coefficient for tunneling-split intersubband transitions in double quantum wells,” Phys. Rev. B 53, 15436–15439 (1996).
[CrossRef]

G. Gumbs and D. H. Huang, Properties of Interacting Low-Dimensional Systems (Wiley, 2011), Chaps. 4 and 5.

Hwang, E. H.

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

B. Y. K. Hu, E. H. Hwang, and S. Das Sarma, “Density of states of disordered graphene,” Phys. Rev. B 78, 165411 (2008).
[CrossRef]

Iurov, A.

A. Iurov, G. Gumbs, O. Roslyak, and D. H. Huang, “Anomalous photon-assisted tunneling in graphene,” J. Phys. Condens. Matter 24, 015303 (2012).
[CrossRef]

O. Roslyak, A. Iurov, G. Gumbs, and D. H. Huang, “Unimpeded tunneling in graphene nanoribbons,” J. Phys. Condens. Matter 22, 165301 (2010).
[CrossRef]

Jääskeläinen, M.

J. Z. Bernád, M. Jääskeläinen, and U. Zülicke, “Effects of a quantum measurement on the electric conductivity: application to graphene,” Phys. Rev. B 81, 073403 (2010).
[CrossRef]

Jablan, M.

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

Jena, D.

T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78, 205403 (2008).
[CrossRef]

Jiang, D.

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, 197–200 (2005).
[CrossRef]

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

Jiang, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Störmer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[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]

Katsnelson, M. I.

M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys. 2, 620–625 (2006).
[CrossRef]

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, 197–200 (2005).
[CrossRef]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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A. F. Young and P. Kim, “Quantum interference and Klein tunnelling in graphene,” Nat. Phys. 5, 222–226 (2009).
[CrossRef]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Störmer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
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Y. Zhang, Y. W. Tan, H. L. Störmer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438, 201–204 (2005).
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T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78, 205403 (2008).
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B. Baumeier, T. A. Leskova, and A. A. Maradudin, “Transmission of light through a thin metal film with periodically and randomly corrugated surfaces,” J. Opt. A 8, S191–S207 (2006).
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J. C. W. Song, M. S. Rudner, C. M. Marcus, and L. S. Levitov, “Hot carrier transport and photocurrent response in graphene,” Nano Lett. 11, 4688–4692 (2011).
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Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Störmer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4, 532–535 (2008).
[CrossRef]

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).
[CrossRef]

Lim, Y. X.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[CrossRef]

Lin, S. Y.

D. H. Huang, G. Gumbs, and S. Y. Lin, “Self-consistent theory for near-field distribution and spectrum with quantum wires and a conductive grating in terahertz regime,” J. Appl. Phys. 105, 093715 (2009).
[CrossRef]

Loh, K. P.

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. Haley, Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[CrossRef]

Lui, C. H.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[CrossRef]

MacDonald, A. H.

A. Bostwick, F. Speck, T. Seyller, K. Horn, M. Polini, R. Asgari, A. H. MacDonald, and E. Rotenberg, “Observation of plasmarons in quasi-freestanding doped graphene,” Science 328, 999–1002 (2010).
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[CrossRef]

Phys. Rev. B

D. H. Huang, T. Apostolova, P. M. Alsing, and D. A. Cardimona, “High-field transport of electrons and radiative effects using coupled force-balance and Fokker–Planck equations beyond relaxation-time approximation,” Phys. Rev. B 69, 075214 (2004).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Effect of photon-assisted absorption on the thermodynamics of hot electrons interacting with an intense optical field in bulk GaAs,” Phys. Rev. B 71, 045204 (2005).
[CrossRef]

D. H. Huang, P. M. Alsing, T. Apostolova, and D. A. Cardimona, “Coupled energy-drift and force-balance equations for high-field hot-carrier transport,” Phys. Rev. B 71, 195205 (2005).
[CrossRef]

G. Gumbs, D. H. Huang, and D. N. Talwar, “Doublet structure in the absorption coefficient for tunneling-split intersubband transitions in double quantum wells,” Phys. Rev. B 53, 15436–15439 (1996).
[CrossRef]

L. Brey and H. A. Fertig, “Elementary electronic excitations in graphene nanoribbons,” Phys. Rev. B 75, 125434 (2007).
[CrossRef]

