Anomalous Photoluminescence Quenching in Metallic Nanohybrids

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Anomalous Photoluminescence Quenching in Metallic Nanohybrids Mahi R. Singh, Jiaohan Guo, Elisabetta Fanizza, and Madan Dubey J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00352 • Publication Date (Web): 02 Apr 2019 Downloaded from http://pubs.acs.org on April 2, 2019

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The Journal of Physical Chemistry

Anomalous Photoluminescence Quenching in Metallic Nanohybrids Mahi R Singh1*, Jiaohan Guo1, Elisabetta Fanizza, 2 , 3 and Madan Dubey4 1Department

of Physics and Astronomy, The University of Western Ontario, London N6A 3K7, Canada di Chimica, Università degli Studi di Bari, Via Orabona 4, 70126, Bari, Italy 3Istituto Processi Chimico Fisici IPCF Consiglio Nazionale delle Ricerche CNR, Via Orabona 4, 70126, Bari, Italy 4U.S. Army Research Laboratory, Adelphi, Maryland 20783-1197, USA 2Dipartimento

Abstract We have developed a theory for the photoluminescence and absorption coefficient in nanohybrids made of an ensemble of metallic nanoparticles and the core-shell quantum emitter. The core-shell quantum emitter is made of a quantum emitter core and a dielectric shell. When a probe laser light falls on metallic nanoparticles, electric dipoles are induced in the ensemble. Hence, these dipoles interact with each other via the dipole-dipole interaction. The surface plasmon polaritons are also present in metallic nanoparticles. Excitons in the quantum emitter interact with these surface plasmon polariton and the dipole-dipole interaction electric fields. Using the quantum mechanical density matrix method, we have developed a theory for the photoluminescence quenching and enhancement, the nonradiative decay rate and absorption coefficient for the quantum emitter in the ensemble of metallic nanoparticles. We showed that the nonradiative energy loss is mainly due to the exciton coupling with the dipole-dipole interaction and it is responsible for the power loss in the quantum emitter. This in turn produces anomalous photoluminescence enhancement and quenching. We have compared our theory with experimental data of core-shell CdSe/ZnS quantum dots embedded in an ensemble of Au nanoparticles. A good agreement between theory and experiment is found. We showed that there is an energy shift and an enhancement in the absorption peak due to the dipole-dipole interaction. Finally, we showed that there is the anomalous quenching and enhancement in the photoluminescence spectrum of the CdSe/ZnS quantum dot embedded in the ensemble of Au-nanoparticles. This phenomenon also occurs mainly due to the dipole-dipole interaction in the ensemble of Au nanoparticles. These are interesting results and can be used to fabricate nanosensors for applications in nanomedicine and nanotechnology.

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I.

Introduction

There is a considerable interest to study the plasmonic properties of quantum emitters (QEs) and metallic nanoparticles (MNPs). 1-28 When a QE is in contact with MNPs, there is a significant enhancement in the light emission in the QE due to the presence of the surface plasmon polaritons (SPPs) created in MNPs.29,30 The enhancement of the light emission in QEs such as molecular fluorophores is very useful for improving detection sensitivity and selectivity in many applications. Examples of applications can be the DNA screening, single molecule detection and image enhancement. Recently Singh et al.4 have developed a theory for photoluminescence (PL) for QE and MNP hybrids. These hybrids can be very important building blocks for nanomedicine due to the desirable SPP resonances. The SPP resonances can be manipulated in these structures by changing the size of the inner nanoparticle and dielectric constants. These structures have important technological applications in the areas of chemical and biological sensors and nanomedicine. Much attention has been paid to investigate the plasmonic properties of metallic nanohybrids made from an ensemble of MNPs and QEs.11-24 This is because of their medical, biological and chemical applications. For example, Wersall et al. 11 synthesized nanohybrids by depositing an ensemble of QEs (i.e. J-aggregate dye) on the surfaces of a Ag nanoprism. They measured the scattering coefficient and photoluminescence (PL) spectrum of these hybrids and observed splitting not only in the scattering spectrum, but also in PL spectrum. Kulakovich et al.12 have studied the enhancement of photoluminescence of CdSe/ZnS core−shell quantum dots embedded in an ensemble of gold colloids. Huang et al.13 have also synthesized nanohybrids by embedding AuMNP dimers and trimers into the ensemble of CdSe/ZnS-QDs and found an enhancement in the PL spectrum. Fanizza et al. 14, 15 have fabricated hybrids made of CdSe/ZnS quantum dots embedded in the ensemble of Au-MNPs and they found a shift and enhancement in absorption peaks. They have also found PL quenching in the CdSe/ZnS QD. Kosarev et al.16 have fabricated coupled ensembles of epitaxial InAs quantum dots and silver metallic nanoparticles. They found the enhancement of the exciton PL intensity from the InAs QDs when they were coupled to the silver nanoparticles. Recently, Singh and Black25 have developed a theory for the PL and scattering cross section of a core-shell hybrid, where the core is the metallic nanoparticle and the shell is made of an ensemble of quantum emitters. They studied the dipole-dipole integration (DDI) between QEs and discovered an anomalous DDI, which is induced by the surface plasmon polaritons. They have shown that the strength of the DDI can be controlled by the surface plasmon polariton frequency. They found that the spectrum of the PL and the scattering cross section splits from one peak into two peaks mainly due to the anomalous dipole-dipole interactions. This finding is consistent with the experimental data of the PL and scattering cross section of the J-aggregate and silver core-shell hybrid11. They have shown that that the splitting and height of the two peaks can be increased or decreased by controlling mainly the strength of the anomalous dipole-dipole interaction. In this paper, we have developed a theory for the anomalous photoluminescence (PL) and absorption coefficient for metallic nanohybrids. Metallic nanohybrids are made of an ensemble of MNPs and a QE-shell. The QE-shell is made of a QE as a core and an outer dielectric shell. We call this structure as the nanohybrid. The main aim of the paper is study the effect of ensemble of MNPs on the PL emission and absorption coefficient in the QE-shell. We applied a probe laser in the 2 ACS Paragon Plus Environment

