Abstract

We demonstrate that giant Faraday rotation in graphene in the terahertz range due to the cyclotron resonance is further increased by constructive Fabry-Perot interference in the supporting substrate. Simultaneously, an enhanced total transmission is achieved, making this effect doubly advantageous for graphene-based magneto-optical applications. As an example, we present far-infrared spectra of epitaxial multilayer graphene grown on the C-face of 6H-SiC, where the interference fringes are spectrally resolved and a Faraday rotation up to 0.15 radians (9°) is attained. Further, we discuss and compare other ways to increase the Faraday rotation using the principle of an optical cavity.

© 2013 OSA

1. Introduction

Graphitic materials, such as carbon nanotubes and graphene, find numerous applications in various fields of optics [14]. The giant terahertz Faraday rotation in graphene [510] suggests that this novel material can be useful in applied magneto-optics. The exceptionally strong Faraday effect, combined with a high doping tunability, which is a hallmark of graphene, may potentially lead to a new class of ultrafast tunable magneto-optical modulators and isolators [5,8,11,12]. Apart from practical importance, the magneto-optical phenomena are helpful to study the charge carrier dynamics in these systems [5, 13, 14].

Even though the observed Faraday angles of a few degrees at fields of only a few Tesla [5] are exceptionally large for a single atomic layer, the use of this effect in practical devices will certainly be facilitated by increasing the rotations even more, while reducing the required magnetic field. Modifying the properties of graphene itself, for example, increasing the number of magneto-optically active layers, enhancing the mobility of charge carriers and fabrication of plasmonic nanostructures, is obviously one of the avenues for this improvement. However, the electromagnetic properties of the environment surrounding a magneto-optical layer, also play an important role. In particular, it is known that small Faraday rotation can be boosted by placing magneto-optically active samples inside a Fabry-Perot cavity. The rotation angle is enhanced after multiple internal beam passages [15]. This principle was used to build magneto-optical devices [16], to increase the sensitivity of magnetic field sensors [17] or to measure ultrasmall Verdet constants [18]. In the context of graphene, the idea was recently studied theoretically in [6], Ferreira et al.

An important issue to be addressed in this context is the influence of a substrate, which is always present in realistic applications. One undesirable effect of the substrate is to reduce the magneto-optical rotation as compared to free standing graphene by a factor, which depends on the substrate refractive index [5]. However, a well polished flat parallel substrate can also develop strong Fabry-Perot interference and thus acts as a cavity. In this work we show that it can be used to increase the rotation angle and simultaneously the total transmission. In order to make a connection between this effect and previous ideas about the Fabry-Perot cavity, we perform several model calculations. This allows us to compare different ways to enhance the Faraday rotation in graphene.

2. Experimental details

Our sample is multilayer epitaxial graphene grown on the C-face [19] of 6H-SiC by annealing silicon carbide in an Ar atmosphere for 90 minutes at 1650 ° C. Before the growth, the substrate was hydrogen-etched at 1600° C for 15 minutes. The total number of graphene layers was about 20, as determined by X-ray photoelectron spectroscopy and confirmed by infrared absorption in the near-infrared range. However, only one or two layers closest to the SiC are highly doped (n-type) [20] and therefore responsible for the classical cyclotron resonance, which dominates the magneto-optical response in the range of energies and magnetic fields [13] considered in this paper. The remaining layers, which are quasineutral, only contribute to the overall absorption at low frequencies [13, 21]. The thickness of the substrate was reduced to d = 80 μm by polishing in order to increase the period of the Fabry-Perot oscillations (about 20 cm−1 in the THz range). We measured magneto-transmission T(ω, B) with unpolarized light and the Faraday rotation θF (ω, B) by a two-polarizer technique between 15 and 700 cm−1 with the help of a Fourier transform spectrometer coupled to a split-coil superconducting magnet [5]. A mercury light source, silicon beamsplitter and liquid-helium cooled Si bolometer were used. The spectral resolution (1 cm−1 for the transmission and 2 cm−1 for the Faraday rotation) was sufficient to fully resolve the interference fringes. The spectra at 5 Kelvin and 7 Tesla are plotted in Fig. 1. At lower fields the data show a qualitatively similar behavior. The energy of the cyclotron resonance (marked by the dashed line) can be identified as a broad minimum in (oscillation-averaged) transmission and a reduced amplitude of the fringes. The (oscillation-averaged) Faraday angle changes sign in this region. The negative value at low frequencies indicates that the layer responsible for the resonance is n-doped.

