Electric Field-Controlled Damping Switches of Coupled Dirac Plasmons

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Electric Field-Controlled Damping Switches of Coupled Dirac Plasmons

Huayang Zhang, Xiaodong Fan, Dongli Wang, Dongbo Zhang, Xiaoguang Li, and Changgan Zeng

Phys. Rev. Lett. 129, 237402 – Published 30 November 2022

Abstract

For quasiparticle systems, the control of the quasiparticle lifetime is an important goal, determining whether the related fascinating physics can be revealed in fundamental research and utilized in practical applications. Here, we use double-layer graphene with a boron nitride spacer as a model system to demonstrate that the lifetime of coupled Dirac plasmons can be remotely tuned by electric field-controlled damping pathways. Essentially, one of the graphene layers serves as an external damping amplifier whose efficiency can be controlled by the corresponding doping level. Through this damping switch, the damping rate of the plasmon can be actively tuned up to 1.7 fold. This Letter provides a prototype design to actively control the lifetime of graphene plasmons and also broadens our horizon for the damping control of other quasiparticle systems.

Received 25 June 2022
Accepted 2 November 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.237402

Physics Subject Headings (PhySH)

Atomic force microscopy Random phase approximation Scanning near-field optical microscopy Transport techniques

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Huayang Zhang ^1,2,3,¶, Xiaodong Fan ^1,2,3,*,¶, Dongli Wang^1,2,3, Dongbo Zhang^1,2,3, Xiaoguang Li ^4,†, and Changgan Zeng^1,2,3,‡

¹CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
²International Center for Quantum Design of Functional Materials (ICQD), Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
³Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui 230088, China
⁴Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, China

^*Corresponding author. fanxd@ustc.edu.cn
^†Corresponding author. xgli@szu.edu.cn
^‡Corresponding author. cgzeng@ustc.edu.cn
^¶These authors contributed equally to this work.

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Vol. 129, Iss. 23 — 2 December 2022

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Images

Figure 1
Coupled plasmon modes in the separated double-layer graphene system. (a) Simplified dispersions of coupled and single-layer plasmon modes. (b) Sketch of the layered heterostructure with top graphene (green), interlayer $h$ -BN (blue), and bottom graphene (red). (c) Plasmon fringes in the graphene/BN (3 nm)/graphene heterostructure detected by scanning near-field microscopy. The edge of the top-layer graphene is marked by a white dashed line. Scale bar, 200 nm. (d) Plasmon line profiles extracted from (c) along the dashed lines.
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Figure 2
Carrier density dependence of the coupled plasmons. (a) Side-view schematic of the dual-gate double-layer graphene device. (b) Plane schematic of the double-layer graphene device, including four regions: coupled region, top-layer graphene, bottom-layer graphene, and $h$ -BN. (c)–(f) Near-field images of the double-layer system (with an $h$ -BN spacer of 6.8 nm) with different carrier densities of the bottom-layer graphene ( $n_{b}$ ). The carrier density of the top-layer graphene ( $n_{t}$ ) is fixed at $- 9.8 \times 10^{12} {cm}^{- 2}$ (positive $n$ corresponds to holes; negative to electrons). All near-field intensities are normalized to the bare $h$ -BN region (the lower right part). Scale bar, 200 nm. (g) Corresponding line profiles along the black dashed lines (coupled region) and blue dashed line (single layer) in (c)–(f). (h) Solid points: the plasmon wavelength and intensity of coupled region as a function of $n_{b}$ (top axis). Open points: the ones of single-layer region as a function of $| n_{s} |$ (bottom axis). The plasmon intensity is defined by the normalized value at the first fringe maximum of the plasmons ( $S_{1} / S_{BN}$ ). (i) The variation of coupled plasmon wavelength when $n_{b}$ and $n_{t}$ simultaneously change for a device with an $h$ -BN spacer of 3.0 nm.
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Figure 3
Dispersions and damping of the coupled plasmon. (a) The calculated dispersion of the coupled plasmon with interlayer spacing $d = 6.8 nm$ and $n_{b} = - n_{t} = 9.8 \times 10^{12} {cm}^{- 2}$ . The blue color plots show the imaginary part of the Fresnel reflection coefficient (see Supplemental Material [25]). The calculated dispersion of the single-layer graphene plasmon (black line) is also provided for comparison ( $n_{s} = - 9.8 \times 10^{12} {cm}^{- 2}$ ). The red dashed line marks the excited photon energy of 115.9 meV. The orange shaded regions indicate the $h$ -BN phonon bands. (b) Experimental (red dots) and theoretical (blue color plots) carrier density dependence of plasmon wavelength and intensity. The color depth of the red dots and blue color plots represents the plasmon intensity. (c) Experimental (black dots) carrier density dependence of the damping rate. The theoretical results include the damping rate due to the impurity scattering $γ_{i}$ (magenta dashed line), and the damping rate $γ_{n}$ (blue dashed line) extracted from the numerical color plots. The red line shows the joint contribution of the two aspects. (d),(e) Illustration of the damping process when the Fermi level of the bottom-layer graphene is near and far away from the Dirac point, respectively. (f), (g) Plasmon dispersions of coupled plasmon for the cases of $n_{t} = - 9.8 \times 10^{12} {cm}^{- 2}$ , $n_{b} \approx 0$ , and $n_{b} = - n_{t} = 9.8 \times 10^{12} {cm}^{- 2}$ . (h),(i) Conceptual schematics of the plasmon damping switch.
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Figure 4
Interlayer spacing dependence of the coupled plasmon mode. (a) Near-field images and corresponding line profiles of coupled plasmons for different interlayer spacing $d$ ( $n_{b} = - n_{t} \approx 8.5 \times 10^{12} {cm}^{- 2}$ for all devices). Scale bar, 200 nm. (b) Experimental (red dots) and theoretical (blue color plots) $d$ of the wavelength and intensity. The color depth of red dots and blue color plots represents the plasmon intensity. The red circle shows the plasmon wavelength of single-layer graphene when $n_{s} \approx - 8.5 \times 10^{12} {cm}^{- 2}$ . (c) Variation in coupled plasmon wavelength when carrier density and $d$ simultaneously change.
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