## Strong enhancement of light absorption and highly directive thermal emission in graphene |

Optics Express, Vol. 21, Issue 10, pp. 11618-11627 (2013)

http://dx.doi.org/10.1364/OE.21.011618

Acrobat PDF (1974 KB)

### Abstract

Graphene is a two-dimensional material with exotic electronic, optical and thermal properties. The optical absorption in monolayer graphene is limited by the fine structure constant *α*. Here we demonstrated the strong enhancement of light absorption and thermal radiation in homogeneous graphene. Numerical simulations show that the light absorbance can be controlled from near zero to 100% by tuning the Fermi energy. Moreover, a set of periodically located absorption peaks is observed at near grazing incidence. Based on this unique property, highly directive comb-like thermal radiation at near-infrared frequencies is demonstrated.

© 2013 OSA

## 1. Introduction

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

4. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. **6**(3), 183–191 (2007). [CrossRef] [PubMed]

*A*≈π

*α*≈2.3%, where

*α*≈1/137 is the fine structure constant [5

5. A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. **100**(11), 117401 (2008). [CrossRef] [PubMed]

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

8. J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B **83**(16), 165113 (2011). [CrossRef]

^{5}Ω [9

9. S. De and J. N. Coleman, “Are there fundamental limitations on the sheet resistance and transmittance of thin graphene films?” ACS Nano **4**(5), 2713–2720 (2010). [CrossRef] [PubMed]

*μ*or Fermi energy

_{c}*E*[10

_{F}10. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science **320**(5873), 206–209 (2008). [CrossRef] [PubMed]

14. H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. **7**(5), 330–334 (2012). [CrossRef] [PubMed]

*et al*. demonstrated that sophisticated tunable terahertz metamaterials can be achieved based on graphene micro-ribbon arrays [10

10. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science **320**(5873), 206–209 (2008). [CrossRef] [PubMed]

11. Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature **459**(7248), 820–823 (2009). [CrossRef] [PubMed]

*et al*. proposed that numerous photonic functions and metamaterial concepts can be achieved by tune the graphene conductivity [13

13. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science **332**(6035), 1291–1294 (2011). [CrossRef] [PubMed]

15. R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express **20**(27), 28017–28024 (2012). [CrossRef] [PubMed]

17. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. **108**(4), 047401 (2012). [CrossRef] [PubMed]

18. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. **100**(20), 207402 (2008). [CrossRef] [PubMed]

21. Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett. **37**(11), 2133–2135 (2012). [CrossRef] [PubMed]

19. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express **19**(18), 17413–17420 (2011). [CrossRef] [PubMed]

17. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. **108**(4), 047401 (2012). [CrossRef] [PubMed]

22. M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, and X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express **20**(3), 2246–2254 (2012). [CrossRef] [PubMed]

23. M. Pu, Q. Feng, C. Hu, and X. Luo, “Perfect absorption of light by coherently induced plasmon hybridization in ultrathin metamaterial film,” Plasmonics **7**(4), 733–738 (2012). [CrossRef]

24. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature **416**(6876), 61–64 (2002). [CrossRef] [PubMed]

27. J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a midinfrared metamaterial,” Appl. Phys. Lett. **98**(24), 241105 (2011). [CrossRef]

28. A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. **8**(3), 902–907 (2008). [CrossRef] [PubMed]

29. K. Kim, W. Regan, B. Geng, B. Alemán, B. M. Kessler, F. Wang, M. F. Crommie, and A. Zettl, “High-temperature stability of suspended single-layer graphene,” Phys. Status Solidi **4**(11), 302–304 (2010) (RRL). [CrossRef]

30. M. Freitag, H. Y. Chiu, M. Steiner, V. Perebeinos, and P. Avouris, “Thermal infrared emission from biased graphene,” Nat. Nanotechnol. **5**(7), 497–501 (2010). [CrossRef] [PubMed]