 

Fig. 1 Transmission (black squares, left axis) and Faraday rotation (red circles, right axis) spectra at 7 Tesla and 5 Kelvin. Note that the Faraday rotation scale is inverted. The horizontal line corresponds to zero Faraday rotation, the vertical line indicates the cyclotron frequency.

Download Full Size | PPT Slide | PDF

3. Discussion

An important observation is that the maxima of the transmission and the absolute value of the Faraday rotation virtually coincide, except close to the cyclotron resonance, ωc. It means that a constructive interference between internally reflected beams is favorable for both quantities. We note also that at some frequencies the Faraday angle reaches 9°, which is 50 percent higher than the value reported earlier [5].

In order to explain this finding, we model the experimental spectra by treating all graphene layers as a thin film with the total conductivity σ+ (σ) for the right- (left-) circular polarized light:

σ±(ω)=2Dπiωωc+iγ+σb
represented by a sum of the cyclotron resonance, described by a Drude weight D, a cyclotron frequency ωc and a scattering rate γ, and a constant background σb, approximating the absorption in other layers [13,22]. This quasi-classical approach is valid in our case since the condition ω, ωc < 2EF is satisfied [6, 23]. The transmission and the Faraday rotation are given by:
T=|t|2+|t+|22,θF=12arg(tt+)
where t± are the complex transmission coefficients for the two circular polarizations. Taking into account multiple internal reflections in the substrate, for which the refractive index n ≈ 3.1 and zero absorption were assumed in the spectral range of interest we get [24]:
t±=4nτs[(n+1)2(n1)2τs2+Z0σ±(n+1+(n1)τs2)]1,
where τs = exp(iωdn/c) is the phase factor acquired by light in the substrate and Z0 is the impedance of vacuum.

The following parameter values were found to fit the data at 7 Tesla in the best way: ωc = 156 cm−1, γ =56 cm−1, D/σ0 = 3620 cm−1, σb0 = 23, where σ0 = e2/4 is the universal conductivity of monolayer graphene [25]. We estimate the Fermi energy EF = 0.24 eV from the Drude weight extracted from the fit through the relation D = 2σ0EF/h̄. The theoretical curves are shown in Fig. 2(a). One can see that this simple model reproduces the data accurately, including the coincidence of maxima of the Faraday rotation and transmission.

 

Fig. 2 Simulation of the magneto-optical transmission and Faraday rotation of graphene on and in SiC for three different configurations. Note that the Faraday rotation scale is inverted. (a) Graphene covers one side of SiC, (b) graphene covers both sides of SiC, (c) graphene is in the middle of SiC slab, (d) graphene is in the middle of a SiC slab covered by metallic layers on both sides.

Download Full Size | PPT Slide | PDF

The physical meaning of this result becomes obvious in the following. The constructive interference occurs at frequencies, where τs = ±1. In this case, Eq. (3) reduces to

tconstr,±=τs(1+Z0σ±2)1,
which is equal, apart from the prefactor τs, to the transmission of free standing graphene with the same optical conductivity [26, 27]. It thus appears that the effect of the constructive Fabry-Perot interference is to exactly compensate the screening effect of the substrate. If monochromatic light is used (such as a terahertz laser), it would be desirable in magneto-optical applications to adjust the substrate thickness in order to achieve this condition.

Developing on this result, we next explore theoretically other possibilities to improve the Faraday rotation in graphene by making use of the cavity principle. For the sake of simplicity, we assume that graphene has the same optical conductivity as the one obtained in the present experiment and the total thickness of the substrate is always the same. In this case the substrate can be formally regarded as a low-finesse (F ≈ 3) optical cavity created by the SiC-vacuum interfaces.

