Observation of Tunable Charged Exciton Polaritons in Hybrid

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Observation of tunable charged exciton polaritons in hybrid monolayer WS2 – plasmonic nanoantenna system Jorge Cuadra, Denis G. Baranov, Martin Wersäll, Ruggero Verre, Tomasz J. Antosiewicz, and Timur Shegai Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b04965 • Publication Date (Web): 25 Jan 2018 Downloaded from http://pubs.acs.org on January 29, 2018

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Observation of tunable charged exciton polaritons in

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hybrid monolayer WS2 – plasmonic nanoantenna system

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Jorge Cuadra1,*, Denis G. Baranov1, Martin Wersäll1, Ruggero Verre1, Tomasz J.

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Antosiewicz1,2 and Timur Shegai1,*

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Department of Physics, Chalmers University of Technology, 412 96, Göteborg, Sweden.

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Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland.

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[email protected]; [email protected]

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ACS Paragon Plus Environment

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Abstract

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Formation of dressed light-matter states in optical structures, manifested as Rabi splitting of

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the eigen energies of a coupled system, is one of the key effects in quantum optics. In

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pursuing this regime with semiconductors, light is usually made to interact with excitons –

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electrically neutral quasiparticles of semiconductors, meanwhile interactions with charged

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three-particle states – trions – have received little attention. Here, we report on strong

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interaction between localized surface plasmons in silver nanoprisms and excitons and trions

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in monolayer tungsten disulphide (WS2). We show that the plasmon-exciton interactions in

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this system can be efficiently tuned by controlling the charged versus neutral exciton

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contribution to the coupling process. In particular, we show that a stable trion state emerges

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and couples efficiently to the plasmon resonance at low temperature by forming three

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bright intermixed plasmon-exciton-trion polariton states. Our findings open up a possibility

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to exploit electrically charged polaritons at the single nanoparticle level.

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Keywords: strong coupling, exciton, trion, TMDC, monolayer WS2.

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Introduction

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Interaction between light and matter is at the heart of modern optics. It is present in

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atomic physics as well as in solid state systems and plays an essential role in cavity

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quantum electrodynamics (cQED). When the rate of energy exchange between photons and

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matter excitations becomes faster than the decoherence rates of both subsystems, a special

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regime of light-matter interactions called strong coupling is achieved

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conditions formation of polaritons, that are hybrid states possessing both light and matter

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character, is observed. Recently it has been shown that metallic nanoparticles enable this

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non-perturbative regime of light-matter interaction due to a combination of deeply

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subwavelength confinement of electromagnetic radiation with large transition dipole

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moments of molecular excitons 6-8.

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1-5

. Under these

Monolayers of transition metal dichalcogenides (TMDC) are semiconductor 9

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materials with a direct band gap transition

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reaching values of 10% for MoS2 and as much as 15% for WS2 at resonance 10, 11. The high

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absorptivity of TMDC monolayers makes them ideal candidates for realization of the strong

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coupling regime. Importantly, TMDCs support both neutral (X) and charged (T) exciton

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resonances

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spin-valley degree of freedom accessible by optical dichroism

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exploring valley polaritons

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nanophotonic resonators have been reported in various systems including optical

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microcavities

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single plasmonic nanoantenna level, strong coupling has been recently demonstrated at

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room temperature between excitons in WS2 and Au nanorods 24 and WSe2 and Ag nanorods

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Indeed, enhancement as well as modification of PL signal has been reported in various

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realizations in the weak coupling regime

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chemically inert, stable and robust at ambient conditions, what makes them advantageous

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for active and nonlinear plasmonics applications 32.

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and exceptionally high optical absorption

. Additionally, the large spin-orbit coupling in these materials permits a

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and opens routes for

. Observations of strong coupling between TMDCs and

and diffractive modes of plasmonic nanoparticle arrays

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. At the

. Photoluminescence (PL) can also be affected by coupling to plasmonic nanoantennas. 26-31

. Importantly, monolayer TMDCs are

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Such active control has been demonstrated in various hybrid nanostructures,

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including controllable and reversible switching of the strong coupling regime in ACS Paragon Plus Environment

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microcavities loaded with photochromic molecules 33, silver nanoparticle arrays under UV

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illumination

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femtosecond pumping

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modification of the polariton composition

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and lasing of plasmon-exciton polaritons have been reported recently

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these works reversible switching was demonstrated in the systems that involved only

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electrically neutral excitations.

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, ultrafast tuning of strongly-coupled metal-molecular aggregates via 35, 36

, electrostatic gating and temperature control 38

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, and dynamical

. Demonstrations of thermalization, cooling, 39-41

. However, in

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Conversely, relatively little attention has been devoted to strong coupling with

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charged excitons. Such interactions would result in the formation of exciton polaritons

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carrying a non-zero net electrical charge and thus open routes to manipulate light with

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electricity and vice versa. Several works report observation of charged polaritons in

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microcavities loaded with quantum wells at low temperature 42-44, charged quantum dots 45,

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tunable polaron polaritons 21 and MoSe2 monolayers in microcavities 17. Electrostatic gating

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of a MoS2 monolayer coupled with a plasmonic diffractive array also showed signatures of

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charged excitons being involved in the coupling, although strong coupling with trions was

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not reported

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. Electro-optical control of trions in the Fano regime was also demonstrated

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very recently . The existence of charged exciton polaritons opens a number of intriguing

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perspectives, as such quasiparticles are anticipated to strongly interact with each other and

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to improve charge and exciton transport properties mediated by strong coupling 44, 48.

