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Graphene modulated by external fields: a nonresonant left-handed metamaterial

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Abstract

Combining Landau diamagnetism and differential magnetic susceptibility to an electromagnetic wave, we theoretically predict a graphene-sheet periodic structure, which exhibits a left-handed property to an electromagnetic wave in the infrared region by modulating external fields. Our new mechanism, unlike the usual mechanism, does not use resonant behavior and is thus able to synthesize broadband left-handed metamaterial.

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Notes

  1. Since the fermion velocity v F=c/300≪c, where c is the vacuum light speed, the long-wave limit is always correct in graphene.

  2. For instance, nonzero ϵ 2 will lead to an optical rotation effect, which we shall discuss in detail elsewhere.

  3. In physics, when a modulating magnetic field is applied perpendicularly to a graphene sheet, it will quantize the carrier energy level, which means that the carrier will possess a discrete energy level rather than a continuous one. One of the effects of this quantization is that the carriers’ total energy varies with the modulating magnetic field, which leads to Landau diamagnetism of the material. In graphene, because of the zero effective mass of the carriers and the relativistic-type spectrum of low-energy electrons and holes, such diamagnetism is more sensitive to the external fields and thus can be modulated efficiently by the external fields.

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Acknowledgements

The authors are very grateful to Prof. F.S. Qiu and Dr. M.G. Xia. This work was supported by the Key Grant Project of the Chinese Ministry of Education (Grant No. 708082), the National Basic Research Program of China (973 Program) (Grant No. 2009CB623306), the International Science & Technology Cooperation Program of China (Grant No. 2010DFR50480), the National Natural Science Foundation of China–NSAF (Grant No. 10976022) and the National Natural Science Foundation of China (Grant Nos. 50632030 and 11074196).

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Authors and Affiliations

  1. Department of Applied Physics, Non-equilibrium Condensed Matter and Quantum Engineering Laboratory KLME, Xi’an Jiaotong University, Xi’an, 710049, China

    Daqing Liu, Ning Ma & Shengli Zhang

  2. Electronic Materials Research Laboratory, Xi’an Jiaotong University, Xi’an, 710049, China

    Zhuo Xu

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  1. Daqing Liu
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  2. Zhuo Xu
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Correspondence to Daqing Liu.

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Liu, D., Xu, Z., Ma, N. et al. Graphene modulated by external fields: a nonresonant left-handed metamaterial. Appl. Phys. A 106, 949–954 (2012). https://doi.org/10.1007/s00339-011-6717-1

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  • DOI: https://doi.org/10.1007/s00339-011-6717-1

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