## 2. Principle and simulation

### 2.1 Tunable absorption in the terahertz regime

15. R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express **20**(27), 28017–28024 (2012). [CrossRef] [PubMed]

*k*is the thermal energy,

_{B}T*μ*

_{c}is the chemical potential and Γ is the scattering rate,

*e*,

*k*, and

_{B}*ћ*are electron charge, Boltzmann constant, and reduced Plank constant (Dirac constant), respectively. The first term in Eq. (1) is due to the contribution of inter-band transition and the second term results from intra-band transition. The frequency of transition between these two regimes is dependent on the chemical potential. The validity of Eq. (1) is checked with the help of numerical and experimental results in [5

5. A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. **100**(11), 117401 (2008). [CrossRef] [PubMed]

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

13. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science **332**(6035), 1291–1294 (2011). [CrossRef] [PubMed]

*t*≈0.5 nm is the thickness of graphene [13

13. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science **332**(6035), 1291–1294 (2011). [CrossRef] [PubMed]

21. Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett. **37**(11), 2133–2135 (2012). [CrossRef] [PubMed]

*d*. The permittivity of dielectric spacer is set as 2.1. To adjust the chemical potential of graphene, a voltage can be added between the graphene and metallic ground plane. The absorbance of the absorber is then calculated using

*A*= 1-

*r*

^{2}, where

*r*is the reflection coefficient obtained through transfer matrix method (TMM) [19

19. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express **19**(18), 17413–17420 (2011). [CrossRef] [PubMed]

*a*,

*b*,

*c*,

*d*are the coefficients of counter-propagating waves,

*Z*is the sheet impedance of graphene,

_{s}*Z*

_{0}= 1/

*Y*

_{0}= 377 Ω is the impedance of vacuum,

*k*=

_{x}*k*

_{0}(

*ε*-sin

^{2}

*θ*)

^{1/2}is the wave vector along

*x*direction,

*k*is the wave vector in vacuum,

_{0}*ε*is the permittivity of dielectric spacer.

*Y*

_{00}and

*Y*

_{1}are the wave impedance at the left and right sides of graphene. For transverse electric (TE) polarization, there are

*Y*

_{00}=

*Y*

_{0}cos

*θ*and

*Y*

_{1}=

*Y*

_{0}(

*ε*-sin

^{2}

*θ*)

^{1/2}. For transverse magnetic (TM) polarization, there are

*Y*

_{00}=

*Y*

_{0}/cos

*θ*and

*Y*

_{1}=

*Y*

_{0}

*ε*(

*ε*-sin

^{2}

*θ*)

^{-1/2}, where

*θ*is the incidence angle.

*b*should be zero, thus the required sheet impedance can be written as:for TE polarization andfor TM polarization.

*n*is the refractive index. If

*Z*=

_{s}*Z*

_{0}= 377 Ω, the maximal absorption condition becomes

*nkd*= π/2, corresponding to traditional Salisbury screen (the lossy material can be either carbon or nichrome) [19

19. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express **19**(18), 17413–17420 (2011). [CrossRef] [PubMed]

*f*= 1.36 THz and

*nkd*= 2.89. The blue shift of absorption peak can be attributed to the increase of imaginary part in graphene conductivity. As shown in Fig. 3(a) and 3(b), the imaginary parts of conductivity are much larger than the real parts (σ

_{2D}= 27.8 + 245

*i*in units of

*f*= 1.36 THz). According to Eq. (6), the large imaginary part in

*Z*will make

_{s}*kd*shift (become larger).

17. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. **108**(4), 047401 (2012). [CrossRef] [PubMed]

31. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. **82**(3), 2257–2298 (2010). [CrossRef]

33. M. Pu, C. Hu, C. Huang, C. Wang, Z. Zhao, Y. Wang, and X. Luo, “Investigation of Fano resonance in planar metamaterial with perturbed periodicity,” Opt. Express **21**(1), 992–1001 (2013). [CrossRef] [PubMed]

*nkd*= π so that the required impedance for perfect absorption becomes

*Z*

_{s}= 0, which can hardly be achieved for graphene with any chemical potential.

