Current-controlled light scattering and asymmetric plasmon propagation in graphene

Tobias Wenger, Giovanni Viola, Jari Kinaret, Mikael Fogelström, and Philippe Tassin

Phys. Rev. B 97, 085419 – Published 14 February 2018

Abstract

We demonstrate that plasmons in graphene can be manipulated using a dc current. A source-drain current lifts the forward/backward degeneracy of the plasmons, creating two modes with different propagation properties parallel and antiparallel to the current. We show that the propagation length of the plasmon propagating parallel to the drift current is enhanced, while the propagation length for the antiparallel plasmon is suppressed. We also investigate the scattering of light off graphene due to the plasmons in a periodic dielectric environment and we find that the plasmon resonance separates in two peaks corresponding to the forward and backward plasmon modes. The narrower linewidth of the forward propagating plasmon may be of interest for refractive index sensing and the dc current control could be used for the modulation of mid-infrared electromagnetic radiation.

Received 3 October 2017

DOI:https://doi.org/10.1103/PhysRevB.97.085419

Physics Subject Headings (PhySH)

Electromagnetic field calculations Surface plasmons

Graphene

Linear response theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tobias Wenger¹, Giovanni Viola¹, Jari Kinaret², Mikael Fogelström¹, and Philippe Tassin²

¹Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-412 96 Göteborg, Sweden
²Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden

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Issue

Vol. 97, Iss. 8 — 15 February 2018

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Images

Figure 1
A schematic view of the system considered in this paper. A source and a drain contact are put far away and a bias voltage can be put over them. This generates a drift current in the graphene sheet and we study its influence on the properties of graphene plasmons. The plasmons can then be probed by infrared light in the subwavelength grating environment shown in the middle. In our calculations, the grating is taken to be infinitely large by use of periodic boundary conditions. The grating we consider has a periodicity of 130 nm and a filling fraction of 0.5, and the grating material has a dielectric constant $ɛ_{r} = 3$ . The height of the grating is taken to be 65 nm.
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Figure 2
The drift velocity $β$ as a function of the drift current. The parameter $β$ is scaled with the Fermi velocity in graphene. For large values of $β$ , the current becomes very large because the electron density also increases. Close to $β = 1$ we do not expect the simple model for the stationary electron distribution to be accurate and we constrain ourselves to $β \leq 0.8$ for this reason. The slope of the curve depends on the carrier density and in this paper we use $n = 1.886 \times 10^{12} {cm}^{- 2}$ ( $E_{F} = 0.16$ eV).
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Figure 3
Plasmon dispersion for various drift currents. For $β > 0$ ( $β < 0$ ), the electrons propagate parallel (antiparallel) to the plasmons. Plasmons propagating parallel to the drift velocity are blueshifted and obtain a higher group velocity. Conversely, the plasmons propagating antiparallel to the drift velocity are redshifted and acquire a lower group velocity. These effects increase with increasing magnitude of the drift velocity.
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Figure 4
The plasmon propagation distance for various drift velocities. At energies around the Fermi energy, the propagation is enhanced for plasmons propagating parallel to the drift velocity and it is reduced for plasmons propagating antiparallel to the drift velocity. For plasmon energies larger than the Fermi energy, the difference between parallel and antiparallel propagation is very large.
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Figure 5
Extinction curves as a function of incident wavelength for various values of $β$ . As $β$ is increased the plasmon peak separates into two distinguishable modes, related with plasmons propagating parallel and antiparallel to the drifting electrons. The separation of the modes grows as the magnitude of $β$ grows and for values around $β \geq 0.4$ the two peaks are visible.
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Figure 6
Propagation asymmetry—propagation length for plasmons parallel with the current divided by propagation length for plasmons antiparallel to the current—as a function of plasmon energy in units of the Fermi energy. The asymmetry is largest above the Fermi energy and grows with longer relaxation times.
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