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nanohybrid to study the photoluminescence and absorption coefficient. Using the quantum mechanical density matrix method31,32, we have derived an expression of the PL and absorption coefficient in the QE-shell in the presence of the DDI and SPP fields. When a probe laser light falls on the nanohybrid, electric dipoles are induced in the ensemble of MNPs and these dipoles interact with each other via the dipole-dipole interaction (DDI). SPPs are also created at the interfaces of a metallic nanoparticle due the DDI field. The DDI field is calculated by using manybody theory in the mean field approximation.33-39 The SPP resonances and SPP electric field are calculated by solving the Maxwell equation in the static-wave approximation. Excitons in the quantum emitter interact with the SPP field and the DDI field. The nonradiative decay rate due to the exciton interaction with the DDI and SPP fields has also been obtained. We found that the PL quenching occurs mainly due to DDI field created by the ensemble of the MNPs. Hence, we call this effect anomalous PL quenching since this type of quenching has not been found before. We showed that the nonradiative decay rate is mainly due to the coupling between exciton and the dipole-dipole interaction. We have compared our theory with experimental data of the PL quantum yield for a nanohybrid which is made of the the silica coated CdSe/ZnS quantum dot and the ensemble of the Au-MNPs.14 We have also compared our theory with experimental data of the energy shift and linewidth of absorption peaks for the above nanohybrid. A good agreement between theory and experiment is found. We showed that there is an energy shift in the absorption peak as the DDI increases. We also showed that the absorption peak enhances as the DDI increases. The enhancement of the DDI is due to the increase of the concentration of Au-MNPs in the ensemble. Finally, we found that there is the anomalous quenching in the PL spectrum of CdSe/ZnS quantum dot embedded in the ensemble of Au-MNPs. It is shown that as the thickness of the shell increases the PL quenching also decreases.

Fig. 1: Schematic diagram of a hybrid which consists of an ensemble of MNPs and a QE-shell. The QE-shell is made of a QE core and a dielectric shell. The hybrid is doped into a substrate. We call this structure the nanohybrid. MNPs are interacting with each other via the DDI.

II. Anomalous photoluminescence and Absorption coefficient In this section we calculate the anomalous PL and absorption coefficient for the nanohybrid where the QE-shell is embedded in the ensemble of MNPs. These types of nanohybrids have been fabricated recently where the QE-shell is made of a CdSe-ZnS quantum dot core and the shell is made of silica14,15. The MNPs are fricated from Au metallic nanoparticles. A schematic diagram 3 ACS Paragon Plus Environment


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of the nanohybrid is depicted in fig. 1. The nanohybrid is immersed in a background material. Examples of the background material can be a bio-cell, a biological solution, chemical materials/solutions and dielectric materials. We consider that the QE-shell has two energy levels and one exciton. The two energy levels are denoted as |𝑎⟩ and |𝑏⟩. The exciton frequency and wavelength are denoted as 𝜔𝑎𝑏 and λab which are due to the transition |𝑎⟩⟷|𝑏⟩. A schematic diagram of the QE-shell is shown in fig. 2.

Fig. 2: A schematic diagram of the QE-shell structure is plotted. The QE-shell is made of the QE core and the dielectric material shell. Energy levels of the QE are shown on the right figure and two energy levels are denoted as |𝑎⟩ and |𝑏⟩. The QE is interacting with the probe field, the SSP field and the DDI field.