We first consider the case where both sides of the substrate are covered with graphene. Although this cannot be done by growing graphene on two sides one can simply press two identical samples together. Equation (3) is now modified as follows:

t±=4nτs.[(n+1)2(n1)2τs2+2Z0σ±(n+1+(n1)τs)2+Z02σ±2(1τs2)]1.
For the constructive interference we obtain tconstr,± = τs (1 + Z0σ±)−1, which is the same result as Eq. (4), except for the factor 2 in the graphene conductivity term, due to the presence of two graphene layers. The computed spectra are plotted in Fig. 2(b). The Faraday rotation now reaches 15°. The transmission is lowered but remains at a reasonable level.

Next, we consider the graphene film to be in the middle of a SiC plate, which can, in principle, be achieved by pressing a substrate with graphene against a bare substrate with the same thickness. This case is described by the equation:

t±=4nτs[(n+1)2(n1)2τs2+Z0σ±2n(n+1+(n1)τs)2]1.
The computed spectra are plotted in Fig. 2(c). Now the cases τs = +1 and −1 are fundamentally different. In the first case the result for free-standing graphene (Eq. (4)) is again recovered. Indeed, the same transmission and rotation as in Fig. 2(a) are observed for these frequencies. However, if τs = −1 then t± =τs(1+Z0σ±/2n2)−1, which means that the effective conductivity of graphene is reduced by a factor of n2 ≈ 10 as compared to Eq. (4). Although this case is beneficial for the overall transmission, the Faraday rotation is so small that this case is not of practical interest for magneto-optical applications. Thus, the configuration with graphene in the middle is not more advantageous for the enhancement of the Faraday rotation than the original one.

Finally, the SiC slab in the previous configuration can be turned into a high-finesse Fabry-Perot cavity by coating each of the SiC-vacuum interfaces with a highly reflecting metallic layer. This can be modeled by substituting n ± 1 → n ± 1 ± Z0σm in Eq. (6), where σm is the sheet optical conductivity of the deposed metal, which we assume to be magneto-optically inactive. In Fig. 2(d) we present such a calculation for a metallic layer with a Drude conductivity of σm(ω) = σDC/(1 − iωτ), a static value σDC = 0.1 Ω−1 and a scattering rate 1/τ = 100 cm−1. The finesse of the cavity is about 10 in the considered spectral range. Now the Faraday rotation reaches about 20 degrees at some frequencies. This is more than twice higher than the maximum achievable value in the uncoated cavity (Fig. 2(c)), which is a manifestation of the cavity boost [6]. Although the cavity principle works, the obvious penalty is that the total transmission is significantly reduced because of the low transmission of the metallic mirrors. By comparing Figs. 2(b) and (d) we conclude that placing graphene on both sides of a low-finesse cavity, i.e increasing the number of magneto-optically active layers, is a better strategy to increase the Faraday rotation without drastically reducing the transmission.

One should note that the magneto-optically inactive graphene layers in the present sample, modeled with the term σb, only reduce the transmission without improving the rotation. In monolayer graphene grown on the Si-face [28, 29], such layers are absent and the transmission is expected to be higher than in the data presented here, with a similar value of the Faraday rotation.

In conclusion, we report a significant enhancement of the Faraday rotation in graphene due to constructive Fabry-Perot interference in the substrate as compared to the case where the interference is not resolved. We show that under these conditions the total transmission of the system is also increased. This observation, as well as our simulations of the Faraday rotation and transmission in related graphene-cavity systems, contribute to a possible use of graphene for novel magneto-plasmonic applications. Even though the absolute rotation angles achievable with graphene do not compete at the moment with the values obtained with the aid of conventional thick magneto-optical materials, the potential possibility to tune the effect by electrostatic gating opens avenues for new functionalities, such as an ultrafast inversion of the rotation angle by electric field. The results obtained in this work may also be of interest when combined with a lasing medium inside the cavity [30].