B. Y. K. Hu, E. H. Hwang, and S. Das Sarma, “Density of states of disordered graphene,” Phys. Rev. B 78, 165411 (2008).
[CrossRef]

K. S. Gupta and S. Sen, “Bound states in gapped graphene with impurities: effective low-energy description of short-range interactions,” Phys. Rev. B 78, 205429 (2008).
[CrossRef]

D. H. Huang, G. Gumbs, and O. Roslyak, “Field enhanced mobility by nonlinear phonon scattering of Dirac electrons in semiconducting graphene nanoribbons,” Phys. Rev. B 83, 115405 (2011).
[CrossRef]

J. Z. Bernád, M. Jääskeläinen, and U. Zülicke, “Effects of a quantum measurement on the electric conductivity: application to graphene,” Phys. Rev. B 81, 073403 (2010).
[CrossRef]

T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78, 205403 (2008).
[CrossRef]

D. H. Huang, G. Gumbs, P. M. Alsing, and D. A. Cardimona, “Nonlocal mode mixing and surface-plasmon-polariton-mediated enhancement of diffracted terahertz fields by a conductive grating,” Phys. Rev. B 77, 165404 (2008).
[CrossRef]

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

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

Phys. Rev. Lett

F. Stern, “Polarizability of a two-dimensional electron gas,” Phys. Rev. Lett 18, 546–548 (1967).
[CrossRef]

Phys. Rev. Lett.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[CrossRef]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[CrossRef]

K. Nomura and A. H. MacDonald, “Quantum Hall ferromagnetism in graphene,” Phys. Rev. Lett. 96, 256602 (2006).
[CrossRef]

Phys. Scr.

M. A. H. Vozmediano and F. Guinea, “Effect of Coulomb interactions on the physical observables of graphene,” Phys. Scr. T146, 014015 (2012).
[CrossRef]

Rep. Prog. Phys.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Rev. Mod. Phys.

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

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

Science

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

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, 1308 (2008).
[CrossRef]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320, 206–209 (2008).
[CrossRef]

A. Bostwick, F. Speck, T. Seyller, K. Horn, M. Polini, R. Asgari, A. H. MacDonald, and E. Rotenberg, “Observation of plasmarons in quasi-freestanding doped graphene,” Science 328, 999–1002 (2010).
[CrossRef]

Semicond. Sci. Technol.

M. Orlita and M. Potemski, “Dirac electronic states in graphene systems: optical spectroscopy studies,” Semicond. Sci. Technol. 25, 063001 (2010).
[CrossRef]

Other

Special issue on “Electronic and photonic properties of graphene layers and carbon nanoribbons,” (Edited by G. Gumbs, D. H. Huang, and O. Roslyak) Philos. Trans. R. Soc. London, Ser. A138, 1932 (2010).
[CrossRef]

G. Gumbs and D. H. Huang, Properties of Interacting Low-Dimensional Systems (Wiley, 2011), Chaps. 4 and 5.

P. M. Platzman and P. A. Wolff, Waves and Interactions in Solid State Plasmas (Academic, 1973).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic representation of a GMRA (blue) with period d and ribbon width W and an InAs QW (red). The lower half-space (z<0) is filled with air with refractive index na=1, whereas the upper half-space (z>0) is filled with a doped semi-infinite GaAs bulk having a complex dielectric function ϵs(q,ω) or a complex refractive index ns=ϵs(q,ω). Both the GMRA [with an optical-response function χ¯2(qx,ω)] and the InAs QW [with an optical-response function χ¯1(qx,ω)] sit on the surface (z=0) of the semi-infinite GaAs bulk. A plane-wave EM field is incident from the z<0 side with an incident angle θi.

Fig. 2.
Fig. 2.

Comparison of the far-field transmissivity spectra Fp(ω) in the absence of both SP and QW for p polarization with two given linear-array periods: d=2μm (red solid curve) and d=4μm (blue dashed curve). Two arrows indicate the shift of two corresponding peaks with d. Other parameters in calculations are given in the text.

Fig. 3.
Fig. 3.

Comparison of the calculated transmissivity spectra Fp(ω) for p polarization with μ2=0.45eV (red solid curve) and μ2=0.9eV (blue dashed curve). Two downward solid-line arrows indicate the shift of two corresponding peaks with μ2, while one upward dashed-line arrow indicates a new peak. Other parameters in calculations are given in the text.