The PL emission occurs when an exciton falls from an excited state to the ground state. Following the method of reference26, the PL expression for the QE-shell in the nanohybrid is I QE  QQEWQE ,

QQE =

r

 r   nr

,

WQE =

hab Im   ab  ETQE 2E p

2

(1)

Where 𝑄𝑄𝐸 is called the PL quantum yield and WQE is the power emitted by the QE. Here 𝜇𝑎𝑏 and 𝜌𝑎𝑏 are the dipole moment and density matrix element of the QE for the transition |𝑎⟩⟷|𝑏⟩, respectively. Here γr is the radiative decay rate of the exciton due to the spontaneous emission and Γnr is the nonradiative decay rate of the exciton due to the exciton interaction with the DDI and SPP fields. The term 𝐸𝑄𝐸 𝑇 is the total electric field falling on the QE-shell. Next, we calculate the absorption coefficient for the transition |𝑎⟩⟶|𝑏⟩. It is calculated in reference26 in terms of the density matrix element 𝜌𝑎𝑏. The absorption coefficient is found as

 abs 

ab b EP

Im   ab 

(2)

Where ϵb is the dielectric constant of the background material. To evaluate eqns. (1) and (2) we need to evaluate the total electric field 𝐸𝑄𝐸 𝑇 appearing in eqn. (1) and the density matrix element 𝜌𝑎𝑏. They are calculated as follows. Let us calculate the total electric field 𝐸𝑄𝐸 falling on the QE-shell. We apply a probe field with 𝑇 4 ACS Paragon Plus Environment

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amplitude EP, frequency ω and wavelength λ. The wavelength and frequency are related to each other via ω = 2πc/λ in this paper where c is the speed of light. The probe field induced an electric dipole in each metallic nanoparticle in the ensemble. These dipoles interact with each other and produce the DDI electric field (𝐸𝑚 𝐷𝐷𝐼). Similarly, the probed field also induces the SPP electric field 𝐸𝑄𝐸 (𝐸𝑚 ) on the each MNP. Hence 𝑆𝑃𝑃 𝑇 is made of three fields (i) the probe field (EP) , (ii) the SPP 𝑚 𝑄𝐸 𝑚 𝑚 field (𝐸𝑆𝑃𝑃) and (iii) the DDI field (𝐸𝑚 𝐷𝐷𝐼). Hence we get 𝐸𝑇 = 𝐸𝑃 + 𝐸𝑆𝑃𝑃 + 𝐸𝐷𝐷𝐼. Recently the DDI electric field has been calculated by Singh and Black25 for the ensemble of quantum emitters which are distributed randomly in 3-dimensional array. We follow the method of Singh and Black 25 to calculate the DDI field produced by the ensemble of MNPs. The MNPs are distributed randomly in 3-dimensional array on the surface of the QE𝑚 shell. Let 𝑝𝑚 𝑖 and 𝑝𝑗 be the induced dipole moments in the ith-MNP and jth-MNP, respectively. These induced dipoles interact with each other via the DDI. The interaction Hamiltonian for MNPs in the ensemble is written as25

1 N m m m H =  J ij pi . p j 2 i, j m ddi

(3)

33-39, the DDI Where 𝐽𝑚 𝑖𝑗 is the DDI coupling constant. In the mean field approximation Hamiltonian given by eqn. (3) can be rewritten as

m m H ddi =  pim .EDDI ,

m EDDI 

i

1 J ijm p mj  2 j i

(4)

Where 𝐸𝑚 𝐷𝐷𝐼 is called the DDI field and it is the average induced electric field created by all MNPs on the ith-MNP. By comparing eqns. (3) and (4), we notice that the many-body problem reduces to a single-body problem in the mean field approximation. We use this approximation to get the analytical expression of the PL and absorption coefficients so that they can be used by experimentalists to plan their new experiments. Without this approximation it is impossible to derive the analytical expressions of the PL and absorption coefficient. However, the main physics of this problem does not change due to this approximation. This approximation is widely used in the literature. 25,33-38 Using the method of Singh and Black25, the average in eqn. (4) has been evaluated and it is found as m  EDDI

m Pm 12 3 b Rm3

(5)

Where λm is the DDI constant and Pm is the average polarization of the ith-MNP. Here ϵb is the dielectric constant of the background material and Rm is the radius of the MNP. The expression of the Pm for the MNP has been calculated in references1.25.26 by solving the Maxwell equations in the static wave approximation. The polarization in the quasi-static wave approximation is found as







Pm  4 0b Rm3 gl  m EP  EQE ,

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 òm  òb    òm  2òb 

m  

(6)