Acknowledgments

We acknowledge Daniel Chablaix, Michaël Tran and Mehdi Brandt for technical assistance. This work was supported by the SNSF through project 140710 and via the NCCR “Materials with Novel Electronic Properties - MaNEP”. We acknowledge support by the EC under Graphene Flagship (contract no. CNECT-ICT-604391).

References and links

1. L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett. 9, 2610–2613 (2009). [CrossRef]   [PubMed]  

2. J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol. 7, 472–478 (2012). [CrossRef]   [PubMed]  

3. N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011). [CrossRef]   [PubMed]  

4. F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009). [CrossRef]   [PubMed]  

5. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics 7, 48–51 (2011). [CrossRef]  

6. A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011). [CrossRef]  

7. I. Fialkovsky and D. V. Vassilevich, “Faraday rotation in graphene,” The European Physical Journal B 85, 1–10 (2012). [CrossRef]  

8. H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98, 261915–261915–3 (2011). [CrossRef]  

9. A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett. 101, 231605–231605–4 (2012). [CrossRef]  

10. R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm. 4, 1841 (2013). [CrossRef]  

11. H. Da and C.-W. Qiu, “Graphene-based photonic crystal to steer giant faraday rotation,” Appl. Phys. Lett. 100, 241106–241106–4 (2012). [CrossRef]  

12. Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013). [CrossRef]  

13. I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B 84, 035103 (2011). [CrossRef]  

14. J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun. 152, 1294–1300 (2012). [CrossRef]  

15. R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics 3, 1079–1083 (1964). [CrossRef]  

16. J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters 26, 849–851 (1990). [CrossRef]  

17. R. Wagreich and C. Davis, “Magnetic field detection enhancement in an external cavity fiber fabry-perot sensor,” Journal of Lightwave Technology 14, 2246–2249 (1996). [CrossRef]  

18. D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett. 66, 3546–3548 (1995). [CrossRef]  

19. C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B 108, 19912–19916 (2004). [CrossRef]  

20. C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006). [CrossRef]   [PubMed]  

21. M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett. 97, 266405 (2006). [CrossRef]  

22. I. Crassee et al., To be published.

23. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095013 (2009). [CrossRef]  

24. O. S. Heavens, Thin film physics (Methuen, 1970).

25. T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn. 71, 1318–1324 (2002). [CrossRef]  

26. 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, 1308–1308 (2008). [CrossRef]   [PubMed]  

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

28. K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8, 203–207 (2009). [CrossRef]   [PubMed]  

29. C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett. 103, 246804 (2009). [CrossRef]  

30. T. Morimoto, Y. Hatsugai, and H. Aoki, “Cyclotron radiation and emission in graphene — a possibility of landau-level laser,” Journal of Physics: Conference Series 150, 022059 (2009). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
    [CrossRef] [PubMed]
  2. J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
    [CrossRef] [PubMed]
  3. N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
    [CrossRef] [PubMed]
  4. F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009).
    [CrossRef] [PubMed]
  5. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
    [CrossRef]
  6. A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
    [CrossRef]
  7. I. Fialkovsky and D. V. Vassilevich, “Faraday rotation in graphene,” The European Physical Journal B85, 1–10 (2012).
    [CrossRef]
  8. H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett.98, 261915–261915–3 (2011).
    [CrossRef]
  9. A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett.101, 231605–231605–4 (2012).
    [CrossRef]
  10. R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
    [CrossRef]
  11. H. Da and C.-W. Qiu, “Graphene-based photonic crystal to steer giant faraday rotation,” Appl. Phys. Lett.100, 241106–241106–4 (2012).
    [CrossRef]
  12. Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
    [CrossRef]
  13. I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
    [CrossRef]
  14. J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun.152, 1294–1300 (2012).
    [CrossRef]
  15. R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics3, 1079–1083 (1964).
    [CrossRef]
  16. J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters26, 849–851 (1990).
    [CrossRef]
  17. R. Wagreich and C. Davis, “Magnetic field detection enhancement in an external cavity fiber fabry-perot sensor,” Journal of Lightwave Technology14, 2246–2249 (1996).
    [CrossRef]
  18. D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett.66, 3546–3548 (1995).
    [CrossRef]
  19. C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
    [CrossRef]
  20. C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
    [CrossRef] [PubMed]
  21. M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett.97, 266405 (2006).
    [CrossRef]
  22. I. Crassee and , To be published.
  23. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics11, 095013 (2009).
    [CrossRef]
  24. O. S. Heavens, Thin film physics (Methuen, 1970).
  25. T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn.71, 1318–1324 (2002).
    [CrossRef]
  26. 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, 1308–1308 (2008).
    [CrossRef] [PubMed]
  27. A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett.100, 117401 (2008).
    [CrossRef] [PubMed]
  28. K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
    [CrossRef] [PubMed]
  29. C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett.103, 246804 (2009).
    [CrossRef]
  30. T. Morimoto, Y. Hatsugai, and H. Aoki, “Cyclotron radiation and emission in graphene — a possibility of landau-level laser,” Journal of Physics: Conference Series150, 022059 (2009).
    [CrossRef]