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Here, we demonstrate strong interactions between plasmons in an individual silver

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nanoprism and neutral as well as charged excitons in monolayer WS2. The latter is

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especially interesting, as this opens up a new way to control and manipulate charge via

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light-matter interactions and vice versa. In this study we show that the degree of plasmon-

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exciton-trion coupling can be tailored by temperature. In particular, by tuning the

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temperature in the wide range between 6 and 300 K, we are able to observe a transition

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from two polaritonic resonances at room temperature, corresponding to plasmon-exciton

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interaction, to the formation of three polaritonic resonances at T=6 K, corresponding to

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three body intermixed plasmon-exciton-trion polaritons.


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Figure 1. Hybrid 2D material – nanoparticle plasmon system. (a) Bright field optical image of the exfoliated WS2 flake. Monolayer regions are marked by the dotted line (scale bar 50 µm). (b) PL spectra of the WS2 as a function of temperature. The red curve shows the PL taken at room temperature. The resonance at 616 nm corresponds to the neutral A-exciton (X), while the trion (T) peak is absent. The blue curve shows the PL at T=6 K. The peak at 598 nm is the neutral A-exciton that blue-shifts at low temperature. The peak at 611 nm is the trion (T) and dominates the PL emission. At intermediate temperatures, T=200 K and T=77 K, PL spectra show both X and T peaks, whose resonance position and relative intensity depend on the temperature. (c) DF microscope image of the WS2 flake covered with silver nanoprisms. Monolayer regions are marked by the red dotted line (scale bar 50 µm). (d) Artist view of the hybrid system: high density of photonic states (hot-spots) is shown at the corners of the nanoprism, which overlaps with the WS2 monolayer for efficient plasmon-exciton interaction. Inset shows the SEM image of such a particle (scale bar 100 nm) and a magnified view of a corresponding DF image.

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Results

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System under study. The coupled system in this work is composed of colloidal silver

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nanoprisms positioned on top of a WS2 monolayer. We start by preparing the monolayer by

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mechanical exfoliation from a high quality crystal and transferring it to a thermally

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oxidized silicon substrate. The monolayer nature of the WS2 flake, which can readily reach

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sizes greater than ~100 µm (see Fig. 1a), is confirmed by optical contrast and a bright PL

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signal – typical for direct bandgap semiconductors (Fig. 1b). The PL spectrum at 300 K


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under ambient conditions shows maximum at 2.012 eV ( ) and corresponds to the neutral

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A-exciton with a binding energy of about 700 meV 49. The PL signal at 200 K and 77 K, in

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contrast to the room temperature data, exhibits two peaks: the high-energy resonance

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(2.07 eV) and the low-energy peak (2.03 eV). We assign the former to the neutral A-

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exciton, which undergoes a blue-shift, whereas the latter corresponds to the positively

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charged exciton ( ) – a trion. Upon further cooling to T=6 K several additional peaks are

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observed in the PL spectrum, the two peaks at high energy being the exciton and trion,

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whereas the additional peaks may arise due to bound excitons, which become stable at low

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temperature 50, 51.

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The trion state dominates the PL at low temperatures and has a binding (or

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dissociation) energy of about 40 meV in agreement with earlier reports 49. The trion state is

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likely positively charged because of the high density of electron acceptors in the polymer

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layer used in this study to facilitate binding of plasmonic nanostructures (see Methods and

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Fig. S3). For comparison, in the Supporting Information (SI) we show reflectivity and PL

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data for the WS2 without the p-doped polymer layer. We note that in recent studies on field

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effect transistors incorporating WS2, trions of both positive and negative polarities and

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dissociation energies, which depend on the applied gate voltage, were reported

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Similarly, positive trions arising from a charge transfer process were observed in van der

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Waals WS2/MoS2 heterostructures 53. The latter effect is analogous to the one caused by the

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p-doped polymer layer in the present work. We also note that the trion states were

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previously reported to be stabilized by molecular doping 54.

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.

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The second ingredient to construct the hybrid system in this study is the silver

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nanoprism (see Fig. 1d). These nanoparticles were prepared by a seed mediated colloidal

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synthesis and are single crystalline in nature, which greatly improves the quality factor of

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the plasmon resonance and thus its coupling to the 2D material 55. A typical nanoprism has

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dimensions of about 60-80 nm in side length and about 10 nm in thickness. Such nanoprism

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dimensions result in a plasmon resonance, , overlapping with the exciton transition, ,

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in the monolayer WS2. Thus, by combining these two materials one could expect strong

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plasmon-exciton interactions. In order to verify this expectation, we positioned Ag

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nanoprisms on top of the WS2 monolayer by drop casting a nanoparticle suspension on a

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polymer pre-coated substrate (see Methods). As a result we obtain a monolayer WS2 flake


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covered with Ag nanoprisms of various sizes as is evidenced by the dark-field (DF) optical

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microscopy (see Fig. 1c). The colourful spots in the image are individual Ag nanoprisms

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(confirmed by SEM measurements) possessing different plasmon resonances. Such

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within the same sample. A combined 2D material - silver nanoprism system is

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configuration allows us to study a variety of plasmon-exciton resonance detunings

depicted schematically in Fig. 1d. The regions of maximal electric field enhancement

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around the nanoprism are localized at the corners of the prism and are shown schematically

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by the bright spots. Insets show a magnified DF image of a single nanoprism and an SEM

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image of the coupled system. The latter confirms that an individual nanoprism is measured

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in the optical microscope.