### 2.2 Absorption at large angle of incidence

*i*. As illustrated Fig. 5, periodically located absorption peaks are observed for TE polarization at

*θ*≈83°. For TM polarization, the absorption mainly located at small angles of incidence.

*Z*

_{0}for frequencies larger than 5 THz and chemical potential less than 200 meV, the prefect absorption condition (Eqs. (4) and (5)) can only be achieved whenThe corresponding angles of incidence are:for TE polarization, andfor TM polarization. It is interesting to note that the absorption angle is only dependent on the sheet impedance. Also, there is no solution for TM polarization because Z

_{s}> Z

_{0.}

*ε*= 1, Δ

*f*would be very large. As a result, the dielectric spacer provides not only mechanical support but also a phase matching for large angle of incidence.

### 2.3 Thermal radiation engineering

24. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature **416**(6876), 61–64 (2002). [CrossRef] [PubMed]

27. J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a midinfrared metamaterial,” Appl. Phys. Lett. **98**(24), 241105 (2011). [CrossRef]

34. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature **450**(7173), 1214–1217 (2007). [CrossRef] [PubMed]

*μ*

_{c}= 0) becomes a universal constant equal to

10. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science **320**(5873), 206–209 (2008). [CrossRef] [PubMed]

*λ*= 1.93 μm). The radiation angle is then calculated to be

*θ*= 88.5°. Since the absorption at

*θ*= 0°, 30°, and 60° is only 0.09, 0.1, 0.17 for TE polarization (the case for TM polarization is even smaller), the emissivity is highly dependent on the angle.

*d*) or multi-frequency comb-like radiation (large

*d*). As illustrated in Fig. 7, the thermal emissions of the structure for different dielectric thicknesses are calculated. When the thickness of dielectric layer is set as 50 μm, 5 μm, and 0.5 μm, the corresponding frequency interval between adjacent peaks becomes 2.86 THz, 28.6 THz and 286 THz, respectively.

*μ*

_{c}, the inter-band transition shift to higher frequency. Due to the abrupt change of conductivity, the emission spectrum will also experience a rapid alteration. The conductivities and emission spectra (

*θ*= 88.5°) for

*μ*

_{c}= 200 meV and 300 meV are illustrated in Fig. 8. Here the thickness of the dielectric spacer is kept as 10 μm. Obviously, the emission spectra at frequency higher than 2

*μ*

_{c}/

*h*are not changed by the chemical potential while the emission at lower frequencies is completely suppressed.

5. A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. **100**(11), 117401 (2008). [CrossRef] [PubMed]

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

*f*= 155 THz (

*d*= 0.46 μm) for 1, 5, and 10 layers of graphene are calculated using transfer matrix method for different radiation angles. As the increase of the layer number, the radiation angle will decrease according to Eq. (8). Meanwhile, the radiation at small angle (such as normal direction) will increase and the beam width would be larger. Thus for practical applications, a trade-off between radiation angle and beam width is required.

21. Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett. **37**(11), 2133–2135 (2012). [CrossRef] [PubMed]

## Conclusion

## Acknowledgments

## References and links

1. | 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 |

2. | Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature |

3. | J. Nilsson, A. H. C. Neto, F. Guinea, and N. M. R. Peres, “Electronic properties of graphene multilayers,” Phys. Rev. Lett. |

4. | A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. |

5. | A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. |

6. | 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 |

7. | S. A. Maier, |

8. | J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B |

9. | S. De and J. N. Coleman, “Are there fundamental limitations on the sheet resistance and transmittance of thin graphene films?” ACS Nano |