Here gl is called the polarization parameter and it has values gl =1 and gl = -2 for 𝑃𝑚 ∥ 𝐸𝑃 and 𝑃𝑚 ⊥ 𝐸𝑃, respectively. The parameter 𝛽𝑚 is called the polarization factor. Here ϵm is the dielectric function of the MNP, ϵb is the dielectric constant of the background material and ϵ0 is the dielectric constant of vacuum. Here EQE is the electric field produced by the QE-shell. Putting eqn. (6) into eqn. (5), one can calculate the DDI field as





m m EDDI   DDI EP  EQE ,

m  gl  DDI

m  m 3

(7)

Note that the DDI field depends on the polarization factor 𝛽𝑚 which in turn depends on the dielectric constant ϵm of MNPs. Let us calculate the electric field EQE produced by the QE-shell and appearing in eqn. (7). We consider a QE-shell structure is made from a QE core and an outer dielectric shell. A schematic diagram of the QE-shell is depicted in fig. 2. The dielectric constants of the QE and the outer dielectric shell are denoted as ϵq and ϵs, respectively. The radius of the QE is taken as 𝑅𝑞 and the radius of the nanoshell is 𝑅𝑞𝑠. Therefore, 𝑡𝑠 = 𝑅𝑞𝑠 ― 𝑅𝑞 is the thickness of the outer shell. The typical size of the QE-shell is of the order of 20 nm and the wavelength λ of light in the visible region is of the order of 600 nm. This means that the size of the QE-shell is much smaller than the wavelength of light. In this case, one can consider that the amplitude of the electric field is constant over the QE-shell and this is known as the quasi-static approximation29,30. Three electric fields are falling on the QE-shell. They are the probe field, the SPP field and the DDI field produced by the 𝑚 𝑚 MNP ensemble. Hence, we have 𝐸𝑄𝐸 𝑇 = 𝐸𝑃 + 𝐸𝑆𝑃𝑃 + 𝐸𝐷𝐷𝐼. Following the method of references1,2,29,30 , the induced electric field emitted by the QE-shell (𝐸𝑄𝐸) is found as EQE =

Rqs3 r3

m m  qs  EP  ESPP  EDDI 

 Rqs3 s  b  q 2 s   2 Rq3 q  b q  s     qs   3 3  Rqs s 2 b  q 2 s   2 Rq q 2 b q  s  

(8)

Here 𝛽𝑞𝑠 is called the polarizability factor for QE-shell respectively. Note that the electric field EQE depends on r-3. It is clear from eqn. (8) that the effect of the dielectric shell is included in this equation via the dielectric constant of the shell (ϵs) and its radius (Rqs). The geometry for MNP array and QE is shown in the schematic diagram of fig.1. The MNP array is made of an ensemble of MNPs and they are randomly deposited on the surface of the QE-shell. Here we have calculated SSP field produced by all MNPs using many-body mean field theory on the QE. Therefore, the distance r in eqn. (8) is taken between the QE and a MNP located on the surface of the QE-shell. 6 ACS Paragon Plus Environment

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Similarly, we calculate the SPP electric field produced by a MNP due to an induced polarization. Three electric fields are falling on the MNP. The first is the probe field, the second is electric field produced by the QE-shell and lastly the DDI field produced by the MNP ensemble. The total field 𝑚 𝑚 falling on the MNP is denoted as 𝐸𝑚 𝑇 and it is written as 𝐸𝑇 = 𝐸𝑃 + 𝐸𝑄𝐸 + 𝐸𝐷𝐷𝐼. The expression of the SPP field can be calculated by using the quasi-static approximation as m ESPP =

Rm3  m m EP  EQE  EDDI 3 r





(9)

Where 𝛽𝑚 is defined in eqn. (6). Note that effect of 𝐸𝑚 𝑇 is included in eqn. (9) and the SPP field also depends on the DDI field. The size effect of the MNP is included via Rm and Rqs in eqn. (9). The SPP resonance frequency (ωsp) does not depend on the radius of the MNP. We have also calculated the SSP field produced other plasmonic materials such as graphene and metamaterials.2, 41-43 We have also studied the shape of the MNP in the calculation of SSP resonances. 43-47 Finally we calculate the density matrix element 𝜌𝑎𝑏 appearing eqns. (1) and (2). To calculate 𝜌𝑎𝑏, we need to know the interaction Hamiltonian between the QE-shell and the ensemble of the MNPs. 𝑚 𝑚 The total electric field falling on the QE is found as 𝐸𝑄𝐸 𝑇 = 𝐸𝑃 + 𝐸𝑆𝑃𝑃 + 𝐸𝐷𝐷𝐼 where expressions 𝑚 of 𝐸𝑚 𝑆𝑃𝑃 and 𝐸𝐷𝐷𝐼 are given in eqns. (7) and (9), respectively. We know that the PL and absorption occur due to the interaction between the QE and the electric field falling on the QEshell (𝐸𝑄𝐸 𝑇 ). With the help of eqns. (7) and (9) and after some mathematical manipulations the interaction Hamiltonian for the QE-shell in the dipole and rotating wave approximation31,32 is found as