Fig. 4.
Fig. 4.

Comparisons of the far-field transmissivity spectra Fp(ω) [in (a)] and the far-field reflectivity spectra Rp(ω) [in (b)] for p polarization with different linear-array periods: d=1μm (blue dash-dot-dotted curves), d=2μm (black dashed curves), d=4μm (red solid curves) and d=8μm (green dash-dotted curves). Two arrows indicate the shift of two corresponding peaks with d. Other parameters in calculations are given in the text.

Fig. 5.
Fig. 5.

Comparison of the calculated transmissivity spectra Fp(ω) for p polarization with d=4μm and ζ=0.5 (red solid curve) as well as with d=8μm and ζ=0.25 (blue dashed curve). The peak indicated by a downward red arrow splits into two indicated by two upward blue arrows. Other parameters in calculations are given in the text.

Fig. 6.
Fig. 6.

Comparison of the calculated transmissivity spectra Fp(ω) is presented in the upper panel for p polarization and four different configurations of the system, including: (i) with GMRA, QW and SP (full, red solid curve), (ii) Ωpl=0 (no SP, blue dash-dot-dotted curve), (iii) χ¯1(qx,ω)=0 (no QW, black dash-dotted curve), and (iv) Ωpl=0=χ¯1(qx,ω)=0 (ribbon only, green dashed curve). Two solid-line arrows indicate the peak associated with the SP. The circled numbers label four peaks in the figure for the case of no SP. For the lower panel, the transmitted p-polarized E-field intensity |E>(x,z|ω)|2 is shown at ω=10.7meV for the full system, where the color scale is indicated. Other parameters in calculations are given in the text.

Fig. 7.
Fig. 7.

Comparison of the transmitted p-polarized E-field intensities |E>(x,z|ω)|2 in the presence of an SP with (left) or without (right) a QW at two indicated resonant photon energies, where two color scales are given in the left and right panels, respectively. Other parameters in calculations are given in the text.

Fig. 8.
Fig. 8.

Comparisons of the calculated partial near-field transmissivity spectra Fn(qn|ω) for p polarization. In (a) we take n=1 (black solid curve), n=0 (blue dashed curve) and n=1 (red dash-dotted curve), while in (b) we choose n=2 (black solid curve), n=0 (blue dashed curve) and n=2 (red dash-dotted curve). Other parameters in calculations are given in the text.

Fig. 9.
Fig. 9.

Comparison of the calculated p-polarized transmissivity spectra Fp(ω) for two compensated structures, including a GMRA plus an InAs QW sheet (G-ribbon, red solid curve) and an InAs quantum-well ribbon array plus a graphene sheet (QW-ribbon, blue dashed curve). A blue upward arrow indicates a weak peak for the QW-ribbon array. Other parameters in calculations are given in the text.

Fig. 10.
Fig. 10.

Comparison of the transmissivity spectra Fp(ω) is made in the upper panel for p polarization with three different bandgaps EG=0 (μ2=450meV, red solid curve), EG=0.25eV (μ2=342meV, black dash-dotted curve) and EG=1eV (μ2=173meV, blue dashed curve). Two pairs of arrows indicate the shift of a pair of corresponding peaks with EG. In the lower panel, a comparison of the calculated transmitted p-polarized E-field intensities |E>(x,z|ω)|2 is displayed for EG=0 (left) and EG=1eV (right) at ω=19.5meV and ω=18.7meV, respectively. Here, we keep the electron areal density (k2F2) in a graphene micro-ribbon unchanged for different values of EG, and two color scales are indicated in the lower-left and lower-right panels. Other parameters in calculations are given in the text.