10. | F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science |

11. | Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature |

12. | 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. |

13. | A. Vakil and N. Engheta, “Transformation optics using graphene,” Science |

14. | H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. |

15. | R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express |

16. | A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B |

17. | S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. |

18. | N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. |

19. | M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express |

20. | P. Bouchon, C. Koechlin, F. Pardo, R. Haïdar, and J.-L. Pelouard, “Wideband omnidirectional infrared absorber with a patchwork of plasmonic nanoantennas,” Opt. Lett. |

21. | Q. Feng, M. Pu, C. Hu, and X. Luo, “Engineering the dispersion of metamaterial surface for broadband infrared absorption,” Opt. Lett. |

22. | M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, and X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express |

23. | M. Pu, Q. Feng, C. Hu, and X. Luo, “Perfect absorption of light by coherently induced plasmon hybridization in ultrathin metamaterial film,” Plasmonics |

24. | J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature |

25. | M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B |

26. | X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. |

27. | J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a midinfrared metamaterial,” Appl. Phys. Lett. |

28. | A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. |

29. | K. Kim, W. Regan, B. Geng, B. Alemán, B. M. Kessler, F. Wang, M. F. Crommie, and A. Zettl, “High-temperature stability of suspended single-layer graphene,” Phys. Status Solidi |

30. | M. Freitag, H. Y. Chiu, M. Steiner, V. Perebeinos, and P. Avouris, “Thermal infrared emission from biased graphene,” Nat. Nanotechnol. |

31. | A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. |

32. | B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. |

33. | M. Pu, C. Hu, C. Huang, C. Wang, Z. Zhao, Y. Wang, and X. Luo, “Investigation of Fano resonance in planar metamaterial with perturbed periodicity,” Opt. Express |

34. | P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature |

**OCIS Codes**

(310.3915) Thin films : Metallic, opaque, and absorbing coatings

(160.3918) Materials : Metamaterials

(290.6815) Scattering : Thermal emission

**ToC Category:**

Materials

**History**

Original Manuscript: January 25, 2013

Revised Manuscript: April 19, 2013

Manuscript Accepted: May 1, 2013

Published: May 6, 2013

**Citation**

Mingbo Pu, Po Chen, Yanqin Wang, Zeyu Zhao, Changtao Wang, Cheng Huang, Chenggang Hu, and Xiangang Luo, "Strong enhancement of light absorption and highly directive thermal emission in graphene," Opt. Express **21**, 11618-11627 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-11618

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### References

- K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature438(7065), 197–200 (2005). [CrossRef] [PubMed]
- Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature438(7065), 201–204 (2005). [CrossRef] [PubMed]
- J. Nilsson, A. H. C. Neto, F. Guinea, and N. M. R. Peres, “Electronic properties of graphene multilayers,” Phys. Rev. Lett.97(26), 266801 (2006). [CrossRef] [PubMed]
- A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6(3), 183–191 (2007). [CrossRef] [PubMed]
- A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett.100(11), 117401 (2008). [CrossRef] [PubMed]
- 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,” Science320(5881), 1308–1308 (2008). [CrossRef] [PubMed]
- S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
- J. Horng, C. F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H. A. Bechtel, M. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Drude conductivity of Dirac fermions in graphene,” Phys. Rev. B83(16), 165113 (2011). [CrossRef]
- S. De and J. N. Coleman, “Are there fundamental limitations on the sheet resistance and transmittance of thin graphene films?” ACS Nano4(5), 2713–2720 (2010). [CrossRef] [PubMed]
- F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science320(5873), 206–209 (2008). [CrossRef] [PubMed]
- Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature459(7248), 820–823 (2009). [CrossRef] [PubMed]
- 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(10), 630–634 (2011). [CrossRef] [PubMed]
- A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011). [CrossRef] [PubMed]
- H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol.7(5), 330–334 (2012). [CrossRef] [PubMed]
- R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express20(27), 28017–28024 (2012). [CrossRef] [PubMed]
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