H int  hb ba  hb  SPP  ba  hb  DDI  ba  hc

(10)

Where





p  SPP   SPP   qSPP ,





p  DDI   DDI   qDDI ,

p  SPP 

Rm3 Rqs3  qs  m Rm3  m q ,   SPP r3 r6

p m  DDI   DDI 

R m m  DDI , r3 3 m

 qDDI 

Rqs3  qs r

3

m  DDI 

Rm3 Rqs3  qs  m r

6

(11) m  DDI

where hc stands for the Hermitian conjugate. Here 𝜎𝑏𝑎 = |𝑏⟩⟨𝑎| is the exciton creation operator for transition |𝑎⟩⟷|𝑏⟩. The parameter Ω𝑏 is called the Rabi frequency. The weaker terms have been neglected in eqn. (10). The first term in eqn. (10) is the interaction Hamiltonian between the exciton and the probe field. The second term is the interaction Hamiltonian between the exciton and the SPP field. The third term is the excitation interaction with DDI field. The Π-term is made of two terms Π𝑝𝑆𝑃𝑃 and Π𝑞𝑆𝑃𝑃. The first term Π𝑝𝑆𝑃𝑃 depends on r-3 and the second term Π𝑞𝑆𝑃𝑃 depends on r-6. Therefore, the Π𝑝𝑆𝑃𝑃term is stronger than the Π𝑞𝑆𝑃𝑃 term. The Ф-term is also made of two terms Φ𝑝𝐷𝐷𝐼 and Φ𝑞𝐷𝐷𝐼. The first term Φ𝑝𝐷𝐷𝐼 depends on r-3 whereas the second term Φ𝑞𝐷𝐷𝐼 depends on r-3 and r-6. 7 ACS Paragon Plus Environment


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The terms containing r-6 are weaker than the term containing r-3. We now calculate the radiative and nonradiative decay rates appearing in eqn. (1). We consider that the power of the QE-shell decays radiatively due to the spontaneous emission and nonradiatively due to the exciton interaction with DDI and SPP fields. The decay interaction Hamiltonian can be written in the dipole and rotating wave approximation as † † †  VDDI k  ak na  VSSP   a  na  hc H decay  Vr k  ak na k

(12)



k

Where the operator 𝑎𝑘 is the photon annihilation operator for energy 𝜔𝑘 and wave vector k. The operator 𝑎𝛽 is the SPP annihilation operator for energy 𝜔𝛽 and wave vector 𝛽. Here 𝑉𝑟(𝜔𝑘) is the coupling constants for the exciton and probe field photons integration and it is responsible for spontaneous emission and the radiative decay rate. Here the quantity 𝑉𝐷𝐷𝐼(𝜔𝑘) is the coupling term between excitons in the QE-shell and the DDI field. The DDI electric field is produced by the ensemble gold nanoparticles. Here we consider that an excited exciton in the QE couples with the DDI field and decay to the ground state and loses its energy through nonradiative decay rate. That is why we call it the nonradiative interaction term. Similarly 𝑉𝑆𝑃𝑃(𝜔𝛽) is the coupling constants for the exciton interaction with the SPP field. Both terms 𝑉𝑆𝑃𝑃(𝜔𝛽) and 𝑉𝐷𝐷𝐼(𝜔𝑘) are responsible for the nonradiative decay rate. They are calculated as  hk Vr k   i   2 0b  Vqs 

1/2

  , 

 hk  DDI VDDI k   i   2 0b  Vqs 

1/2

  , 

 h  SSP VSSP    i   2 0b  Vqs 

1/2

  

(13)

where 𝜖𝑏 is the dielectric constant of the background material. Here 𝑉𝑞𝑠 is the volume of the QE-shell. Let us calculate the density matrix element ρab = (ρba) *. Using the master equation for the density matrix method of references31,32 and eqn. (12) for the interaction Hamiltonian of the system, we obtained the following equations of motion for the density matrix elements, d bb *  2   r   nr  bb  i INT  ab  i   INT  ba dt d ba     r / 2   nr  i  ba   nr  ba  i INT 1  2 bb  dt

(14)

Where ∆𝑛𝑟 is the nonradiative energy shift and Γ𝑛𝑟 is the nonradiative decay rate in the QE-shell. They are found as





 INT  b 1   DDI   SPP ,





 nr   r Re  SPP   DDI ,  r   nr   DDI   SPP ,

(15)

ba2 (hab )3 3 b h4 c3





 DDI   r Im  DDI ,



 SPP   r Im  SPP




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In eqn. (14), δ𝑏𝑎 = 𝜔𝑏𝑎 - 𝜔 is called the probe field detuning. Here Ωb is called the Rabi frequency related the probe field and it is defined in reference. 31 Finally, we obtain the expression of the PL quenching and absorption coefficient in the strong coupling limit. The expression of ρab is obtained from eqn. (14). Substituted ρab in eqn, (1) and (2) and after some mathematical manipulations, we found the expressions of the PL and absorption coefficient as