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Figure 2. Coupled system at various temperatures. Left: Dark-field scattering spectra at T=300, 200, 77 and 6 K. At room temperature the DF spectrum depicts two peaks, namely the upper and lower polaritons. At lower temperatures the DF spectrum shows three peaks that are identified as upper, middle and lower polaritons. Arrows represent the splitting caused by excitons at 300 K whereas the splitting is caused by excitons and trions at 6 K. (Inset: SEM image of the corresponding individual Ag nanoprism. Scale bar = 100 nm). Right: Artist view of plasmon-exciton mixture at T=300 K and plasmon-exciton-trion interaction at T=6 K.

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Temperature evolution of the coupled system. We now explore the evolution of the

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strongly coupled system by varying its temperature (see Methods for experimental details).

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Since the PL spectrum exhibits appearance of an additional trion resonance at low

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temperatures, one could expect involvement of this additional resonance into plasmon-

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exciton coupling process. The temperature evolution of the DF spectra of the coupled


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system is shown in Fig. 2. SEM confirms that the system is an individual Ag nanoprism

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(inset Fig. 2). At room temperature, the scattering reveals the splitting of the resonance into

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two peaks, which, as will be demonstrated later arises from strong plasmon-exciton

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coupling, i.e. the formation of polaritons. By cooling the system, the trion contribution to

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the PL spectrum starts to emerge due to oscillator strength redistribution between the

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exciton and trion resonances. This redistribution in turn affects the coupling between the

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plasmonic nanoprism and the 2D material, which we monitor via the DF spectroscopy. We

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observe an emergence of two dips in the DF spectra as the temperature is reduced (Fig. 2).

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Upon cooling to liquid nitrogen (77 K) and liquid helium (6 K) temperatures, the trion state

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becomes more and more pronounced in both PL and DF spectra. Cooling is also

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accompanied by a blue shift of both exciton and trion resonances. This behavior is

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consistent with the standard semiconductor behavior under low temperatures (see SI and

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Fig. S5). It is also worth noting that at T=6 K we do not observe any signature of

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interaction between localized/bound states and the plasmonic cavity, likely due to the

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insignificant oscillator strength these states possess 56.

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As exciton and trion resonances are spectrally detuned by only ∼40 meV with

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respect to each other, the interaction of both exciton and trion resonances with the

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plasmonic cavity can occur, because the plasmon line width is typically much broader than

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the exciton-trion spectral detuning. The hybrid system thus experiences a transition from

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plasmon-exciton interactions at room temperature to more complex plasmon-exciton-trion

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interactions at low temperatures, which is schematically illustrated in Fig. 2 (right panel).

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To shed more light on the nature of the coupled states, we perform DF scattering

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measurements for nanoparticles of several different sizes and therefore plasmonic

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resonances. These experiments in turn allow to extract the anti-crossing relations

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characterizing the strong coupling regime of interaction.


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Figure 3. Anti-crossing behaviour of the coupled system. (a) Left: Red and blue circles represent experimental upper and lower polariton (UP and LP) eigen energies as a function of plasmon resonance position extracted from dark field spectra of individual silver nanoprism – monolayer WS2 hybrids of various sizes and plasmon-exciton detuning at T = 300 K. Solid red and blue lines represent the eigen energies extracted from the Hamiltonian analysis Eq. (1a). Black solid lines indicate exciton and plasmon resonances. Right: Hopfield coefficients for plasmon and exciton contributions to UP and LP states as a function of plasmon resonance. (b) Left: Red, green and blue circles represent experimental UP, MP (middle polariton) and LP eigen energies as a function of plasmon resonance position extracted from dark field spectra of individual silver nanoprism – monolayer WS2 hybrids of various sizes and plasmon-exciton-trion detuning at T = 6 K. Solid red, green and blue lines represent the eigen energies extracted from the Hamiltonian analysis Eq. (1b). Black solid lines indicate exciton, trion and plasmon resonances. Right: Hopfield coefficients for plasmon, exciton and trion contributions to UP, MP and LP states as a function of plasmon resonance.

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Hamiltonian analysis and anti-crossing. Depending on the temperature, the hybrid system

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can be described by plasmon-exciton or plasmon-exciton-trion interactions. To describe

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these interactions we use a matrix representation of a corresponding Hamiltonian (see

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Eq. 1). We choose to analyse T=6 K and 300 K temperature points in depth, as these

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temperatures represent the most extreme coupling scenarios in this study. The intermediate

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temperature points can be considered as a smooth transition between these two extremes.

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The composition of the hybrid states can be modelled by diagonalizing the Hamiltonian of the coupled system:


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ℏ ℋ

ℏ ℋ

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(1a) 0

(1b)

where , , and are the widths of the plasmon, exciton and trion, respectively, while

and are the plasmon-exciton and plasmon-trion interaction constants, respectively.

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At room temperature, we adopt Eq. 1a, while at 6 K we use Eq. 1b. Note, that we assume

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no direct coupling between excitons and trions and any interaction between them is

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mediated by the plasmon.

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The diagonalization of these Hamiltonians yields new polaritonic eigenfrequencies

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and Hopfield coefficients, which represent the contribution of plasmons, excitons and trions

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to each polariton state

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. To perform the analysis, we first obtain the corresponding

eigenfrequencies for the upper − , middle −

,

and lower − ! polaritons (or ,

! for the room temperature), from experimental DF data. Since and are known

from independent PL and/or reflectivity measurements, we obtain the unknown from

the equalities that connect the hybrid eigenfrequencies with the original uncoupled ones:

+

+ ! + + (or + ! + ). These equalities

naturally follow from trace invariance of the matrix representation of the Hamiltonian. We

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plot the dispersion (or anti-crossing) curves obtained by measuring several different

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plasmonic nanoantennas of slightly different plasmon resonance frequencies. The

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experimental anti-crossing curves are then fitted with polariton eigenfrequencies, extracted

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using the corresponding Hamiltonian model. The results are shown in Fig. 3 with

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corresponding spectra plotted in Fig. S2.

