Control of Strong Light-matter Interaction in Monolayer WS2 Through

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Control of Strong Light-matter Interaction in Monolayer WS Through Electric Field Gating 2

Biswanath Chakraborty, Jie Gu, Zheng Sun, Mandeep Khatoniar, Rezlind Bushati, Alexandra L Boehmke, Rian Koots, and Vinod M. Menon Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b02932 • Publication Date (Web): 30 Aug 2018 Downloaded from http://pubs.acs.org on August 30, 2018

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Control of Strong Light-matter Interaction in Monolayer WS2 Through Electric Field Gating Biswanath Chakraborty,† Jie Gu,†,‡ Zheng Sun,†,‡,¶ Mandeep Khatoniar,†,‡ Rezlind Bushati,†,‡ Alexandra L. Boehmke,† Rian Koots,† and Vinod M. Menon∗,†,‡ †Department of Physics, City College of New York, City University of New York, New York 10031, USA ‡Department of Physics, The Graduate Center, City University of New York, New York 10016, USA ¶Present address:Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA 15260, USA E-mail: [email protected]

Abstract Strong light-matter coupling results in the formation of half-light half-matter quasiparticles that take on the desirable properties of both systems such as small mass and large interactions. Controlling this coupling strength in real-time is highly desirable due to the large change in optical properties such as reflectivity that can be induced in strongly coupled systems. Here we demonstrate modulation of strong exciton-photon coupling in a monolayer WS2 through electric field induced gating at room temperature. The device consists of a WS2 field effect transistor embedded inside a microcavity structure which transitions from strong to weak coupling when the monolayer WS2 becomes more n-type under gating. This transition occurs due to the reduction

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in oscillator strength of the excitons arising from decreased Coulomb interaction in the presence of electrostatically induced free carriers. The possibility to electrically modulate a solid state system at room temperature from strong to weak coupling is highly desirable for realizing low energy optoelectronic switches and modulators operating both in quantum and classical regime.

Keywords WS2 , microcavity, polariton, strong coupling,

Introduction Atomically flat monolayer transition metal dichalcogenides (TMDs) have triggered intense research activity in recent times due to their attractive optoelectronic properties . 1 In the monolayer limit, the two-dimensional (2D) TMDs become direct bandgap semiconductor with large excitonic binding energy and strong oscillator strength. 2 In fact the unusually large interaction strength of the excitons in TMDs with photons have led to the observation of strong light-matter coupling resulting in the formation of exciton polaritons in microcavities and plasmonic arrays

3–20

even at room temperature. These exciton polaritons have also

demonstrated some of the interesting characteristics of 2D TMD excitons such as valley polarization and their optical control . 9–11 Strong light matter coupling has been studied in a variety of solid-state systems ranging from inorganic III-V semiconductors to organic molecular materials . 21–26 The 2D TMDs are a recent entrant into this field and presents some unique opportunities that was impossible or harder to implement in the other material systems. Specifically, the possibility to electrically control the strength of coupling between the excitons and photons is needed to realize such devices as polaritonic modulators, switches and logic elements. In the 2D TMDs, the screened Coulomb interaction affects the binding energy and oscillator strength . 27–31 In the presence 2


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of electrostatically induced free carriers, the attractive interaction between the electrons and holes decrease, which results in significant reduction in the oscillator strength. Here we exploit this property to demonstrate active control of exciton polariton formation in 2D TMDs by integrating a WS2 field effect transistor into a microcavity structure at room temperature. The Rabi splitting between the upper and lower polariton branch which is a measure of the strength of exciton-photon coupling is reduced when electrons are introduced into the system. Under the charge neutral condition, we observe Rabi splitting of ∼60 meV which vanishes under highest electron concentration (corresponding to gate bias of 3V). The observed modification in Rabi splitting and associated decrease in light-matter interaction strength are in good agreement with theory based on coupled oscillator model.