2013 (2)

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
[CrossRef]

2012 (5)

H. Da and C.-W. Qiu, “Graphene-based photonic crystal to steer giant faraday rotation,” Appl. Phys. Lett.100, 241106–241106–4 (2012).
[CrossRef]

J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun.152, 1294–1300 (2012).
[CrossRef]

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

I. Fialkovsky and D. V. Vassilevich, “Faraday rotation in graphene,” The European Physical Journal B85, 1–10 (2012).
[CrossRef]

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett.101, 231605–231605–4 (2012).
[CrossRef]

2011 (5)

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett.98, 261915–261915–3 (2011).
[CrossRef]

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
[CrossRef]

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
[CrossRef]

2009 (6)

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009).
[CrossRef] [PubMed]

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics11, 095013 (2009).
[CrossRef]

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett.103, 246804 (2009).
[CrossRef]

T. Morimoto, Y. Hatsugai, and H. Aoki, “Cyclotron radiation and emission in graphene — a possibility of landau-level laser,” Journal of Physics: Conference Series150, 022059 (2009).
[CrossRef]

2008 (2)

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, 1308–1308 (2008).
[CrossRef] [PubMed]

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

2006 (2)

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett.97, 266405 (2006).
[CrossRef]

2004 (1)

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

2002 (1)

T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn.71, 1318–1324 (2002).
[CrossRef]

1996 (1)

R. Wagreich and C. Davis, “Magnetic field detection enhancement in an external cavity fiber fabry-perot sensor,” Journal of Lightwave Technology14, 2246–2249 (1996).
[CrossRef]

1995 (1)

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett.66, 3546–3548 (1995).
[CrossRef]

1990 (1)

J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters26, 849–851 (1990).
[CrossRef]

1964 (1)

R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics3, 1079–1083 (1964).
[CrossRef]

Ando, T.

T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn.71, 1318–1324 (2002).
[CrossRef]

Aoki, H.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

T. Morimoto, Y. Hatsugai, and H. Aoki, “Cyclotron radiation and emission in graphene — a possibility of landau-level laser,” Journal of Physics: Conference Series150, 022059 (2009).
[CrossRef]

Avouris, P.

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009).
[CrossRef] [PubMed]

Bai, J.

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
[CrossRef]

Berger, C.

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett.97, 266405 (2006).
[CrossRef]

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Blake, P.

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, 1308–1308 (2008).
[CrossRef] [PubMed]

Bludov, Y. V.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
[CrossRef]

Booshehri, L. G.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Booth, T. J.

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, 1308–1308 (2008).
[CrossRef] [PubMed]

Bostwick, A.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Bretenaker, F.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett.66, 3546–3548 (1995).
[CrossRef]

Brown, N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

Carbone, F.

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

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics11, 095013 (2009).
[CrossRef]

Castro Neto, A. H.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
[CrossRef]

Coletti, C.