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Figure 3a depicts the resulting dispersion curves at room temperature. In order to

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claim strong coupling one needs to observe anti-crossing behavior between the involved

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resonances. Moreover, the mode splitting needs to be larger than the decay rate of the

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polaritonic eigenstates. The Rabi splitting is extracted as the minimal splitting between the

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two polariton branches, which occurs at zero detuning. For T = 300 K the analysis yields


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Rabi splitting of Ω ≈ 120 meV. This value has to be compared with the plasmon and exciton linewidths. The linewidths of the non-interacting plasmonic nanoparticles are measured in an independent experiment and yield ≈ 190 meV (see Fig. S1 for details)

and the exciton width = 20 meV. One thus finds that Ω > ( + )/2, implying that

the system satisfies the strong coupling criterion 2, 58. The resulting Hopfield coefficients of

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the upper and lower polariton versus the plasmon energy are shown in Fig. 3a and display a

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standard plasmon-exciton intermixing behavior, whose contribution depends on the

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plasmon-exciton detuning. We note that the Rabi splitting observed in this study exceeds

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those in recently reported observations claiming strong coupling on individual nanoantenna 24, 25

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level at room temperature

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nanoprisms used in this study. In the Numerical calculations section below we further

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discuss this point and complement the experimental scattering results with calculated

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absorption spectra and anti-crossing. We thus conclude that the mode splitting observed at

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room temperature arises due to strong coupling between nanoparticle plasmons and neutral

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excitons in WS2.

, likely due to a more compressed mode volume of Ag

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Let us now turn our attention to the more interesting low temperature case T = 6 K

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(Fig. 3b). In this case, we observe emergence of three anti-crossed bands, corresponding to

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upper, middle and lower polaritons. We notice immediately (see Eq. 1b) that at low

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temperatures the splitting between any polaritonic branches depends on both plasmon-

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exciton and plasmon-trion coupling strengths, as well as the resonant frequencies

and widths of all contributing parts, resulting in no simple analytical expressions for

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polariton eigenfrequencies. As a consequence, no simple criteria for the strong coupling in

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this case apply. We therefore rely on fitting the experimental data with Eq. 1b in order to

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extract the parameters of the coupled system. Based on the fitting, the minimal splitting

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between the upper and lower polariton branches is around Ω()*+) ≈ 150 meV, which is about 30 meV larger than the Rabi splitting at room temperature. Such an increase can be

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explained by the fact that exciton and trion are detuned with respect to each other by

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∼40 meV. At the same time, both plasmon and exciton resonances are narrowed upon

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cooling. Exciton line narrowing at low temperature is a well-documented behaviour

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consistent with previous results

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trion system (see Fig. S3). Plasmon narrowing under cooling was also reported previously

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and confirmed here for the uncoupled exciton and


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can be as narrow as 110 meV and up to 150 meV for particles with similar morphology as

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the ones studied in the hybrid system (see Fig. S1). We adopt an average value of

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and confirmed here in a control experiment (see Fig. S1). The plasmon decay rate at 6 K

= 130 meV for the plasmon linewidth. The exciton and trion line widths at this

temperature can be extracted from the corresponding PL (or reflectivity) spectra, yielding = 10 meV and = 20 meV, respectively. These values are much narrower than the

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plasmon resonance width. The collective plasmon-exciton-trion interaction at this

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, )/2. Moreover, the emergence of three polariton bands also allows to experimentally

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temperature thus satisfies the simplified strong coupling criterion as Ω()*+) > > ( +

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measure the splittings between the upper and middle polariton and middle and lower

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polariton, respectively. These splittings extracted at the zero detuning between plasmon and

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Ω-)*+) ≈ 77 meV and thus both of them individually also satisfy the simplified strong

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exciton and plasmon and trion bands respectively are Ω()*-) ≈ 81 meV and

coupling condition as Ω()*-) , Ω-)*+) > ( + , )/2 . However, due to the

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abovementioned complexity of the eigenvalue problem in this case, these criteria should be

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considered as crude estimations only. In the Numerical calculations section below we

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complement these estimations with more solid arguments such as observation of anti-

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crossing in absorption spectra of the coupled system. Based on these calculations, we

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conclude that the mode splitting observed at 6 K arises due to just reached strong coupling

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between nanoparticle plasmons and excitons and trions in WS2.

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We note that the Hopfield coefficients show that all the polariton branches arise as a

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result of contribution from all the system components – plasmons, excitons and trions (see

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Fig. 3b right panel). Thus in the coupled plasmon-exciton-trion system the intermixing of

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all three system constituents is observed. This is a very intriguing situation, because it

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implies that all the polariton branches possess non-zero net electrical charge. For this

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reason these hybrid states can potentially have an impact on charge transport, a situation

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reported recently in the organic semiconductor microcavity system 48. Optical nonlinearity

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should also be strongly affected by the fermionic nature of the trion which can result in

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strong nonlinear behavior compared to the pure bosonic case of a neutral exciton.

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The plasmon-exciton (and plasmon-trion) coupling rates can be deduced by fitting

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the experimental anti-crossing data in Fig. 3. The extracted values from the fitting give


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≈ 74 meV for room temperature, and ≈ 54 meV and ≈ 59 meV for 6 K. The

emergence of , together with the reduction of , can be attributed to a redistribution of

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oscillator strength from excitons to trions upon cooling. This is consistent with both PL and

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reflectivity data measured on bare WS2 monolayers (see Fig. S3) and can be explained by

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the amount of p-doping in the WS2 and the increased stability of the trion at low

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temperature

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. Another important observation is that (T 300K) 2 (T

6K)+ (T 6K) , indicating that a total number of particles interacting with the

plasmonic field is conserved in the experiments.