Results Figure 1a shows the schematic of the electrically gated microcavity device. The monolayer WS2 based field effect transistor is fabricated on a bottom silver mirror and Al2 O3 spacer, which also acts as the gate dielectric (see Methods). Monolayer WS2 , exfoliated on a Polydimethylsiloxane (PDMS) stamp, was transferred on the Al2 O3 layer using dry transfer technique . 32 Layer identification was done by photoluminescence (PL) spectroscopy (Figure 1b): observed PL peak peak at 616 nm, attributed to the A exciton confirms the presence of monolayer. Contacts on the monlayer flake was fabricated using electron beam lithography followed by evaporation of Ti/Au. Following this, Poly(methyl methacrylate) (PMMA) was spin coated to define the top spacer layer of the cavity (see Methods). Before growing the top mirror, electrostatic gating of the monolayer WS2 was done in a back gate geometry with doped silicon substrate and bottom silver mirror acting as gate to investigate the gate dependent optical signatures of the bare WS2 layer. Gate dependent photoluminescence (PL) and differential reflectance spectra (∆R/R = (Rsample - Rsubstrate )/Rsubstrate ) is shown in Figure 1b and c, respectively. For the range of voltages applied, a gradual change from charge neutral

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(b)

(a)

(c)

(d)

Microcavity

Objective Fourier plane Beam splitter

Slit spectrometer

Converging lens White light

Figure 1: (Color Online) (a) Schematic of the device. Inset shows the optical image of the monolayer WS2 device. (b) PL spectrum of the monolayer WS2 . (c) Differential reflectance spectra at different gate voltages. (d) Schematic of the Fourier space imaging set up. Scale bar is 10 µm to n-type transition of the WS2 is observed. As electrons are induced, absorption originating form A exciton in monolayer WS2 weakens . 29–31 In PL spectra, we observe a relative increase of low energy emission attributed to negative trion . 29 The decrease in PL intensity of emission from neutral exciton, is due to the reduction in exciton oscillator strength induced by free carrier screening . 29 The change in doping concentration is estimated from the spectroscopic data. From our results, we infer that -4 V corresponds to the charge neutral configuration of the monolayer (i.e. -4 V is the threshold voltage). Carrier concentration in the monolayer can be estimated by the standard MOSFET expression q = Coxide (Vg − Vt ), 4


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(a)

-4 V

vit Ca

-2 V

(b)

UPB Exciton

y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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LPB

0.0 V

3V

(c)

(d)

Figure 2: (Color Online) Angle-resolved reflectance at different gate voltages. The left panel shows the experimental results while the right panel shows simulations from transfer matrix. The lines denote coupled oscillator mode fits. Dashed lines indicate the bare cavity and exciton dispersions. The white solid lines correspond to the lower and upper polariton branches, respectively. where Coxide is the capacitance of Al2 O3 , Vg and Vt are the applied gate and threshold voltages, respectively. The oxide capacitance per unit area in our experiments is estimated to be 104nF cm−2 with oxide dielectric being 8.5 . 33 The maximum carrier concentration achieved is estimated to be ∼ 4.5 × 1012 cm−2 . Following the characterization of the monolayer on bottom mirror, the top silver mirror is deposited to complete the metal-mirror-cavity. The empty cavity is designed to have a negative detuning (EExciton - ECavity at kk = 0) of around 15meV (Supporting Information Figure S1a). The thicknesses of the metal mirrors on either side and the spacer layers (consisting of

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(a)

(b)

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(c)

Figure 3: (Color Online)Contour plor from cut along ∼ -21o from the images in Figure 2 at different gate voltages. Exciton and photon fraction at different gate voltages for (b) UPB and (c) LPB. Al2 O3 and PMMA) are so chosen as to have the WS2 monolayer at the cavity antinode (Supporting Information Figure S1b). Angle resolved differential reflectance spectra were recorded using a home made imaging set up comprising of white light (broad band halogen source) and Olympus inverted microscope coupled with Princeton Instruments monochromator with a Pixis 1024B EMCCD camera. A 50X, 0.8 NA objective was used for reflectivity measurements. The polariton dispersion is revealed by imaging the objective back aperture (Fourier plane) on to the camera (Figure 1d). All measurements reported here were done at room temperature. Angle resolved differential reflectivity is shown in Figure 2a-d for different applied back gate voltages. For the charge neutral configuration, clear anticrossing is observed with a Rabi splitting (¯hΩ) of ∼60 meV (Figure 2a). As the Fermi level in WS2 monolayer is tuned across the conduction band, the separation between upper polariton branch (UPB) and lower polariton branch (LPB) becomes almost indistinguishable, associated with a steady decrease of the Rabi splitting. At 3V, anticrossing is no longer be resolved (Figure 2d) and the dispersion resembles a red shifted bare cavity. The observed trend suggests a crossover from the strong coupling to weak coupling regime. To capture the unique doping dependence of anticrossing behavior, in Figure 3a we plot the vertical slice extracted from Figure 2 at ∼ -21o . With electron doping, the Rabi splitting between the upper and lower polariton branches gradually decreases, and becomes unresolvable at higher electron concentration.