I PL



 



2 2   i3INT   r / 2   nr   ba   nr   r       hab b   Im   2 2   r   nr     r / 2   nr  i  ba   nr    r / 2   nr   ba   nr  2  INT       



 abs

 

 

 



2 2   i INT   r / 2   nr    ba   nr       Im   2 2  b hb    / 2     i        / 2          2   nr ba nr   nr ba nr INT    r   r

ab2

(16)

(17)

Note that the nonradiative decay rate Γ𝑛𝑟 is responsible for the PL quenching in the QE-shell. The PL also depends on the DDI term Φ𝐷𝐷𝐼. The DDI term is the dominant terms in the PL and they are responsible for the enhancement of PL. Similarly, absorption spectrum depends on the DDI term Φ𝐷𝐷𝐼. This term is also the dominant term in the absorption spectrum and is responsible for enhancement of the absorption spectrum. The peaks of the PL and absorption spectra are shifted due to the nonradiative interaction term Δnr.

III. Results and Discussions In this section we compare our theory with experiments of a QE-shell hybrid from reference. 14 One of authors (i.e. Fanizza et al. 14) has measured the PL and absorption coefficient for a hybrid made of a QE-shell and ensemble of MNPs. Their QE-shell is fabricated from a CdSe/ZnS-QD and a silica outer shell. This structure is called QD-shell in the rest of the paper. The diameter of the QD-shell is 2Rqs = 16 nm and the thickness of the shell is ts = 6 nm. 14 Therefore, the diameter of the CdSe/ZnS-QD is about 2Rq = 4 nm. The QD-shell structure was embedded in the ensemble of Au-MNPs. The diameter of the Au-MNPs was about 2Rm = 4 nm. 14 They measured the absorption coefficient of the QD-shell as a function of SSP resonance wavelengths (λsp). The experimental data are plotted in fig. 3. The expression of the SSP and DDI fields contains the polarization parameter 𝛽𝑚 which is given in eqn. (4). The polarization parameter contains the dielectric constant (function) for metallic nanoparticles ϵm which is taken as follows m  

 p2  2  i m

(18)

where 𝜔𝑝 is the plasmon frequency and 𝜖∞ is the permittivity at very large energies (𝜔 ≫ 𝜔𝑝) and 𝛾𝑚 is the decay rate which is due to the thermal energy loss in the MNP. We have considered ℏ𝜔𝑝 = 9 𝑒𝑉, 𝜖∞ = 8 and 𝛾𝑚 = 0.3 𝑒𝑉4 for gold in our numerical simulations.



Fig. 3: Plot of the absorption coefficient of the CdSe/ZnS quantum dot as a function of the SPP resonance wavelength (λsp). The solid squares are experimental data for samples 0.5 M, 2.0 M, 4.0 M and the dotted curve is the theoretical simulation. Parameters used in the theoretical simulations are taken as ℏ𝜔𝑝 = 9 𝑒𝑉 and 𝜖∞ = 8, 𝛾𝑚 = 0.3 𝑒𝑉, 𝜖b = 1.3.

We have compared our theory of the absorption coefficient with experiments of the nanohybrid. 14 Experiments were performed by one of authors (Fanizza). The nanohybrid is fabricated by embedding QD-shell (CdSe/ZnS-QD core and silica shell) in the ensemble of Au-MNPs. The results for this the nanohybrid are plotted in fig. 3 as the function of the SPP resonance wavelength (λsp). The solid squares are the experimental data for the absorption peak positions for samples 0.5 M, 2.0 M and 4.0 M. The absorption peaks for nanohybrid samples 0.5 M, 2.0 M and 4.0 M are located at λsp =523 nm, λsp =539 nm and λsp =568 nm, respectively. Here λsp stands for the SPP resonance wavelength. The dashed-dotted curve is our theoretical simulation. We have included the radiative and nonradiative decay rates γr and Γnr in the calculation of the absorption coefficient. The wavelength dependence of the nonradiative decay rate has been included in our calculations. From fig. 3, one can see a good agreement between theory and experiment is found. Note that our theory shows that there is an enhancement in the absorption of light in the QE-Shell as SPP resonance wavelength (λsp) increases. Our theory predicts that the enhancement in the absorption spectrum is mainly due to the SPP field and the DDI field. This means that the both fields play an important role in the enhancement of the absorption peak. One can also say that the QE-shell can be used as nanosensors to find the SSP resonance wavelength which is related to the concentration of MNPs.


