Supporting information for strong exciton-plasmon coupling in MoS2 ...
Supporting information for strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattice Wenjing Liu1‡, Bumsu Lee1‡, Carl H. Naylor2, Ho-Seok Ee1, Joohee Park1, A.T. Charlie Johnson1,2, and Ritesh Agarwal1* Department of Materials Science and Engineering1 and Department of Physics and Astronomy2, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA E-mail: [email protected]
MoS2 growth: Single crystal MoS2 flakes were grown directly on a 275nm Si/SiO2 substrate by chemical vapor deposition1. A 1% sodium cholate solution was initially spin coated onto the SiO2 substrate to help promote the growth region. A micro-droplet of a saturated solution of ammonium heptamolybate (AHM) was deposited onto a corner of the substrate, which acted as the molybdenum feedstock. The substrate was placed in the center of a 1-inch Lindberg blue furnace and 25 mg of solid sulfur (part number 213292, SigmaAldrich) was placed upstream at a distance of 18 cm from the growth substrate. 700 s.c.c.m of nitrogen was flown through the chamber and the temperature of the furnace was ramped up to 800 ℃, while the sulfur pellet was heated up to 150℃. After a 30 min growth, the furnace was then stopped and rapidly cooled to room temperature.
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Device fabrication: A layer of PMMA 950 A2 was spin coated onto the as grown MoS2 sample at 2000 r.p.m. for 45 s and baked at 180 ℃ for 90 s. Electron beam lithography was used to define the nanodisk arrays. 50 nm thick silver film was deposited by electron-beam deposition followed by a lift-off process. The nanodisk diameter and array pitch were measured by scanning electron microscopy (SEM). Angle-resolved reflectance measurement: A home-built angle-resolved system2 was used to measure the reflectance spectra of the sample, as shown in figure 1 (b). A white light beam was focused on the sample by a microscope objective (60×, NA = 0.7, Nikon) to a spot size that could be adjusted from ~5-10 μm. Parallel light reflected from the sample was focused at the back focal plane (Fourier plane) of the objective and a lens was used to project the Fourier plane onto the entrance slit of a spectrometer (Princeton Instruments). The spectrometer CCD (2048 × 512 pixels) recorded both the wavelength of light and its spatial position at the entrance slit (angles of the reflected light) to extract the angle- and wavelength- resolved reflectance spectrum. Exciton-plasmon coupling strengths fitting and polariton composition calculation: A coupled oscillator model involving five oscillators was utilized to fit the angle-resolved reflectance data of MoS2 coupled with plasmonic lattice. The system’s Hamiltonian is given by:
⎡ E A - iγ A ⎢ 0 ⎢ H = ⎢ g AS ⎢ ⎢ g AS ⎢⎣ g AL
0 EB - iγ B g BS g BS g BL
g AS g BS ES + - iγ S + 0 g SL
g AS g BS 0 ES- - iγ Sg SL
g AL ⎤ ⎥ g BL ⎥ ⎥ g SL ⎥ g SL ⎥ ELSPR - iγ LSPR ⎥⎦
where the diagonal terms represent the uncoupled states: E and γ denote the energy and the damping (half-width at half-maximum) of each mode, and the subscripts A, B, S+, S-, and LSPR
2
stand for A- and B- excitons, (+1,0), (-1,0) diffractive order and LSPR, respectively. The offdiagonal terms represent the coupling strength between each two resonances. In the model, coupling strengths between the A and B excitons, and between the two diffractive orders were set to zero, while other coupling strengths were used as fitting parameters. The arrays are assumed to be symmetric for positive and negative in-plane wavevector k||, hence the coupling strengths of other resonances to both the (+1,0) and (-1,0) diffractive orders were set to be the same. The system’s eigenstates were then solved and fitted to the experimental data to obtain the coupling strength values. The system’s eigenstates, i.e. the polariton states, can be expressed as the linear combination of the five uncoupled states: 5
P ( kP ) = ∑ xi X i ( kP ) i =1
where P stands form the polariton state, Xi (i=1,2,3,4,5) stands for the five uncoupled states, and xi is the component of the eigenvector associated with each polariton state, analogous to the Hopfield Coefficient in the two-states strong coupling model3. The fraction of each component 2
that forms the polariton is given by xi . The total exciton fraction is the sum of the fraction of both A- and B- excitons: 2
2
2
xexciton = xA + xB while the plasmon fraction: 2
2
2
2
x plasmon = x+ + x− + xLSPR where they satisfy, 2
2
xexciton + x plasmon = 1
3
Figure S1. LSPR modes of individual (uncoupled) nanodisks patterned on Si/SiO2 substrate and on monolayer MoS2 with disks diameter of d = 140 nm and lattice constant, a = 1000 nm. (a) angle-resolved reflectance spectra of the Ag nanodisk array patterned on Si/SiO2 substrate. No clear lattice resonances can be observed. (b) Far-field reflectance measurement of the Ag nanodisk array on Si/SiO2 substrate and on monolayer MoS2. The resonance position (reflectance dip) is redshifted from 640 nm to 695 nm due to the presence of MoS2. (c) The difference of the reflectance spectra between the array patterned on MoS2 and bare MoS2 from (b). The LSPR position (reflectance dip) can be clearly observed at 695 nm.