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n (10

12

1.4

0.0

0.65

1.30

-2

cm )

1.94

2.60

3.24

3.90

4.54

1.2

Oscillator strength f

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1.0

0.8

0.6

0.4

0.2

0.0 -4

-3

-2

-1 V

g

0

1

2

3

(volts)

Figure 4: (Color Online)Oscillator strength as a function of gate voltage. The carrier concentration n is also shown.

Discussion We fit the experimental data to a coupled oscillator model

22,23,34–36

with the exciton-photon

interaction strength, g as the free parameter (Figure 2). The coupled oscillator fits (UPB and LPB) are shown by the solid white curves in Figure 2 (see method section for details). The dashed lines correspond to the bare cavity and exciton dispersions. The Rabi splitting is found to be ∼ 60 meV (Figure 2a) for the charge neutral configuration and decreases as the gate voltage increases. Using the observed reduction in Rabi splitting obtained from coupled oscillator model fits, we infer the transition from strong to weak coupling. The Hopfield coefficients

37

(see Methods) obtained from coupled oscillator model, are 7


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plotted in Figure 3b and c. With increasing angles, the UPB (LPB) becomes more photon (exciton) like as the voltage is tuned from neutral regime (-4 V) to electron doped configuration (Figure 3b and c). The observed trend of decrease in Rabi splitting with electron doping can be explained by many body effects such as Pauli blocking and screened Columb interaction which modify the exciton binding energy and oscillator strength . 29–31 Given the moderate doping, our experiment can be explained in terms of screened Columb interaction . 29 To better substantiate the modification in oscillator strength of the two dimensional TMD, we perform transfer matrix simulations to model the experiment. We fit the complex dielectric function (E) = 1 (E) + i2 (E) using Lorentz oscillator model : 2

(E) = 1 +

N X

Ej2 j=1

fj − E 2 − iEγj

(1)

where fj and γj are oscillator strength and linewidth of the jth oscillator. The result of the transfer matrix simulations are shown in Figure 2 (right panels) in excellent agreement with the experiments. For different gate voltages, the oscillator strengths in transfer matrix simulations were varied to agree with the experimental results and the extracted oscillator strength is shown in Figure 4. The reduction in oscillator strength can be explained as follows. The screened interaction under the presence of electrostatically induced free carriers reduces the attractive interaction between electron and holes causing a significant decrease in the exciton oscillator strength. This in turn reduces the interaction strength g as shown previously in coupled oscillator mode fits. Depleting the excess free carriers by application of negative voltages, creates an intrinsic WS2 channel, where the exciton oscillator strength is restored. In our experiment, the change in oscillator strength is manifested as a reduction in the PL and reflection intensities. Similar doping concentrations have resulted in binding energy reduction of ∼100 meV and associated blue shift in exciton resonance by ∼15 meV . 29 Given the room temperature operation of our present device, the spectral shift is not observed. This is attributed to the elevated temperature as well as the competing effect of 8


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band gap renormalization and binding energy changes . 30 The binding energy of nth exciton state in 2D TMD can be calculated from Eb = e4 µ , 2¯ h2 (n−1/2)2

where µ is the reduced exciton mass (µ = 0.16 m0 , m0 being electron rest

mass) and is the effective dielectric constant . 28 The exciton Bohr radius aex B , could be evaluated from aex B =

m0 aH (n − 1/2), µ

particle band gap of 2.4 eV

28,29

where aH is hydrogen Bohr radius. Assuming a quasi-

and exciton resonance around 2.015 eV for undoped sample

in our experiment, we estimate a binding energy Eb to be ∼ 380 meV and around ∼ 4.8, similar to what has been reported earlier for n =1 exciton state . 28 Thus, the exciton Bohr radius, comes out to be ∼7˚ A. Assuming a binding energy reduction of ∼100 meV , 29 due to electron doping, the effective dielectric constant is estimated to be ∼ 5.6. This results in an enlarged excitonic Bohr radius ∼ 10˚ A. These values of exciton Bohr radius agrees well with that reported by Zhang et al. for monolayer MoS2 with similar doping range . 27 Since the 3 23 oscillator strength varies as f ∝ 1/(aex we estimate our oscillator strength to decrease B) ,