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Fig. 4: Plot of the energy shift in the absorption coefficient of the CdSe/ZnS quantum dot as a function of the SPP resonance wavelength (λsp). The solid squares are experimental data for sample 0.5 M, 2.0 M and 4.0 M and the dashed-dotted curve is the theoretical simulation. Parameters used in the theoretical simulations are taken as ℏ𝜔𝑝 = 9 𝑒𝑉 and 𝜖∞ = 8, 𝛾𝑚 = 0.3 𝑒𝑉, 𝜖b = 1.3.

One of the collaborators (Fanizza) has also measured the energy shift of absorption peaks for the nanohybrid. 14 Their nanohybrids is fabricated by embedding QD-shell (CdSe/ZnS-QD core and silica shell) in the ensemble of Au-MNPs. We have compared our theory of energy shift with Fanizza’s experiments. The results are plotted in fig. 4 where solid squares are experimental data for nanohybrid samples 0.5 M, 2.0 M and 4.0 M. In this figure, we have also plotted the energy shift as a function of the SPP resonance wavelength (λsp). The dotted curve is the theoretical simulation. A good agreement between theory and experiment is found. Note that our theory shows that as the SSP resonance wavelength (i.e. the concentration of MNPs) increases, the energy shift also increases. Our theory predicts that the energy shift in the absorption is due to the nonradiative energy shift (i.e. ∆𝑛𝑟). We found that the energy shift is mainly due to the SPP field and the DDI field. This is also an interesting finding and can be used to develop new types of nanosensors by using QE-shell hybrids. They can detect the energy shift in the absorption peaks due to the change in the concentration of MNPs. Next, we have calculated the PL quenching in terms of the quantum yield of the PL spectra for the CdSe/ZnS-QD, the silica coated CdSe/ZnS-QD (QD-shell) and the QD-shell embedded in the AuMNPs (nanohybrid). In the calculation of the quantum yield for the CdSe/ZnS-QD, we have neglected the nonradiative decay rates Γshell, ΓDDI and ΓSPP since the shell and the ensemble of MNPs are absent. Here Γshell is the nonradiative decay rate due the coupling of exciton with the induced electric field (Es) produced by the shell. The quantum yield for CdSe/ZnS-QD is found to be 100%. On the other hand, in the calculation of the quantum yield for the QD-shell we put Γnr = Γshell and neglected ΓSSP and ΓDDI since MNPs are absent. The nonradiative decay rate due the shell is calculated as Γshell = γr Im (П S) where П s = ES / EP. The electric field ES is calculated from EQE (eqn. (8)) by putting 𝜖q = 1 i.e. ES = EQE (ϵq = 1). The quantum yield for the QD-shell is found as 11 ACS Paragon Plus Environment


64%. Finally, the quantum yield for the nanohybrid is calculated as 27.3%. One of the author (Fanizza) have measured the quantum yield for the CdSe/ZnS-QD, the QD-shell and the nanohybrid, they found quantum yield for the CdSe/ZnS-QD as 100%, the quantum yield for the QD-shell as 61.1% and the quantum yield for the nanohybrid as 27.7%. The authors are publishing these quantum yield experimental results in this paper. Our theoretical calculations agree with the experimental. We found that the photoluminescence quenching occurs mainly due to the dipoledipole interaction. Hence, we call this effect as anomalous photoluminescence quenching. We have also found that the anomalous photoluminescence quenching decreases as the shell thickness increases. Finally, we compare our theory for the PL with experiments on the PL emission of nanohybrids fabricated from the QD-shell (CdSe/ZnS-QD core and silica shell) and the ensemble of Au-MNPs. One of authors (Fanizza) has also measured the PL spectrum for this nanohybrid. 14 The results are plotted in fig. 5. The solid circles are experimental data for CdSe/ZnS-QD alone. Whereas the open squares are the PL spectrum for the nanohybrid. The solid and dotted curves are theoretical simulations for CdSe/ZnS-QD alone and the nanohybrid, respectively. In our simulations, we have considered that the CdSe/ZnS-QD has two states |𝑎⟩ and |𝑏⟩ and this is also consistent with their experimental data. The resonance wavelength of the exciton due to the transition |𝑎⟩→|𝑏⟩ is denoted as λab and lies near the SPP resonance wavelength λsp.

Fig. 5: Plot of the PL(A.U.) of the CdSe/ZnS-QD as a function of wavelength. The solid circles are experimental data for CdSe/ZnS-QD alone. Whereas the open squares are the PL spectrum for the CdSe/ZnS-QD embedded in the ensemble of Au-MNPs. The solid and dashed-dotted curves are theoretical simulations for CdSe/ZnS-QD alone and the CdSe/ZnS-QD embedded in the ensemble of Au-MNPs, respectively. The parameters used are the same as fig. 4.