C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett.103, 246804 (2009).
[CrossRef]

Conrad, E. H.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Crassee, I.

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
[CrossRef]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

I. Crassee and , To be published.

Da, H.

H. Da and C.-W. Qiu, “Graphene-based photonic crystal to steer giant faraday rotation,” Appl. Phys. Lett.100, 241106–241106–4 (2012).
[CrossRef]

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett.98, 261915–261915–3 (2011).
[CrossRef]

Dai, Z.

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Davis, C.

R. Wagreich and C. Davis, “Magnetic field detection enhancement in an external cavity fiber fabry-perot sensor,” Journal of Lightwave Technology14, 2246–2249 (1996).
[CrossRef]

de Heer, W. A.

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett.97, 266405 (2006).
[CrossRef]

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Drew, H. D.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

Elle, J. A.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

Emtsev, K. V.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Fallahi, A.

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett.101, 231605–231605–4 (2012).
[CrossRef]

Fan, H.

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
[CrossRef]

Feng, R.

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Ferreira, A.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
[CrossRef]

Fialkovsky, I.

I. Fialkovsky and D. V. Vassilevich, “Faraday rotation in graphene,” The European Physical Journal B85, 1–10 (2012).
[CrossRef]

First, P. N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Fuhrer, M. S.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

Gabor, N. M.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Geim, A. K.

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, 1308–1308 (2008).
[CrossRef] [PubMed]

Grigorenko, A. N.

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, 1308–1308 (2008).
[CrossRef] [PubMed]

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics11, 095013 (2009).
[CrossRef]

Hass, J.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

Hatsugai, Y.

T. Morimoto, Y. Hatsugai, and H. Aoki, “Cyclotron radiation and emission in graphene — a possibility of landau-level laser,” Journal of Physics: Conference Series150, 022059 (2009).
[CrossRef]

Hauge, R. H.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Heavens, O. S.

O. S. Heavens, Thin film physics (Methuen, 1970).

Heer, W. A. d.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

Herriott, D. R.

R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics3, 1079–1083 (1964).
[CrossRef]

Hibino, H.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

Hilton, D. J.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Horn, K.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Iwasaki, T.

C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett.103, 246804 (2009).
[CrossRef]

Jacob, D.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett.66, 3546–3548 (1995).
[CrossRef]

Jarillo-Herrero, P.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Jenkins, G. S.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

Jobst, J.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Jopson, R.

J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters26, 849–851 (1990).
[CrossRef]

Kawayama, I.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Kellogg, G. L.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Kim, M.-H.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

Kono, J.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Kuzmenko, A. B.

J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun.152, 1294–1300 (2012).
[CrossRef]

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
[CrossRef]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

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

Le Floch, A.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett.66, 3546–3548 (1995).
[CrossRef]

Le Naour, R.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett.66, 3546–3548 (1995).
[CrossRef]

Levallois, J.

J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun.152, 1294–1300 (2012).
[CrossRef]

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
[CrossRef]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

Levitov, L. S.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Ley, L.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Li, T.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Li, X.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Liang, G.

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett.98, 261915–261915–3 (2011).
[CrossRef]

Licht, S.

J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters26, 849–851 (1990).
[CrossRef]

Lin, Y.-m.

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009).
[CrossRef] [PubMed]

Ma, Q.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Marchenkov, A. N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Marel, D. v. d.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

Martinez, G.

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett.97, 266405 (2006).
[CrossRef]

Matsunaga, R.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

Mayou, D.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

McChesney, J. L.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Milchberg, H. M.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

Morimoto, T.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

T. Morimoto, Y. Hatsugai, and H. Aoki, “Cyclotron radiation and emission in graphene — a possibility of landau-level laser,” Journal of Physics: Conference Series150, 022059 (2009).
[CrossRef]

Mueller, T.

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009).
[CrossRef] [PubMed]

Nair, N. L.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Nair, R. R.

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, 1308–1308 (2008).
[CrossRef] [PubMed]

Naud, C.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

Novoselov, K. S.