Equations (75)

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E<(x,z|ω)=eiqxx+iηz[Ax(qx|ω)Ay(qx|ω)(qx/η)Ax(qx|ω)]+n=eiqnxiβ1,nz[Bx(qn|ω)By(qn|ω)(qn/β1,n)Bx(qn|ω)],forz<0,
E>(x,z|ω)=n=eiqnx+iβ2,nz[Cx(qn|ω)Cy(qn|ω)(qn/β2,n)Cx(qn|ω)],forz>0.
[(β1,n)2(β2,n)2]=ω2c2[na2ϵs(qn,β2,n,ω)]qn2,
ϵs(qx,β;ω)=ϵb[1Ωpl2ω(ω+iγ0)],
H=iωμ0×E,
H<x(x,z|ω)=1ωμ0[ηeiqxx+iηzAy(qx|ω)n=β1,neiqnxiβ1,nzBy(qn|ω)],
H<y(x,z|ω)=ωϵ0na2[1ηeiqxx+iηzAx(qx|ω)n=1β1,neiqnxiβ1,nzBx(qn|ω)],
H<z(x,z|ω)=1ωμ0[qxeiqxx+iηzAy(qx|ω)+n=qneiqnxiβ1,nzBy(qn|ω)].
H>x(x,z|ω)=1ωμ0n=β2,neiqnx+iβ2,nzCy(qn|ω),
H>y(x,z|ω)=ωϵ0n=1β2,neiqnx+iβ2,nzϵs(qn,β2,n,ω)Cx(qn|ω),
H>z(x,z|ω)=1ωμ0n=qneiqnx+iβ2,nzCy(qn|ω),
E>x(x,z=0|ω)E<x(x,z=0|ω)=0,
E>y(x,z=0|ω)E<y(x,z=0|ω)=0,
H>x(x,z=0|ω)H<x(x,z=0|ω)=iωPsy(x|ω)+αsy(x|ω),
H>y(x,z=0|ω)H<y(x,z=0|ω)=iωPsy(x|ω)+αsx(x|ω),
Ps(x|ω)=n=Ps(qn|ω)eiqnx,
[Psx(qn|ω)/ϵ0Psy(qn|ω)/ϵ0]=χ1(qn,ω)[Cx(qn|ω)Cy(qn|ω)]+ζn=χ2(qn,ω)sinc[(nn)πζ][Cx(qn|ω)Cy(qn|ω)].
αs(x|ω)=n=αs(qn|ω)eiqnx,
[αsx(qn|ω)αsy(qn|ω)]=σ1(qn,ω)[Cx(qn|ω)Cy(qn|ω)]+ζn=σ2(qn,ω)sinc[(nn)πζ][Cx(qn|ω)Cy(qn|ω)],
χ¯j(q,ω)=χj(q,ω)+iσj(q,ω)ωϵ0,
χ¯2(q,ω)=e2ϵ0q2Π2(q,ω),
Π2(q,ω)=4An1,n2,k|n1,k|eiq·r|n2,k+q|2f0(εn1,k)f0(εn2,k+q)εn2,k+qεn1,k(ω+i0+),
Π2(q,ω)=2μ2π2vF2q24π|vF2q2ω2|×{i[G>(x1,)G>(x1,+)]Q1<(x2,)+[G<(x1,)+iG>(x1,+)]Q2<(x2,,x2,+)+[G<(x1,+)+G<(x1,)]Q3<(x2,)+[G<(x1,)G<(x1,+)]Q4<(x2,+)+[G>(x1,+)G>(x1,)]Q1>(x2,,x3)+[G>(x1,+)+iG<(x1,)]Q2>(x2,,x2,+)+[G>(x1,+)G>(x1.)iπ[2x02]]Q3>(x2,+)+[G>(x1,)+G>(x1,+)iπ[2x02]]Q4>(x2,,x3)+[G0(x1,+)G0(x1,)]Q5>(x3)},
ε±,k=±2vF2k2+EG2/4,
G<(x)=xx02x2(2x02)cos1(xx0),
G>(x)=xx2x02(2x02)cosh1(xx0),
G0(x)=xx2x02(2x02)sinh1(xx02).
Q1<(x2,)=θ(μ2x2,ω),
Q2<(x2,,x2,+)=θ(ωμ2+x2,)θ(ω+μ2x2,)θ(μ2+x2,+ω),
Q3<(x2,)=θ(μ2+x2,ω),