One can see from fig. 5 that our theory of PL agrees well with their experimental data. In our simulations, the wavelength dependence nonradiative decay rates are calculated. We found the enhancement of the PL spectrum is associated with quantity ΩINT in eqn. (16). The expression of ΩINT is given in eqn. (15) and it depends mainly on the DDI field produced by the ensemble of MNPs. It is responsible for the enhancement of the PL. The quenching of PL is controlled by the nonradiative decay rate Γnr. The quenching and enhancement mechanisms compete in the 12 ACS Paragon Plus Environment

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nanohybrid. We found that the enhancement mechanism is the dominant one in these hybrids. It has also been found that the main contribution to the enhancement mechanism is the DDI field produced by the ensemble of MNPs. Note that the shoulder at 575nm for the nanohybrid case in Fig 5 is due to the extra enhancement from the SSP and DDI fields of the Au nanoparticles. We can say that the QE-shell nanohybrid can be used to measure the enhancement of PL spectrum. Hence this finding can be used to make PL nanosensors for applications in nanomedicine and nanotechnology. In this paper we have studied the enhancement and quenching of the PL in nanohybrids. The enhancement mechanism in our theory is due to the physical parameter ΩINT defined in eqn. (15)). The physical meaning of this parameter is that the electric field falling on the QE is enhanced due to the presence of the SSP and DDI fields. The quenching mechanism in our theory is due to the nonradiative decay rate calculated in eqn. (15). It is found that enhancement mechanism plays an important role when the of the spacer layer is present between the QE and the MNP. In our present work, the role of the spacer layer is played by the shell in QE-shell. On the other hand, the quenching mechanism plays an important role when the of the spacer layer is NOT present. In the presence of the spacer layer both enhancement and quenching mechanisms are present. As the thickness of the spacer layer increase the enhance mechanism increases and the quenching mechanism decreases. We will make comment on the strength of the DDI field and SSP field in the calculation of the PL and absorption coefficient. The strength of the DDI field and SSP fields are represented by the physical parameters ΦDDI and ПSPP, respectively. Both are given in eqn. (11). To compare strengths of the DDI and SSP fields, let us define the strength of the DDI coupling ratio as

Ratio 

 DDI  SPP

(19)

Where Ratio is called the DDI strength ratio. Putting the expressions of ΦDDI and ПSPP from eqn. (11) into the above eqn. (19), we get m  DDI 

Rqs3  qs r3

Ratio 

Rm3 Rqs3  qs  m m Rm3  m m   DDI  DDI r3 r6 3 3 Rm3  m Rm Rqs  qs  m  r3 r6

m  DDI 

(20)

Breaking the numerator into two parts and performing simple mathematical manipulations the above expression (eqn. (20)) reduces to

 Rm3  m Rm3 Rqs3  qs  m Rqs3  qs  m    DDI  3  r3 r r6    Ratio    3 3 3 Rm3  m Rm Rqs  qs  m Rm3  m  Rqs  qs   1   r3 r6 r 3  r 3  

m  DDI 1 


  

(21)


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After cancelling out the terms in numerator and denominators and putting the expression of ηDDI from eqn. (7), we get the following expression of the DDI strength ration as Ratio  gl

m  m 3

 gl

m  r 

3

  3  Rm 

(22)

One can see from eqn. (22) that the DDI strength ratio depends on (r/Rm) and the polarization parameter βm. One can see that Ratio >> 1 since (r/Rm) > 1 and βm>> 1. We have also calculated the DDI strength ratio numerically from eqn. (20) at r = Rqs and λ=λsp and found it is about 30. This means the strength of the of DDI field is about 30 times stronger than the SSP field.

IV. Conclusions A theory for the anomalous PL quenching and absorption enhancement has been developed for nanohybrids made of an ensemble of metallic nanoparticles and the QE-shell. Using the quantum mechanical density matrix method, we have derived an expression for the PL, absorption coefficient and the nonradiative decay rate. Electric dipoles are induced in the ensemble of MNPs and these dipoles interact with each other via the DDI. Surface plasmon polaritons are created at the interfaces of a metallic nanoparticle due to the DDI field. Excitons in the quantum emitter interact with the DDI field. We showed that PL quenching and enhancement occurs mainly due to the DDI in the ensemble of MNPs. We showed that energy shift in the absorption peak increases as the DDI increases. We also found that the absorption coefficient enhances as the DDI increases. The increase of the DDI is due to the increase of concentration of MNPs in the ensemble. We have compared our theory with experimental data of the silica coated CdSe/ZnS-QD embedded in the ensemble of Au-MNPs. A good agreement between theory and experiment is found. Author Information Corresponding Author *e-mail:

[email protected] (M.S.)

Acknowledgments: One of authors (MRS) is thankful to the Natural Sciences and Engineering Research Council of Canada (NSERC) for the research grant. We also thank Mr. Kevin Black for the English editing of the paper.


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Anomalous Photoluminescence Quenching in Metallic Nanohybrids

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