Resonant Edge Magnetoplasmons and Their Decay in Graphene

N. Kumada, P. Roulleau, B. Roche, M. Hashisaka, H. Hibino, I. Petković, and D. C. Glattli

Phys. Rev. Lett. 113, 266601 – Published 22 December 2014

Abstract

We investigate resonant edge magnetoplasmons (EMPs) and their decay in graphene by high-frequency electronic measurements. From EMP resonances in disk shaped graphene, we show that the dispersion relation of EMPs is nonlinear due to interactions, giving rise to the intrinsic decay of EMP wave packets. We also identify extrinsic dissipation mechanisms due to interaction with localized states in bulk graphene from the decay time of EMP wave packets. We indicate that, owing to the linear band structure and the sharp edge potential, EMP dissipation in graphene can be lower than that in GaAs systems.

Received 2 July 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.266601

Authors & Affiliations

N. Kumada^1,2,*, P. Roulleau², B. Roche², M. Hashisaka³, H. Hibino¹, I. Petković², and D. C. Glattli²

¹NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi 243-0198, Japan
²Nanoelectronics Group, Service de Physique de l’Etat Condensé, IRAMIS/DSM (CNRS URA 2464), CEA Saclay, F-91191 Gif-sur-Yvette, France
³Department of Physics, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152-8551, Japan

^*kumada.norio@lab.ntt.co.jp

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Vol. 113, Iss. 26 — 31 December 2014

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Images

Figure 1
Schematic of the device. Disk shaped graphene is covered with 160 nm thick insulating layer. The capacitive injector and detector were deposited on top of the insulating layer. The overlap between the injector (detector) and graphene are $3 μ m$ in width. A sinusoidal wave or a voltage step is sent to the injector and the current response is detected through the detector.
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Figure 2
Results of frequency domain measurement. (a) and (b) Transmission signals of the 200- and $1000 − μ m$ samples, respectively. The differentiated transmission power ( $d | S_{21} |^{2} / d B$ ) is plotted as a function of the frequency and $B$ . Open dots with error bar indicate the resonant frequency at high $B$ (details for the accurate determination of the resonant frequency are given in [23]). Inset in (a) shows the longitudinal resistance ( $R_{x x}$ ; red thick trace) and the Hall resistance ( $R_{x y}$ ; blue trace) of a Hall bar device fabricated from the same graphene wafer obtained by standard dc measurement. (c) Dispersion relation of the EMP mode: the resonant frequencies [open dots in (a) and (b)] are plotted as a function of $λ^{- 1}$ determined by Eq. (1). The data point for the 5th harmonics in the $1000 − μ m$ sample coincides with that for the fundamental mode in the $200 − μ m$ sample at $λ^{- 1} = 5 {mm}^{- 1}$ . The solid curve is the dispersion relation given by Eq. (2). The dashed line is the result of the linear fit for small $λ^{- 1}$ regime, which gives the group velocity $v_{g} = d f / d λ^{- 1} = 1.7 \times 10^{6} m / s$ .
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Figure 3
Results of time domain measurement. (a) Differential signal ( $d S / d B$ ) of the $200 − μ m$ sample a function of time and $B$ . Inset shows $d S / d B$ at $B = 6.5 T$ (red thick trace) and $B = - 6.5 T$ (blue trace). The chirality of the EMP orbital motion is counterclockwise (clockwise) for positive (negative) $B$ . (b) $S (B > 0) - S (B < 0)$ for the $200 − μ m$ sample.
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Figure 4
Temperature dependence of EMP decay. (a) and (b) $S (10 T) - S (- 10 T)$ at $T = 4 K$ for the 200- and $1000 − μ m$ samples, respectively. Insets show the traces at $T = 30 K$ . Black traces represent results of the simulation (details are indicated in the main text). (c) $τ$ for the $200 − μ m$ sample as a function of $T$ . (d) $ln (β T)$ as a function of $T^{- 1 / 2}$ . Linear fit gives $T_{0}^{1 / 2} = 26.9 \pm 1.4 K^{1 / 2}$ in Eq. (3). (e) Illustration and equivalent circuit model for the EMP dissipation through interaction with localized states in the interior of graphene.
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