Q4<(x2,+)=θ(ω+μ2x2,+)θ(vFqω),
Q1>(x2,,x3)=θ(2k2Fq)θ(ωx3)θ(μ2+x2,ω),
Q2>(x2,,x2,+)=θ(ωμ2x2,)θ(μ2+x2,+ω),
Q3>(x2,+)=θ(ωμ2x2,+),
Q4>(x2,,x3)=θ(q2k2F)θ(ωx3)θ(μ2+x2,ω),
Q5>(x3)=θ(ωvFq)θ(x3ω),
x0=1+EG22vF2q22ω2,
x1,±=2μ2±ωvFq,
x2,±=2vF2(q±k2F)2+EG2/4,
x3=2vF2q2+EG2.
χ¯1(q,ω)=2ρse2ms*ϵ02k1Fq3{[2zC(zu)21C+(z+u)21]+i[D1(zu)2D+1(z+u)2]},
Bx(qx|ω)Cx(qx|ω)=Ax(qx|ω),
By(qx|ω)Cy(qx|ω)=Ay(qx|ω),
ic2β1,0ω2By(qx|ω)ic2β2,0ω2Cy(qx|ω)ζn=sinc(nπζ)χ¯2(qn,ω)By(qn|ω)χ¯1(qx,ω)By(qx|ω)=(χ¯1(qx,ω)+ζχ¯2(qx,ω)ic2ηω2)Ay(qx|ω),
iβ1,0na2Bx(qx|ω)iβ2,0ϵs(qx,β2,0,ω)Cx(qx|ω)ζn=sinc(nπζ)χ¯2(qn,ω)Bx(qn|ω)χ¯1(qx,ω)Bx(qx|ω)=(χ¯1(qx,ω)+ζχ¯2(qx,ω)iη)Ax(qx|ω).
Bx(qn|ω)Cx(qn|ω)=0,
By(qn|ω)Cy(qn|ω)=0,
ic2β1,nω2By(qn|ω)ic2β2,nω2Cy(qn|ω)ζn=sinc[(nn)πζ]χ¯2(qn,ω)By(qn|ω)χ¯1(qn,ω)By(qn|ω)=0,
iβ1,nna2Bx(qn|ω)iβ2,nϵs(qn,β2,n,ω)Cx(qn|ω)ζn=sinc[(nn)πζ]χ¯2(qn,ω)Bx(qn|ω)χ¯1(qn,ω)Bx(qn|ω)=0,
|Ex(x,z=0|ω)|2=[Ax(qx|ω)]2+n=|Bx(qn|ω)|2+2Ax(qx|ω)Re[Bx(qx|ω)]+n,n(nn)Bx(qn|ω)[Bx(qn|ω)]*ei(nn)Gx+2Ax(qx|ω)Re(n0Bx(qn|ω)einGx),
|Ey(x,z=0|ω)|2=[Ay(qx|ω)]2+n=|By(qn|ω)|2+2Ay(qx|ω)Re[By(qx|ω)]+n,n(nn)By(qn|ω)[By(qn|ω)]*ei(nn)Gx+2Ay(qx|ω)Re(n0By(qn|ω)einGx),
|Ez(x,z=0|ω)|2=qx2η2[Ax(qx|ω)]2+n=qn2|β1,n|2|Bx(qn|ω)|22qx2η2Ax(qx|ω)Re[Bx(qx|ω)]+n,n(nn)qnqnβ1,n(β1,n)*Bx(qn|ω)[Bx(qn|ω)]*×ei(nn)Gx2Ax(qx|ω)Re(n(n0)qxqnηβ1,nBx(qn|ω)einGx),
R(x|ω)=|Exr(x,z=0|ω)|2+|Eyr(x,z=0|ω)|2+|Ezr(x,z=0|ω)|2(1+qx2/η2)Ax2(qx|ω)+Ay2(qx|ω),
|Exr(x,z=0|ω)|2=n,nBx(qn|ω)[Bx(qn|ω)]*ei(nn)Gx,
|Eyr(x,z=0|ω)|2=n,nBy(qn|ω)[By(qn|ω)]*ei(nn)Gx,
|Ezr(x,z=0|ω)|2=n,nqnqnβ1,n(β1,n)*Bx(qn;ω)[Bx(qn|ω))]*ei(nn)Gx.
F(x|ω)=|Ext(x,z=0|ω)|2+|Eyt(x,z=0|ω)|2+|Ezt(x,z=0|ω)|2(1+qx2/η2)Ax2(qx|ω)+Ay2(qx|ω),
|Ext(x,z=0|ω)|2=n,nCxT(qn|ω)[Cx(qn|ω)]*ei(nn)Gx,
|Eyt(x,z=0|ω)|2=n,nCy(qn|ω)[Cy(qn|ω)]*ei(nn)Gx,