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, 1308–1308 (2008).
[CrossRef] [PubMed]

Ogbazghi, A. Y.

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Ohta, T.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Ostler, M.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

Pereira, V.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
[CrossRef]

Peres, N. M. R.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
[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,” Science320, 1308–1308 (2008).
[CrossRef] [PubMed]

Perruisseau-Carrier, J.

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett.101, 231605–231605–4 (2012).
[CrossRef]

Pint, C. L.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Potemski, M.

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett.97, 266405 (2006).
[CrossRef]

Qiu, C.-W.

H. Da and C.-W. Qiu, “Graphene-based photonic crystal to steer giant faraday rotation,” Appl. Phys. Lett.100, 241106–241106–4 (2012).
[CrossRef]

Ren, L.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Ren, Z.

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
[CrossRef]

Reshanov, S. A.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Rice, W. D.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Riedl, C.

C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett.103, 246804 (2009).
[CrossRef]

Röhrl, J.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Rosenberg, R.

R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics3, 1079–1083 (1964).
[CrossRef]

Rotenberg, E.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Rubinstein, C. B.

R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics3, 1079–1083 (1964).
[CrossRef]

Sadowski, M. L.

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett.97, 266405 (2006).
[CrossRef]

Schmid, A. K.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Seyller, T.

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
[CrossRef]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics11, 095013 (2009).
[CrossRef]

Shimano, R.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

Song, J. C. W.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Song, Z.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

Starke, U.

C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett.103, 246804 (2009).
[CrossRef]

Stauber, T.

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, 1308–1308 (2008).
[CrossRef] [PubMed]

Stone, J.

J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters26, 849–851 (1990).
[CrossRef]

Stulz, L.

J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters26, 849–851 (1990).
[CrossRef]

Sushkov, A. B.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

Suzuura, H.

T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn.71, 1318–1324 (2002).
[CrossRef]

Takeya, K.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Tanabe, S.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

Taniguchi, T.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Taychatanapat, T.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Tonouchi, M.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Tran, M.

J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun.152, 1294–1300 (2012).
[CrossRef]

Valdes-Garcia, A.

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009).
[CrossRef] [PubMed]

Vallet, M.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett.66, 3546–3548 (1995).
[CrossRef]

van der Marel, D.

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
[CrossRef]

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

van Heumen, E.

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

Vassilevich, D. V.

I. Fialkovsky and D. V. Vassilevich, “Faraday rotation in graphene,” The European Physical Journal B85, 1–10 (2012).
[CrossRef]

Viana-Gomes, J.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
[CrossRef]

Wagreich, R.

R. Wagreich and C. Davis, “Magnetic field detection enhancement in an external cavity fiber fabry-perot sensor,” Journal of Lightwave Technology14, 2246–2249 (1996).
[CrossRef]

Waldmann, D.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Walter, A. L.

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
[CrossRef]

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

Wang, L.

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
[CrossRef]

Wang, X.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Watanabe, K.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

Weber, H. B.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Wu, X.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

Xia, F.

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009).
[CrossRef] [PubMed]

Xu, X. L.

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
[CrossRef]

Yan, J.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

Yoo, J. Y.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

Yumoto, G.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

Zakharov, A. A.

C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett.103, 246804 (2009).
[CrossRef]

Zheng, Y.

T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn.71, 1318–1324 (2002).
[CrossRef]

Zhou, Y.

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
[CrossRef]

Appl. Phys. Lett. (4)

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett.98, 261915–261915–3 (2011).
[CrossRef]

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett.101, 231605–231605–4 (2012).
[CrossRef]

H. Da and C.-W. Qiu, “Graphene-based photonic crystal to steer giant faraday rotation,” Appl. Phys. Lett.100, 241106–241106–4 (2012).
[CrossRef]

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett.66, 3546–3548 (1995).
[CrossRef]

Applied Optics (1)

R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics3, 1079–1083 (1964).
[CrossRef]

Electronics Letters (1)