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10 11 12 13 14 15 16 17 18

Figure 4. Numerical calculations. (a,b) Scattering cross-sections spectra as a function of temperature. At T = 300 K the dielectric function of WS2 was assumed to have only one resonance energy corresponding to uncharged exciton X, while at T=6 K both T and X contribute to the signal. The points as well as the curves are the experimental data and the fitting obtained in Fig. 3. Parameters of the model: 456 () dielectric

function for silver is taken from Palik 63, WS2 from Ref. 10, nanoprism side length L=70 nm, height H=10 nm, nanoprism edges are rounded with radius of curvature r ~ 5 nm. TMDC layer was positioned on a dielectric slab with refracting index n = 1.5 that mimics a glass substrate. The whole system is embedded in vacuum. (c) Scattering cross section at zero detuning for 300 and 6 K. (d) Total, silver and WS2 absorption cross-sections


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spectra as a function of temperature. Note splitting observed at both temperatures, which confirms the intermediate coupling regime. (e) Electromagnetic energy density distribution within the nanoparticle and the 2D material at λ = 577. Note logarithmic scale. Both top and side views are shown. Scale bar = 30 nm.

Numerical calculations.

6

We have previously shown that observation of anti-crossing in scattering data of

7

individual plasmonic nanoparticles cannot alone warrant reaching the strong coupling 64, as

8

such anti-crossing can be confused with enhanced absorption

9

66

65

or Fano resonance regime

. The safest way to rule out the weak coupling scenario is to increase the Rabi splitting

10

until it significantly overcomes the plasmon linewidth. This was achieved previously in J-

11

aggregate based systems in scattering 6, 7 and photoluminescence 8 experiments. In the case

12

studied here the observed splitting does not significantly overcome the plasmon linewidth.

13

Thus to draw a definitive conclusion about the regime of interaction in this study, we

14

perform additional numerical calculations, which show that anti-crossing is observed not

15

only in scattering, but also in absorption of the coupled system and its independent

16

constituents. These calculations provide additional evidence that the strong coupling

17

scenario in these experiments is indeed achieved 65.

18

Numerical calculations were performed using the finite-difference time domain

19

(FDTD) method (see Methods). We first perform the numerical anti-crossing calculation in

20

a manner similar to our previous study 65. In particular, we fit the dielectric function of Ag

21

by the Drude dispersion model and then vary the plasma frequency. This allows to tune the

22

plasmon resonance with respect to the exciton at 300 K, whose permittivity is extracted

23

from literature and used without any further open parameters 10. By doing so we obtain the

24

anti-crossing curves while only slightly changing the coupling conditions on account of the

25

mode volume being predominantly defined by the geometrical volume of the particle. This

26

is shown in Fig. 4a (plasmon-exciton coupling). We then superimpose the numerical anti-

27

crossing in scattering with experimental data from Fig. 3a and find a striking agreement

28

between experimental and theoretical results (see Fig. 4a). We thus proceed to resolve anti-

29

crossing in total absorption as well as in its individual components – Ag nanoprism and the

30

WS2 monolayer, which all exhibit the anti-crossing behaviour, thereby proving that strong

31

coupling is reached in this system

32

scattering spectrum obtained for the case of zero detuning. Excellent matching to

65

(see Fig. 4a). Additionally, in Fig. 4c we plot the


14

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1

experimental spectra is observed, considering the only free parameter is the size of the Ag

2

nanoprism. Of course, this freedom is limited by the span of dimensions of the Ag

3

nanoprism observed in SEM.

4

To conduct a corresponding study of the plasmon-exciton-trion system, we first

5

model it at zero detuning to match the exciton and trion lines to experimental data (see

6

Methods) with the nanoprism size fixed in the previous calculations. The matching of the

7

numerical scattering spectrum (Fig. 4c) and the experimental one (Fig. 2) demonstrates the

8

correctness of our phenomenological description of the exciton and trion at 6 K. We thus

9

proceed to investigate anti-crossing, with results shown in Fig. 4b

10

The computed scattering spectra for the plasmon-exciton-trion case match

11

extremely well with the experimental anti-crossing (overlaid points) as shown in Fig. 4b.

12

The total absorption as well as its components in Ag nanoprism and the WS2 monolayer

13

also exhibit the anti-crossing behaviour between the three hybrid eigen states (see Fig. 4b).

14

With our Ag-WS2 model validated, we plot the absorption cross-section of the coupled

15

system along with its components in Fig. 4d. The data show clear splitting of absorption in

16

the Ag nanoprism, on the other hand, absorption spectra of the WS2 monolayers shows only

17

a shoulder development, demonstrating that our system is marginally reaching the strong

18

coupling regime 65. The small splitting in the 2D material absorption is explained by a lack

19

of long-lived oscillations between Ag and WS2. As shown in Fig. S6, the time evolution of

20

the Rabi oscillations is short-lived and exhibits only one significant period. A similar

21

observation can be drawn from the oscillations of the electric fields around the Ag triangle,

22

where the excitation energy alternates between the plasmon-polariton (visible enhanced

23

fields) and the 2D material (see SI movies).