|Ezt(x,z=0|ω)|2=n,nqnqnβ2,n(β2,n)*Cx(qn|ω)[Cx(qn|ω)]*ei(nn)Gx.
R(ω)=limLx12LxLxLxdxR>(x|ω)=n=Rn(qn|ω)θ(naω|qn|c),
F(ω)=limLx12LxLxLxdxF>(x|ω)=n=Fn(qn|ω)θ(ϵsω|qn|c)θ(ϵs),
Rn(qn|ω)=(1+qn2/|β1,n|2)|Bx(qn|ω)|2+|By(qn|ω)|2(1+qx2/η2)Ax2(qx|ω)+Ay2(qx|ω),
Fn(qn|ω)=(1+|qn2/|β2,n|2)|Cx(qn|ω)|2+|Cy(qn|ω)|2(1+qx2/η2)Ax2(qx|ω)+Ay2(qx|ω).
Mu=b,
b=[Ax(qx|ω)Ay(qx|ω)[(ω/c)χ¯1(qx,ω)+(ω/c)ζχ¯2(qx,ω)(icη/ω)]Ay(qx|ω)[(ω/c)χ¯1(qx,ω)+(ω/c)ζχ¯2(qx,ω)(iω/cη)]Ax(qx|ω)00].
u=[Bx(qN|ω)Bx(qN|ω)By(qN|ω)By(qN|ω)Cx(qN|ω)Cx(qN|ω)Cy(qN|ω)Cy(qN|ω)].
M(1,j)={1forj=N+11forj=5N+30for all otherj,M(2,j)={1forj=3N+21forj=7N+40for all otherj,M(3,j)={i(cβ1,0/ω)(ω/c)[χ¯1(qx,ω)+ζχ¯2(qx,ω)]forj=3N+2i(cβ2,0/ω)forj=7N+4(ω/c)ζsinc(mπζ)χ¯2(qm,ω)forj[J1,J2],[J2+2,J3]0for all otherj,
M(4,j)={i(na2ω/cβ1,0)(ω/c)[χ¯1(qx,ω)+ζχ¯2(qx,ω)]forj=N+1i(ω/cβ2,0)ϵs(q0,β2,0,ω)forj=5N+3(ω/c)ζsinc(mπζ)χ¯2(qm,ω)forj[1,N],[J1,J2]0for all otherj,
M(j,j)={1forj=j4[1,N]orj=j3[N+2,2N+1]1forj=J1[4N+3,5N+2]orj=J1+1[5N+4,6N+3]0for all otherj
M(j,j)={1forj=j3[2N+2,3N+1]orj=j2[3N+3,4N+2]1forj=J1[6N+4,7N+3]orj=J1+1[7N+5,8N+4]0for all otherj
M(j,j)={i(cβ1,m/ω)(ω/c)[ζχ¯2(qm,ω)+χ¯1(qm,ω)]forj=j(J1+1)i(cβ2,m/ω)forj=j+(J13)(ω/c)ζsinc[(mm)πζ]χ¯2(qm,ω)forj[J1,J2]butjJ30for all otherj,
M(j,j)={i(cβ1,m/ω)(ω/c)[ζχ¯2(qm,ω)+χ¯1(qm,ω)]forj=jJ1i(cβ2,m/ω)forj=j+J12(ω/c)ζsinc[(mm)πζ]χ¯2(qm,ω)forj[J1,J2]butjJ30for all otherj,
M(j,j)={i(na2ω/cβ1,m)(ω/c)[ζχ¯2(qm,ω)+χ¯1(qm,ω)]forj=jJ2i(ω/cβ2,m)ϵs(qm,β2,m,ω)forj=j(J1+1)(ω/c)ζsinc[(mm)πζ]χ¯2(qm,ω)forj[1,J1]butjJ30for all otherj,
M(j,j)={i(na2ω/cβ1,m)(ω/c)[ζχ¯2(qm,ω)+χ¯1(qm,ω)]forj=jJ2i(ω/cβ2,m)εs(qm,β2,m,ω)forj=jJ1(ω/c)ζsinc[(mm)πζ]χ¯2(qm,ω)forj[1,J1]butjJ30for all otherj,

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