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Figure S2. Angle-resolved reflectance spectra of four different arrays with disks diameter fixed at d = 120 nm and for various lattice constants (a). (a) a = 380 nm. (b) a = 420 nm. (c) a= 460 nm. (d) a = 500 nm. White dashed line represents the wavelength of the LSPR modes and the red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results obtained from the coupledoscillator model. In (d), the second order diffractive modes have also been considered in the COM fitting.
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Figure S3. Angle-resolved reflectance and COM fitting of the silver nanodisk array with disk diameter d = 100 nm and lattice constant a = 460 nm. White dashed lines correspond to the LSPR positions. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled-oscillator model. The second order diffractive modes have also been taken into account in the fitting. Although the strong lattice-LSPR coupling is not evident in this plasmonic array with smaller disk diameter, the dispersion bending near the LSPR wavelength and the COM fitting indicate a non-vanishing lattice-LSPR coupling, which implies that the system is in the intermediate coupling regime.
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Figure S4. Strong exciton-plasmon coupling of silver plasmonic lattice-coupled monolayer MoS2 at 77K with disk diameter d = 110 nm and lattice constant a = 380 nm. (a) Angleresolved reflectance spectrum of the Ag nanodisk array. (b) Angle-resolved reflectance spectrum of bare MoS2. (c) Angle-resolved reflectance spectrum of MoS2 coupled with Ag nanodisk array. (d) Line cuts from the angle-resolved reflectance data in (a)-(c) at k = 0. In (a)-(c), white dashed lines correspond to the LSPR positions and yellow dashed lines represent the A (low energy) and B (high energy) excitons. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled-oscillator model. Strong coupling between the LSPR and both the A and B excitons are clearly observed in (c) and (d) while the lattice resonance is detuned from the excitonic region, therefore highlights the critical role of the LSPR to enhance the exciton-plasmon coupling. References 1. Han, G. H.; Kybert, N. J.; Naylor, C. H.; Lee, B. S.; Ping, J.; Park, J. H.; Kang, J.; Lee, S. Y.; Lee, Y. H.; Agarwal, R.; Johnson, A. T. C. Nat Commun. 2015, 6. 2. 3.
Sun, L.; Ren, M.-‐L.; Liu, W.; Agarwal, R. Nano Lett. 2014, 14, (11), 6564-‐6571. Hopfield, J. J. Phys. Rev. 1958, 112, (5), 1555-‐1567.
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MoS2 growth: Single crystal MoS2 flakes were grown directly on a 275nm Si/SiO2 substrate by chemical vapor deposition1. A 1% sodium cholate solution was initially spin coated onto the SiO2 substrate to help promote the growth region. A micro-droplet of a saturated solution of ammonium heptamolybate (AHM) was deposited onto a corner of the substrate, which acted as the molybdenum feedstock. The substrate was placed in the center of a 1-inch Lindberg blue furnace and 25 mg of solid sulfur (part number 213292, SigmaAldrich) was placed upstream at a distance of 18 cm from the growth substrate. 700 s.c.c.m of nitrogen was flown through the chamber and the temperature of the furnace was ramped up to 800 ℃, while the sulfur pellet was heated up to 150℃. After a 30 min growth, the furnace was then stopped and rapidly cooled to room temperature.