24

We further inspect the electromagnetic energy density distributions 67 in the coupled

25

system (Fig. 4e). We observe that the mode in the nanoprism is confined mainly to its

26

interior. We also observe that while the energy density in the WS2 is greater than in Ag, the

27

monolayer occupies only a small volume due to its two-dimensionality and therefore the

28

total energy stored in the metal and the 2D material is similar. For single nanoparticles the

29

mode is concentrated within its volume

30

excitonic material needs not only a large transition dipole moment, but it is also necessary

31

to maximize the overlap between the plasmonic field mode and the exciton states 7, 66, what

68-70

and to obtain long-lived Rabi oscillations the


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Page 16 of 25

1

in the present case would ideally amount to saturating the small fraction of the mode

2

volume located outside the metal resonator. In the present case this is not possible (Fig. 4e),

3

yet filling up a small fraction of the mode volume with the 2D material is enough to reach

4

the strong coupling, due to the large transition dipole moment of WS2 (78 ≈56 Debye

5

We thus conclude that a coupled plasmon-exciton-trion polariton system comprising a

6

silver nanoprism and monolayer WS2 is very useful for practical realization of strong

7

coupling.

71

).

8 9

Discussion

10

To conclude, we have demonstrated that the optical response of the strongly coupled

11

system can be tailored by tuning the temperature. At low temperatures the plasmonic cavity

12

strongly interacts with excitons and trions in the monolayer WS2, whereas at room

13

temperature only the neutral exciton is coupled to the plasmon.

14

We note that the temperature-dependent PL signal of the WS2 monolayer and in

15

particular the second resonance at low energy appearing upon decreasing of temperature

16

follows the trend associated with the trion state 13. Other low energy states like bound states

17

or localized excitons

18

temperatures

19

we assign the low energy peak observed in the PL spectrum (Fig. 1b) and the low energy

20

dip in the scattering spectra (Fig. 2) to the trion. Here, the trion state is stabilized by low

21

temperature and chemical p-doping 54.

72

50, 51

have lower dissociation energies and are not stable at elevated

. Moreover, the bound states have low oscillator strength

56

. Based on this,

22

We note that there are several other processes that may play an important role in our

23

study and in general in plasmon-TMDC coupled systems. First, a charge transfer process

24

between monolayer TMDC and metallic surfaces can occur as a result of the proximity

25

effect

26

study, the 2D material and Ag nanoprism were separated by a polymer and citrate

27

stabilizing layers, which prevent direct metal-TMDC contact. Second, exciton and trion

28

states in close proximity to a metallic surface may have renormalized binding energies and

29

oscillator strength due to non-local screening effects, which is unique for 2D materials

73

. This can potentially affect the behavior of the coupled system; however, in this


74

.

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1

This effect can also affect the behaviour of the coupled system; however, in our DF

2

scattering data, we do not observe large renormalization effects. Finally, the plasmon-trion

3 4

coupling here, ≈ 70 meV, exceeds the trion binding energy, ≈ 40 meV, which

is an interesting regime since the light-matter coupling surpasses the Coulomb interaction

5

in this case. It was recently predicted theoretically that in this regime the trion orbital and

6

spin properties are strongly modified

7

exciton-trion interactions in the present case and were not taken into account in the FDTD

8

calculations. Future theoretical investigations involving the quantum mechanical nature of

9

interacting quasiparticles are needed to properly account for these interactions.

75

. These effects may have an impact on plasmon-

10

In this work we achieve strong coupling with the Rabi splitting of ∼120 meV at

11

room temperature, which is higher than in previous realizations 24, 25. In addition to that, we

12

also demonstrate formation of plasmon-exciton-trion polaritons at low temperature. Trions

13

were observed previously in more extended systems, like microcavities and plasmonic

14

lattices

15

an individual nanoparticle and with a very small number of involved trions and excitons,

16

making this contribution especially interesting for quantum and nonlinear applications 76, 77.

17

Based on the analysis above, it is tempting to estimate the number of excitons

18

contributing to the coupling process in this case, especially keeping in mind the large

19

transition dipole moment of WS2. Our estimation is based on the well-known relation for

20 21

42-44, 46

. However, in the present case this is achieved at a truly nanoscopic scale of

the coupling strength √:78 |? | √:78 @ℏ/(244A B) . For the nanotriangles considered in the present work (side lengths in the range 60–80 nm and 10 nm thick) the

22

geometrical volume is on the order of (1.5 – 2.8) × 104 nm3. For such small single particles

23

the mode volume is mainly determined by the geometrical one, however, a nearby high-

24

refractive index material can substantially decrease it

25

permittivity of monolayer WS2 decreases the mode volume by approximately 50%. Thus

26 27 28 29 30

66

. In our case the high background

using the above quoted lower bound of B=0.7 × 104 nm3, a value which was verified in

FDTD calculations using the approach for dispersive weakly radiating cavities

68

and

78 =56 D for exciton resonant at 2 eV coupled to such a cavity yields a coupling strength of

∼30 meV. To account for the measured splitting of 120 meV at room temperature the

required coupling strength needs to be ≈ 74 meV due to the mismatch in the plasmon ACS Paragon Plus Environment

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1 2 3 4 5 6 7

Page 18 of 25

and exciton widths. Hence, the upper bound of the number of excitons is : < 10. The

measured Rabi splitting at 6 K is around 150 meV, giving an approximate exciton and trion coupling strength of ≈ ≈ 50 meV. As the energy difference of both transitions is negligible for the purposes of this estimation, in both cases the expected lower bound on the

number of interacting excitons and trions is : 2 : < 5, when accounting for the

influence of the permittivity of the surrounding material. This number closely approaches

the quantum optics limit of : 1, thus making this system potentially interesting for

8

studying photon-photon interactions at the nanoscale. Moreover, due to Coulomb repulsion

9

charged exciton-polaritons are expected to interact with each other stronger than their

10

neutral counterparts. Thus, this system might exhibit stronger nonlinear response as

11

compared to a purely bosonic situation.

