Plasmon-exciton polaritons in two-dimensional semiconductor/metal interfaces

Rapid Communication

Plasmon-exciton polaritons in two-dimensional semiconductor/metal interfaces

P. A. D. Gonçalves, L. P. Bertelsen, Sanshui Xiao, and N. Asger Mortensen

Phys. Rev. B 97, 041402(R) – Published 5 January 2018

Abstract

The realization and control of polaritons is of paramount importance in the prospect of novel photonic devices. Here, we investigate the emergence of plasmon-exciton polaritons in hybrid structures consisting of a two-dimensional transition-metal dichalcogenide (TMDC) deposited onto a metal substrate or coating a metallic thin film. We determine the polaritonic spectrum and show that, in the former case, the addition of a top dielectric layer and, in the latter case, the thickness of the metal film can be used to tune and promote plasmon-exciton interactions well within the strong-coupling regime. Our results demonstrate that Rabi splittings exceeding 100 meV can readily be achieved in planar dielectric/TMDC/metal structures under ambient conditions. We thus believe that this Rapid Communication provides a simple and intuitive picture to tailor strong coupling in plexcitonics with potential applications for engineering compact photonic devices with tunable optical properties.

Received 16 October 2017
Revised 13 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.041402

Physics Subject Headings (PhySH)

Exciton polariton Excitons Surface plasmon polariton Surface plasmons

2-dimensional systems Transition metal dichalcogenides

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. A. D. Gonçalves^1,2,3, L. P. Bertelsen², Sanshui Xiao^2,3, and N. Asger Mortensen^1,3,4,*

¹Center for Nano Optics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
²Department of Photonics Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
³Center for Nanostructured Graphene, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
⁴Danish Institute for Advanced Study, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

^*asger@mailaps.org

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Issue

Vol. 97, Iss. 4 — 15 January 2018

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Images

Figure 1
(a) Illustration of the dielectric/TMDC/metal system under consideration in this Rapid Communication. (b) Scheme of a TMDC electronic structure around the $K$ point, showing optical transitions from the spin-orbit split valence band to the exciton ground state (dubbed $A$ and $B$ excitons). Also plotted is the dielectric function data of ${WS}_{2}$ measured by Li et al. [21] together with the corresponding Lorentz oscillator fit $ε_{{WS}_{2}} (ω) = ε_{\infty} + \sum_{j} f_{j} / (ω_{j}^{2} - ω^{2} - i ω γ_{j})$ (see Ref. [22] for details on the parameters).
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Figure 2
Dispersion relation $ℏ ω$ versus $Re {q}$ of plasmon-exciton polaritons in $dielectric / {WS}_{2} / Au$ structures (the red solid lines) with different top dielectrics as indicated at the top of each panel. The dispersion of the SPP in the corresponding dielectric/Au interfaces is also plotted (the blue dashed lines) along with the energy of the ${WS}_{2}$ exciton $A$ (the horizontal dashed line) and the light lines (the dashed lines in light brown). The insets in each panel show a zoom of the area around the mode back-bending/anticrossing together with the Rabi splitting (marked by the arrows). The retrieved Rabi splitting energies are shown at the top of each panel and were used as a parameter in the analytical COM, whose result (up to a minute absolute vertical shift) is depicted by the green dashed lines in the insets.
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Figure 3
Rabi splitting energy (in meV) as a function of the dielectric constant of the top insulator in $dielectric / {WS}_{2} / Au$ structures.
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Figure 4
Reflectance spectra in an ATR configuration. (a) ATR spectra collected at different incident angles. The two uppermost (bottommost) curves are shifted vertically by 0.4 ( $- 0.4$ ) each in the interest of clarity. (b) Two-dimensional plot of the reflectance in an ATR experiment for arbitrary incident angles and excitation energies. The avoided crossing between each polariton branch can clearly be seen around the $A$ exciton energy at $ℏ Ω_{ex} = 2.014 eV$ . Parameters: $ε_{d} = 5, L = 90 nm$ (dielectric layer thickness), and $ε_{prism} = 16$ . We have halved the exciton $γ_{j}$ 's used thus far to simulate the effect of reducing the temperature (nevertheless, the general features remain essentially unchanged at room temperature, save for a slight increase in the linewidths).
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Figure 5
(a) Dispersion diagram $(Re {q}, ℏ ω)$ of plasmon-exciton polaritons in $dielectric / {WS}_{2} / Au / {WS}_{2} / dielectric$ structures with varying film thicknesses. The horizontal dashed line indicates the resonance of the $A$ exciton at $ℏ Ω_{ex} = 2.014 eV$ . The corresponding Rabi splittings are $ℏ Ω_{R} = 39, 49, 66, 101 meV$ in order of decreasing thickness. (b) Rabi splitting energy (in meV) as a function of the Au thin-film thickness in ${WS}_{2}$ -coated Au films embedded in a homogeneous dielectric medium with $ε_{d} = 2.1$ . The colored spheres correspond to the cases plotted in the top panel with matching colors. The horizontal dashed line indicates the $t \to \infty$ limit (corresponding to a thick Au substrate). In both panels we have used the experimentally obtained optical constants of Au [24] and of ${WS}_{2}$ [21].
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