Investigation of non-linear electrodynamic properties of graphene
Final Report Abstract
Graphene, a two-dimensional allotrope of carbon, has that unique electronic property that electrons in it behave like massless relativistic particles with an effective “velocity of light” which is about 300 times smaller than the real light velocity. This property was shown to lead to a strongly nonlinear electrodynamic response of graphene. Such physical phenomena as the frequency mixing, harmonics generation, optical rectification and so on, are observed in graphene under the electromagnetic irradiation substantially weaker than in many other nonlinear materials. In the project different nonlinear electrodynamic effects in graphene have been theoretically investigated. It was shown that conventional electromagnetic resonances like, e.g. the cyclotron and the plasma resonance, should have a broad linewidth even in the absence of any scattering, due to the specific massless spectrum of electrons in graphene. The third-order nonlinear electromagnetic response functions of graphene have been calculated within the quasi-classical and quantum theory. In particular, it has been predicted that the third harmonic generation should have a strong resonance at the near-infrared and optical frequencies, with the resonant frequency determined by the electron density in graphene which can be electrically controlled. A resonant enhancement of the second and third harmonics near the plasma resonances has been predicted, both in graphene, as well as in semiconductor electron systems. It was found that, under certain conditions, semiconductor low-dimensional electron systems can compete with graphene in the strength of the nonlinear response. Therefore, a general quantum theory of the second- and third-order electrodynamic response of a uniform electron-gas plasma (with conventional, “massive”, electrons) has been also developed. Effects of the microwave induced photoresistance response and the second harmonic generation have been investigated in a semiconductor plasma in a magnetic field. A new, unexpected phenomenon of the ferroelectric transition in the ground state of graphene and other two-dimensional crystals has been predicted. A graphene-based current-driven emitter of a coherent terahertz radiation has been proposed and patented, its theory has been developed. Most of the predicted nonlinear phenomena can be used for the design and development of new devices, such as detectors, rectifiers, frequency multipliers, mixers and oscillators, for microwave, terahertz, infrared and optical frequency ranges. The work on the creation of a prototype of one of such devices is currently running in collaboration with experimental groups in Europe (EU project www.gosfel.eu). The work on the theory of the nonlinear electrodynamics of graphene will be continued within the European project Graphene Flagship.
Publications
- Dielectric function and plasmons in graphene, Europhys. Lett. 87, 27005 (2009)
A. Hill, S. A. Mikhailov and K. Ziegler
- Nonlinear cyclotron resonance of a massless quasiparticle in graphene, Phys. Rev. B 79, 241309(R) (2009)
S. A. Mikhailov
- Coherent nonlinear optical response of graphene, Phys. Rev. Lett. 105, 097401 (2010)
E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko and S. A. Mikhailov
- Intervalley plasmons in graphene, Phys. Rev. B 82, 073411 (2010)
T. Tudorovskiy and S. A. Mikhailov
- Theory of the giant plasmon-enhanced second-harmonic generation in graphene and semiconductor two-dimensional electron systems, Phys. Rev. B 84, 045432 (2011)
S. A. Mikhailov
- Nonlinear broadening of the plasmon linewidth in a graphene stripe, New J. Phys. 14, 115024 (2012)
S. A. Mikhailov and D. Beba
(See online at https://doi.org/10.1088/1367-2630/14/11/115024) - Graphene-based voltage-tunable coherent terahertz emitter, Phys. Rev. B 87, 115405 (2013)
S. A. Mikhailov
(See online at https://doi.org/10.1103/PhysRevB.87.115405) - Graphene-based nanodevices for terahertz electronics, European patent No. 2602821 (granted in February 2014)
S. A. Mikhailov
- Microwave-induced zero-resistance states and second-harmonic generation in an ultraclean two-dimensional electron gas, Phys. Rev. B 89, 045410 (2014)
S. A. Mikhailov
(See online at https://doi.org/10.1103/PhysRevB.89.045410) - Nonlinear electromagnetic response of a uniform electron gas, Phys. Rev. Lett. 113, 027405 (2014)
S. A. Mikhailov
(See online at https://doi.org/10.1103/PhysRevLett.113.027405) - Quantum theory of third-harmonic generation in graphene, Phys. Rev. B 90, 241301(R) (2014)
S. A. Mikhailov
(See online at https://doi.org/10.1103/PhysRevB.90.241301)