12

More generally, our findings demonstrate the principal possibility of studying

13

electrically charged polaritons in a form of plasmon-exciton-trion hybrids. Here, this is

14

done at low temperature to ensure the trion stability, however, by stabilization of the trion

15

state by other means, for example by electrostatic doping, similar effects can be anticipated

16

at room temperature

17

constitute a coherent mixture of excitons, trions and cavity excitations may find use in

18

charge transport and optoelectronic devices by boosting the carrier mobility 48 in analogous

19

way to the theoretically predicted exciton transport enhancement mediated by a cavity 78, 79.

20

This new degree of freedom – charged polaritons is the central observation of this work. In

21

view of the discussion above, we envision that these findings may find potential

22

implications for various optoelectronic applications, such as light harvesting and light

23

emitting devices, and for strong photon-photon interactions.

46, 47, 49

. Constructing macroscopic coherent polariton states that will

24 25

Methods

26

Sample preparation: Silver nanoprisms were synthesized from solution using a seed-

27

mediated protocol. WS2 were mechanically exfoliated from bulk crystal (HQ-graphene) and

28

transferred to a Si wafer with a thermally oxide layer (50 nm-thick) using the all-dry

29

transfer method

80

. Monolayers were identified by photoluminescence spectra and optical


18

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1

contrast. In order to ensure a proper density of nanoprisms covering the monolayer flake, an

2

adhesion layer was deposited before the nanoprism (Polylisine 0.25 mg/mL), then

3

nanoparticles are drop-cast and let them rest for 2 min, the excess of solution is gently

4

removed by an absorptive tissue.

5

We note that the polymer layer that we utilize to adhere silver nanoprisms to the

6

monolayer WS2 plays an important role in the stabilization of the trions. This is likely

7

induced by the chemical doping

8

state since the adhesion layer tends to p-dope WS2. To demonstrate this, in the Supporting

9

information (see Fig. S4) we perform a control experiment which shows that strong

54

. The trion in this case is mostly a positively charged

10

plasmon-trion coupling is not observed in the absence of the poly-lysine adhesion layer.

11

Optical measurements: Dark-field optical microscopy and spectroscopy measurements

12

were done using a laser driven light source (ENERGETIQ EQ-99XFC) with side

13

illumination configuration at an angle of about 500. For photoluminescence experiments,

14

the sample was excited by a CW 532 nm (2.33 eV) laser under irradiance of ∼100 W/cm2.

15

PL and DF signals were collected using a 20× objective (Nikon, NA=0.45) and directed to

16

a fibre-coupled 30 cm spectrometer (Andor Shamrock SR-303i) equipped with a CCD

17

detector (Andor iDus 420). Low temperature measurements were performed using a cold

18

finger optical cryostat (Janis).

19

FDTD anti-crossing: FDTD calculations were carried out using the commercial solver

20

from Lumerical, Inc. The silver prisms are assumed to be triangular in shape with an edge

21

length in the range of 60-80 nm, thickness 10 nm, edge rounding of 3 nm and corner

22

rounding of 10 nm. They are modelled as a dispersive Drude metal with parameters

23

180 THz to match the experimental permittivity around 600 nm. For anti-crossing studies

24

obtained by fitting tabulated data from Palik with DE 3.7 , 13 PHz, and

25

the plasma frequency was varied from about 7 to 10 eV. The silver prisms in experiments

26

are coated by a molecular stabilizing layer which was modelled as a dispersionless

27

dielectric with a refractive index of 1.4. The dielectric susceptibility of WS2 monolayer at

28

room temperature (corresponding solely due to neutral exciton contribution) is taken from

29

literature and is used without further modification

10

. To obtain the permittivity of a WS2


19

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Page 20 of 25

1

monolayer at 6 K we use reflectivity and photoluminescence measurements (see Fig. S3) to

2

estimate the exciton and trion linewidths and spectral positions. The oscillator strengths of a

3

1 nm thick layer representing the WS2 monolayer are based on available literature and

4

further refined based on our own measurements in FDTD by matching the calculated and

5

experimental scattering spectra. The monolayer and coated Ag nanoprism are placed on a

6

glass substrate (n = 1.45) and illuminated by a plane wave at normal incidence. The

7

meshing which assured converged results was 0.5 nm in the x and y directions (transverse)

8

and 0.2 nm in the longitudinal direction (z-axis).

9 10

The authors declare no competing financial interest.