1
Device fabrication: A layer of PMMA 950 A2 was spin coated onto the as grown MoS2 sample at 2000 r.p.m. for 45 s and baked at 180 ℃ for 90 s. Electron beam lithography was used to define the nanodisk arrays. 50 nm thick silver film was deposited by electron-beam deposition followed by a lift-off process. The nanodisk diameter and array pitch were measured by scanning electron microscopy (SEM). Angle-resolved reflectance measurement: A home-built angle-resolved system2 was used to measure the reflectance spectra of the sample, as shown in figure 1 (b). A white light beam was focused on the sample by a microscope objective (60×, NA = 0.7, Nikon) to a spot size that could be adjusted from ~5-10 μm. Parallel light reflected from the sample was focused at the back focal plane (Fourier plane) of the objective and a lens was used to project the Fourier plane onto the entrance slit of a spectrometer (Princeton Instruments). The spectrometer CCD (2048 × 512 pixels) recorded both the wavelength of light and its spatial position at the entrance slit (angles of the reflected light) to extract the angle- and wavelength- resolved reflectance spectrum. Exciton-plasmon coupling strengths fitting and polariton composition calculation: A coupled oscillator model involving five oscillators was utilized to fit the angle-resolved reflectance data of MoS2 coupled with plasmonic lattice. The system’s Hamiltonian is given by:
⎡ E A - iγ A ⎢ 0 ⎢ H = ⎢ g AS ⎢ ⎢ g AS ⎢⎣ g AL
0 EB - iγ B g BS g BS g BL
g AS g BS ES + - iγ S + 0 g SL
g AS g BS 0 ES- - iγ Sg SL
g AL ⎤ ⎥ g BL ⎥ ⎥ g SL ⎥ g SL ⎥ ELSPR - iγ LSPR ⎥⎦
where the diagonal terms represent the uncoupled states: E and γ denote the energy and the damping (half-width at half-maximum) of each mode, and the subscripts A, B, S+, S-, and LSPR
2
stand for A- and B- excitons, (+1,0), (-1,0) diffractive order and LSPR, respectively. The offdiagonal terms represent the coupling strength between each two resonances. In the model, coupling strengths between the A and B excitons, and between the two diffractive orders were set to zero, while other coupling strengths were used as fitting parameters. The arrays are assumed to be symmetric for positive and negative in-plane wavevector k||, hence the coupling strengths of other resonances to both the (+1,0) and (-1,0) diffractive orders were set to be the same. The system’s eigenstates were then solved and fitted to the experimental data to obtain the coupling strength values. The system’s eigenstates, i.e. the polariton states, can be expressed as the linear combination of the five uncoupled states: 5
P ( kP ) = ∑ xi X i ( kP ) i =1
where P stands form the polariton state, Xi (i=1,2,3,4,5) stands for the five uncoupled states, and xi is the component of the eigenvector associated with each polariton state, analogous to the Hopfield Coefficient in the two-states strong coupling model3. The fraction of each component 2
that forms the polariton is given by xi . The total exciton fraction is the sum of the fraction of both A- and B- excitons: 2
2
2
xexciton = xA + xB while the plasmon fraction: 2
2
2
2
x plasmon = x+ + x− + xLSPR where they satisfy, 2
2
xexciton + x plasmon = 1
3
Figure S1. LSPR modes of individual (uncoupled) nanodisks patterned on Si/SiO2 substrate and on monolayer MoS2 with disks diameter of d = 140 nm and lattice constant, a = 1000 nm. (a) angle-resolved reflectance spectra of the Ag nanodisk array patterned on Si/SiO2 substrate. No clear lattice resonances can be observed. (b) Far-field reflectance measurement of the Ag nanodisk array on Si/SiO2 substrate and on monolayer MoS2. The resonance position (reflectance dip) is redshifted from 640 nm to 695 nm due to the presence of MoS2. (c) The difference of the reflectance spectra between the array patterned on MoS2 and bare MoS2 from (b). The LSPR position (reflectance dip) can be clearly observed at 695 nm.
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Figure S2. Angle-resolved reflectance spectra of four different arrays with disks diameter fixed at d = 120 nm and for various lattice constants (a). (a) a = 380 nm. (b) a = 420 nm. (c) a= 460 nm. (d) a = 500 nm. White dashed line represents the wavelength of the LSPR modes and the red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results obtained from the coupledoscillator model. In (d), the second order diffractive modes have also been considered in the COM fitting.
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Figure S3. Angle-resolved reflectance and COM fitting of the silver nanodisk array with disk diameter d = 100 nm and lattice constant a = 460 nm. White dashed lines correspond to the LSPR positions. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled-oscillator model. The second order diffractive modes have also been taken into account in the fitting. Although the strong lattice-LSPR coupling is not evident in this plasmonic array with smaller disk diameter, the dispersion bending near the LSPR wavelength and the COM fitting indicate a non-vanishing lattice-LSPR coupling, which implies that the system is in the intermediate coupling regime.
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Figure S4. Strong exciton-plasmon coupling of silver plasmonic lattice-coupled monolayer MoS2 at 77K with disk diameter d = 110 nm and lattice constant a = 380 nm. (a) Angleresolved reflectance spectrum of the Ag nanodisk array. (b) Angle-resolved reflectance spectrum of bare MoS2. (c) Angle-resolved reflectance spectrum of MoS2 coupled with Ag nanodisk array. (d) Line cuts from the angle-resolved reflectance data in (a)-(c) at k = 0. In (a)-(c), white dashed lines correspond to the LSPR positions and yellow dashed lines represent the A (low energy) and B (high energy) excitons. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled-oscillator model. Strong coupling between the LSPR and both the A and B excitons are clearly observed in (c) and (d) while the lattice resonance is detuned from the excitonic region, therefore highlights the critical role of the LSPR to enhance the exciton-plasmon coupling. References 1. Han, G. H.; Kybert, N. J.; Naylor, C. H.; Lee, B. S.; Ping, J.; Park, J. H.; Kang, J.; Lee, S. Y.; Lee, Y. H.; Agarwal, R.; Johnson, A. T. C. Nat Commun. 2015, 6. 2. 3.
Sun, L.; Ren, M.-‐L.; Liu, W.; Agarwal, R. Nano Lett. 2014, 14, (11), 6564-‐6571. Hopfield, J. J. Phys. Rev. 1958, 112, (5), 1555-‐1567.
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