J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters26, 849–851 (1990).
[CrossRef]

J. Phys. Chem. B (1)

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B108, 19912–19916 (2004).
[CrossRef]

J. Phys. Soc. Jpn. (1)

T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn.71, 1318–1324 (2002).
[CrossRef]

Journal of Lightwave Technology (1)

R. Wagreich and C. Davis, “Magnetic field detection enhancement in an external cavity fiber fabry-perot sensor,” Journal of Lightwave Technology14, 2246–2249 (1996).
[CrossRef]

Journal of Physics: Conference Series (1)

T. Morimoto, Y. Hatsugai, and H. Aoki, “Cyclotron radiation and emission in graphene — a possibility of landau-level laser,” Journal of Physics: Conference Series150, 022059 (2009).
[CrossRef]

Nano Lett. (1)

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009).
[CrossRef] [PubMed]

Nat. Comm. (1)

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm.4, 1841 (2013).
[CrossRef]

Nat. Mater. (1)

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater.8, 203–207 (2009).
[CrossRef] [PubMed]

Nat. Nanotechnol. (2)

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012).
[CrossRef] [PubMed]

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol.4, 839–843 (2009).
[CrossRef] [PubMed]

Nature Physics (1)

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics7, 48–51 (2011).
[CrossRef]

New Journal of Physics (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics11, 095013 (2009).
[CrossRef]

Phys. Chem. Chem. Phys. (1)

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013).
[CrossRef]

Phys. Rev. B (2)

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B84, 035103 (2011).
[CrossRef]

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B84, 235410 (2011).
[CrossRef]

Phys. Rev. Lett. (3)

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett.97, 266405 (2006).
[CrossRef]

C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett.103, 246804 (2009).
[CrossRef]

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

Science (3)

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, 1308–1308 (2008).
[CrossRef] [PubMed]

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science334, 648–652 (2011).
[CrossRef] [PubMed]

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science312, 1191–1196 (2006).
[CrossRef] [PubMed]

Solid State Commun. (1)

J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun.152, 1294–1300 (2012).
[CrossRef]

The European Physical Journal B (1)

I. Fialkovsky and D. V. Vassilevich, “Faraday rotation in graphene,” The European Physical Journal B85, 1–10 (2012).
[CrossRef]

Other (2)

I. Crassee and , To be published.

O. S. Heavens, Thin film physics (Methuen, 1970).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Transmission (black squares, left axis) and Faraday rotation (red circles, right axis) spectra at 7 Tesla and 5 Kelvin. Note that the Faraday rotation scale is inverted. The horizontal line corresponds to zero Faraday rotation, the vertical line indicates the cyclotron frequency.

Fig. 2
Fig. 2

Simulation of the magneto-optical transmission and Faraday rotation of graphene on and in SiC for three different configurations. Note that the Faraday rotation scale is inverted. (a) Graphene covers one side of SiC, (b) graphene covers both sides of SiC, (c) graphene is in the middle of SiC slab, (d) graphene is in the middle of a SiC slab covered by metallic layers on both sides.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

σ ± ( ω ) = 2 D π i ω ω c + i γ + σ b
T = | t | 2 + | t + | 2 2 , θ F = 1 2 arg ( t t + )
t ± = 4 n τ s [ ( n + 1 ) 2 ( n 1 ) 2 τ s 2 + Z 0 σ ± ( n + 1 + ( n 1 ) τ s 2 ) ] 1 ,
t constr , ± = τ s ( 1 + Z 0 σ ± 2 ) 1 ,
t ± = 4 n τ s . [ ( n + 1 ) 2 ( n 1 ) 2 τ s 2 + 2 Z 0 σ ± ( n + 1 + ( n 1 ) τ s ) 2 + Z 0 2 σ ± 2 ( 1 τ s 2 ) ] 1 .
t ± = 4 n τ s [ ( n + 1 ) 2 ( n 1 ) 2 τ s 2 + Z 0 σ ± 2 n ( n + 1 + ( n 1 ) τ s ) 2 ] 1 .

Metrics