11


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References

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43. Rapaport, R.; Qarry, A.; Cohen, E.; Ron, A.; Pfeiffer, L. N. physica status solidi (b) 2001, 227, (2), 419-427. 44. Rapaport, R.; Cohen, E.; Ron, A.; Linder, E.; Pfeiffer, L. N. Physical Review B 2001, 63, (23), 235310. 45. Rakher, M. T.; Stoltz, N. G.; Coldren, L. A.; Petroff, P. M.; Bouwmeester, D. Physical Review Letters 2009, 102, (9), 097403. 46. Lee, B.; Liu, W.; Naylor, C. H.; Park, J.; Malek, S. C.; Berger, J. S.; Johnson, A. T. C.; Agarwal, R. Nano Letters 2017, 17, (7), 4541-4547. 47. Li, B.; Zu, S.; Zhou, J.; Jiang, Q.; Du, B.; Shan, H.; Luo, Y.; Liu, Z.; Zhu, X.; Fang, Z. ACS Nano 2017, 11, (10), 9720-9727. 48. Orgiu, E.; George, J.; Hutchison, J. A.; Devaux, E.; Dayen, J. F.; Doudin, B.; Stellacci, F.; Genet, C.; Schachenmayer, J.; Genes, C.; Pupillo, G.; Samori, P.; Ebbesen, T. W. Nat Mater 2015, 14, (11), 1123-1129. 49. Zhu, B.; Chen, X.; Cui, X. Scientific Reports 2015, 5, 9218. 50. Jones, A. M.; Yu, H.; Ghimire, N. J.; Wu, S.; Aivazian, G.; Ross, J. S.; Zhao, B.; Yan, J.; Mandrus, D. G.; Xiao, D.; Yao, W.; Xu, X. Nat Nano 2013, 8, (9), 634-638. 51. Wang, G.; Bouet, L.; Lagarde, D.; Vidal, M.; Balocchi, A.; Amand, T.; Marie, X.; Urbaszek, B. Physical Review B 2014, 90, (7), 075413. 52. Liu, B.; Zhao, W.; Ding, Z.; Verzhbitskiy, I.; Li, L.; Lu, J.; Chen, J.; Eda, G.; Loh, K. P. Advanced Materials 2016, 28, (30), 6457-6464. 53. Xu, W.; Liu, W.; Schmidt, J. F.; Zhao, W.; Lu, X.; Raab, T.; Diederichs, C.; Gao, W.; Seletskiy, D. V.; Xiong, Q. Nature 2017, 541, (7635), 62-67. 54. Mouri, S.; Miyauchi, Y.; Matsuda, K. Nano Letters 2013, 13, (12), 5944-5948. 55. Jin, R.; Cao, C. Y.; Hao, E.; Me'traux, G. S.; Schatz, G. C.; Mirkin, C. A. Nature 2003, 425, 487-490. 56. Kavokin, A. V. Physical Review B 1994, 50, (11), 8000-8003. 57. Hopfield, J. J. Physical Review 1958, 112, (5), 1555-1567. 58. Savasta, S.; Saija, R.; Ridolfo, A.; Di Stefano, O.; Denti, P.; Borghese, F. ACS Nano 2010, 4, (11), 6369-6376. 59. Moody, G.; Kavir Dass, C.; Hao, K.; Chen, C.-H.; Li, L.-J.; Singh, A.; Tran, K.; Clark, G.; Xu, X.; Berghäuser, G.; Malic, E.; Knorr, A.; Li, X. Nature Communications 2015, 6, 8315. 60. Dey, P.; Paul, J.; Wang, Z.; Stevens, C. E.; Liu, C.; Romero, A. H.; Shan, J.; Hilton, D. J.; Karaiskaj, D. Physical Review Letters 2016, 116, (12), 127402. 61. Liu, M.; Pelton, M.; Guyot-Sionnest, P. Physical Review B 2009, 79, (3), 035418. 62. Arora, A.; Koperski, M.; Nogajewski, K.; Marcus, J.; Faugeras, C.; Potemski, M. Nanoscale 2015, 7, (23), 10421-10429. 63. Palik, E. D., Handbook of Optical Constants of Solids I. Academic Press: San Diego, 1998. 64. Zengin, G.; Johansson, G.; Johansson, P.; Antosiewicz, T. J.; Käll, M.; Shegai, T. Sci. Rep. 2013, 3, 3074. 65. Antosiewicz, T. J.; Apell, S. P.; Shegai, T. ACS Photonics 2014, 1, (5), 454-463. 66. Yang, Z.-J.; Antosiewicz, T. J.; Shegai, T. Optics Express 2016, 24, (18), 2037320381. 67. Ruppin, R. Physics Letters A 2002, 299, (2–3), 309-312. 68. Koenderink, A. F. Optics Letters 2010, 35, (24), 4208-4210.


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69. Sauvan, C.; Hugonin, J. P.; Maksymov, I. S.; Lalanne, P. Physical Review Letters 2013, 110, (23), 237401. 70. Kristensen, P. T.; Hughes, S. ACS Photonics 2014, 1, (1), 2-10. 71. Sie, E. J.; McIver, J. W.; Lee, Y.-H.; Fu, L.; Kong, J.; Gedik, N. Nat Mater 2015, 14, (3), 290-294. 72. Ganchev, B.; Drummond, N.; Aleiner, I.; Fal’ko, V. Physical Review Letters 2015, 114, (10), 107401. 73. Chhowalla, M.; Jena, D.; Zhang, H. 2016, 1, 16052. 74. Qiu, D. Y.; da Jornada, F. H.; Louie, S. G. Physical Review B 2016, 93, (23), 235435. 75. Grenier, C.; Ciuti, C.; Imamoglu, A. arXiv preprint 2015, arXiv:1507.02480. 76. Santhosh, K.; Bitton, O.; Chuntonov, L.; Haran, G. Nat Commun 2016, 7, 11823. 77. Chikkaraddy, R.; de Nijs, B.; Benz, F.; Barrow, S. J.; Scherman, O. A.; Rosta, E.; Demetriadou, A.; Fox, P.; Hess, O.; Baumberg, J. J. Nature 2016, advance online publication. 78. Feist, J.; Garcia-Vidal, F. J. Physical Review Letters 2015, 114, (19), 196402. 79. Schachenmayer, J.; Genes, C.; Tignone, E.; Pupillo, G. Physical Review Letters 2015, 114, (19), 196403. 80. Andres, C.-G.; Michele, B.; Rianda, M.; Vibhor, S.; Laurens, J.; Herre, S. J. v. d. Z.; Gary, A. S. 2D Materials 2014, 1, (1), 011002.


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Observation of Tunable Charged Exciton Polaritons in Hybrid

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