by factor of 6 for the highest doping which agrees with earlier reported values . 29 In summary, we present an approach to dynamically control the interaction between excitons in monolayer WS2 and microcavity photons at room temperature. This is achieved by tuning the oscillator strength of the WS2 excitons in the presence of charged carriers induced by electrostatic gating. Anticrossing between exciton and cavity photons were observed as a result of the strong coupling nature of the interaction resulting in the formation of excitonpolaritons. When the WS2 channel inside the FET, was depleted of free carriers, Rabi splitting of ∼ 60 meV was observed. As the monolayer channel was electrostatically doped, the Rabi splitting decreased and eventually became unresolvable. The experimental findings are supported by theoretical model involving coupled oscillator model fit and transfer matrix calculations. The present demonstration of using a FET in a microcavity structure presents the first step towards low energy ultrafast polariton modulators and optoelectronic switches based on 2D materials.

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Methods Sample Preparation The metal mirror microcavity consists of silver mirror on either sides with a spacer layer of Al2 O3 and PMMA as shown in Figure 1a. Highly doped Silicon wafers acting as back gate was used as substrate. Atomic layer deposition (ALD) technique was used to grow the bottom Al2 O3 . As a precursor, Tetramethylammonium hydroxide (TMAH) and H2 O were used in ALD. WS2 monolayer was exfoliated on polydimethyl siloxane (PDMS) stamps and optically characterized before transferring to the bottom Al2 O3 layer. Electronbeam lithography followed by e-beam evaporation of 5nm of Ti and 70 nm Au was done to write the contacts. PMMA 495 A-2 (from Michrochem) was spin coated to form the top spacer layer. PMMA thicknesses at various spin speed was characterized using ellipsometry. Second step lithography was done to expose the contacts. Finally metallic sliver (∼40 nm) was deposited in e-beam evaporator to define the top mirror. Keithley 2400 source meter was used to apply the gate voltage. Optical measurement The reflectivity measurements were done using emission from broadband tungsten halogen lamp. A telescope (1:1 arrangement) with a 100 µ pinhole at the beam waist was used to collimate the beam. The reflected signal was collected by the 50X objective (same as one used to focus the incident beam) followed by deflection from beam splitter to the spectrometer. Coupled Oscillator Model The polariton dispersion can be obtained by solving for the eigen value of the coupled Hamiltonian which reduces to a 2×2 matrix  ECav − H= g

8,23

iγCav 2

 g EEx −

iγEx 2

 

(2)

ECav and EEx are energy levels of the uncoupled cavity and exciton respectively. g (2g = h ¯ Ω) denotes exciton-photon coupling strength and γEx and γCav are FWHM (full width at halfmaximum) of exciton and cavity modes respectively. 10


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The new eigenvectors of this Hamiltonian is a superposition of the constituent exciton and photon states, the UPB and LPB which are represented by

|U P Bi = C(k) |excitoni + X(k) |photoni (3) |LP Bi = X(k) |excitoni − C(k) |photoni where C(k) and X(k) are Hopfiled coefficients

37

describing the photon and exciton fraction

in the polariton branches. In the coupled oscillator picture, the interacting energies are expressed as 1 EU P B,LP B = (ECav + EEx + i(γCav + γEx )) 2 q 2 1 (4g)2 + EEx − ECav − i(γCav + γEx ) ± 2

(4)

where EU P B and EU P B are energies of upper and lower polariton branches respectively, with “+” for UPB and “-” for LPB.

Acknowledgement This work was supported by the NSF under EFMA-1542863 (BC, ZS), ECCS 1509551 (JG), MRSEC program1420634 (BC), and ARO under W911NF-16-1-0256 (VM and MK). Authors also acknowledge the use of the nanofabrication facility at ASRC, CUNY.

Supporting Information Available Reflection from bare cavity and the electric field distribution inside the microcavity are shown in Figure S1.

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(37) Hopfield, J. J. Phys. Rev. 1958, 112, 1555.

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Control of Strong Light-matter Interaction in Monolayer WS2 Through

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