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Gravitational-Like Lens Based on Graphene Ripple

Published online by Cambridge University Press:  26 August 2015

Daqing Liu ,
Shuyue Chen ,
Ning Ma ,
Xiang Zhao  and
Zhuo Xu
Daqing Liu*
Affiliation:
School of Mathematics and Physics, Changzhou University, Changzhou 213164, China School of Science, Xi’an Jiaotong University, Xi’an 710049, China
Shuyue Chen
Affiliation:
School of Mathematics and Physics, Changzhou University, Changzhou 213164, China
Ning Ma
Affiliation:
Department of Physics, Taiyuan University of Technology, Taiyuan 030024, China School of Science, Xi’an Jiaotong University, Xi’an 710049, China
Xiang Zhao
Affiliation:
School of Science, Xi’an Jiaotong University, Xi’an 710049, China
Zhuo Xu
Affiliation:
Electronic Materials Research Laboratory, Xi’an Jiaotong University, Xi’an 710049, China
*
*Corresponding author.liudq@cczu.edu.cn
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Abstract

We conducted a semiclassical study on carrier movement in curved graphene. A previous attempt was made to show that curved graphene is a readily available and cheap laboratory material used to study general relativity effects, especially if the electron energies satisfy ${\rm 4}\:\mu {\rm eV}\,\ll\,\left| E \right|\,\ll\,{\rm 3}\:{\rm eV}$ . Furthermore, a gravitational-like lens can be constructed based on a special graphene ripple; this lens has neither chromatic nor cometic aberration. One can design an ideal electron lens using a graphene ripple.

Keywords

electron lensgravitational-like lenscometic aberrationgrapheneripple
Type
Equipment and Software Development
Information
Microscopy and Microanalysis , Volume 21 , Issue 5 , October 2015 , pp. 1207 - 1213
Copyright
© Microscopy Society of America 2015 

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References

Ahmedov, H. & Aliev, A.N. (2001). Exact solutions in 3D new massive gravity. Phys Rev Lett 106, 021301.Google Scholar
Banados, M., Teitelboim, C. & Zanelli, J. (1992). The black hole in three dimensional space time. Phys Rev Lett 69, 1849–1851.Google Scholar
Bao, W., Miao, F., Chen, Z., Zhang, H., Jang, W., Dames, C. & Lau, C.N. (2009). Controlled ripple texturing of suspended graphene and ultrathin graphite membranes. Nat Nanotechnol 4, 562–566.Google Scholar
Berry, M. (1976). Waves and Thom’s theorem. Adv Phy 25, 1–26.Google Scholar
Calmet, X. & Landsberg, G. (2012). Lower dimensional quantum black holes. In Black Holes: Evolution, Theory and Thermodynamics, Bauer, A.J. & Eiffel, D.G. (Eds.), pp. 157–202). USA: Nova Pub.Google Scholar
Cheianov, V.V., Fal’ko, V. & Altshuler, B.L. (2007). The focusing of electron flow and a Veselago lens in graphene p-n junctions. Science 315, 1252–1255.Google Scholar
Crassee, I., Levallois, J., Walter, A.L., Ostler, M., Bostwick, A., Rotenberg, E., Seyller, T., Marel, D.V.D. & Kuzmenko, A.B. (2010). Giant Faraday rotation in single- and multilayer graphene. Nat Phys 7, 48–51.Google Scholar
Cserti, J., P’alyi, A. & P’eterfalvi, C. (2007). Caustics due to a negative refractive index in circular graphene p-n junctions. Phys Rev lett 99, 246801.Google Scholar
Darabi, F., Atazadeh, K. & Rezaei-Aghdam, A. (2013). Generalized (2+1) dimensional black hole by Noether symmetry. Eur Phys J C 73, 2657–2663.Google Scholar
Deser, S., Jackiw, R. & ‘t Hooft, G. (1984). Three-dimensional Einstein gravity: Dynamics of flat space. Ann Phys 152, 220–235.Google Scholar
Emtsev, K.V., Bostwick, A., Horn, K., Jobst, J., Kellogg, G.L. & Ley, L. (2009). Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide. Nat Mater 8, 203–207.Google Scholar
Gonz’alez, J., Guinea, F. & Herrero, J. (2009). Propagating, evanescent, and localized states in carbon nanotube-graphene junctions. Phys Rev B 79, 165434.Google Scholar
Iorio, A. (2011). Weyl-gauge symmetry of graphene. Ann Phys 326, 1334–1353.Google Scholar
Iorio, A. (2012). Using Weyl symmetry to make graphene a real lab for fundamental physics. Eur Phys J Plus 127, 156–166.Google Scholar
Iorio, A. (2013). Graphene: QFT in curved spacetimes close to experiments. J Phys Conf Ser 442, 012056.Google Scholar
Iorio, A. & Lambiase, G. (2012). The Hawking-Unruh phenomenon on graphene. Phys Lett B 716, 334–337.Google Scholar
Iorio, A. & Lambiase, G. (2014). Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that. Phys Rev D 90, 025006.Google Scholar
Juan, F.D., Cortijo, A. & Vozmediano, M.A.H. (2007). Charge inhomogeneities due to smooth ripples in graphene sheets. Phys Rev B 76, 165409.Google Scholar
Juan, F.D., Sturla, M. & Vozmediano, M.A.H. (2012). Space dependent Fermi velocity in strained graphene. Phys Rev Lett 108, 227205.Google Scholar
Lee, Y., Bae, S., Jang, H., Jang, S., Zhu, S., Sim, S.H., Song, Y. II., Hong, B.H. & Ahn, J.H. (2010). Wafer-scale synthesis and transfer of graphene films. Nano Lett 10, 490–493.Google Scholar
Lemos, J.P.S. (1995). Cylindrical black hole in general relativity. Phys Lett B 353, 46–51.Google Scholar
Liu, D., Xu, Z., Ma, N. & Zhang, S. (2012 a). Graphene modulated by external fields: A nonresonant left-handed metamaterial. Appl Phys A 106, 949–954.Google Scholar
Liu, D., Zhang, S., Ma, N. & Li, X. (2012 b). Faraday rotation effect in periodic graphene structure. J Appl Phys 112, 023115.Google Scholar
Liu, D., Zhang, S., Zhang, E., Ma, N. & Chen, H. (2010). Anomalous valley magnetic moment of graphene. Europhys Lett 89, 37002.Google Scholar
Neto, A.H.C., Guinea, F., Peres, N.M.R., Novoselov, K.S. & Geim, A.K. (2009). The electronic properties of graphene. Rev Mod Phys 81, 109–162.Google Scholar
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V. & Firsov, A.A. (2004). Electric field effect in atomically thin carbon films. Science 306, 666–669.Google Scholar
Vozmediano, M.A.H., Katsnelson, M.I. & Guinea, F. (2010). Gauge fields in graphene. Phys Rep 496, 109–148.Google Scholar
Wallace, P. (1947). The band structure of graphite. Phys Rev 71, 622–639.Google Scholar
Weinberg, S. (1972). Gravitation and Cosmology: Principle and Applications of the General Theory of Relativity. USA: John Wiley and Sons, Inc. Pub.Google Scholar
Witten, E. (1988). 2+1 gravity as an exactly soluble system. Nucl Phys B 311, 46–78.Google Scholar
Zwierzycki, M. (2014). Transport properties of rippled graphene. J Phys Cond Mater 26, 135303.Google Scholar