Mechanism of Bimodal Light Emission in a Molecule-Mediated

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Mechanism of Bimodal Light Emission in a Molecule-Mediated Scanning Tunneling Microscopy Junction Lei-Lei Nian and Jing-Tao Lü*

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School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, P. R. China ABSTRACT: We simulate the light emission from C60 films driven by the tunneling electrons injected from a scanning tunneling microscope (STM) tip. Considering a model Hamiltonian which contains electron−photon and exciton−plasmon interactions, the emission spectrum is calculated by using the nonequilibrium Green’s function method. Our simulations indicate that the two emission channels induced by the exciton and gap plasmon are almost independent in such a system, which gives rise to a bimodal-shaped light emission, and the emission ratio between the two channels can be controlled by varying the position of the STM tip. These results are consistent with recent experimental observations. Furthermore, the light emission is shown to be sensitive to the energy detuning and the bias voltage. The connection between bimodal and typical Fano line shape is also clarified. In particular, the stronger Purcell effect that is manifested by a significant enhancement of the spectrum in weak molecule−substrate coupling regime can be observed.

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INTRODUCTION Molecular electroluminescence (EL) driven by localized tunneling electrons injected from the tip of a scanning tunneling microscope (STM) has been extensively studied in recent years.1−9 When a molecule is positioned nearby a STM tip, there are two important EL sources. One is the molecular exciton induced by the recombination of electron and hole injected from the tip and substrate; the other is radiative damping of gap plasmons driven by inelastic tunneling current.10−12 Strong evidence has indicated that EL of a single molecule confined in a STM is mediated by gap plasmons, especially when the molecule cannot be excited by the tunneling current directly;5,8,13−18 that is, the energy transfer from gap plasmons makes it possible to excite molecules indirectly. Moreover, the gap plasmons are also confirmed to participate in the process of light emission when the molecules is directly attached to the STM tip. The molecules can be excited directly by the injected electrons from the tip in this case.15 Therefore, the molecular light emission in a STM junction can be significantly affected by the appearance of coupling between molecular exciton and gap plasmons.5,11,19 Recently, the Fano resonance in the emission spectrum has been observed in a series of independent experiments.8,15−18 In such STM-induced luminescence (STML) experiments, the Fano resonance results from the coherent energy transfer between molecular exciton and gap plasmons and manifests itself in light spectra as an asymmetric line shape,8,15−18,20,21 which can be modeled theoretically.18,22 In addition to the Fano resonance, there are some interesting effects in the coupled plasmon−exciton systems, such as resonance energy transfer induced by plasmons,23,24 strong plasmon−exciton coupling,25−28 and plasmon-enhanced emission and absorption,29,30 forming an important platform to © XXXX American Chemical Society

study light−matter interaction in the nanoscale. Correspondingly, new optical devices based on such hybrid systems have been proposed, including nanolasers, ultrafast switching, and biosensors.31−33 Very recently, bimodal light emission from C60 crystallites positioned nearby a STM tip has been observed by Merino et al.34 Unlike the conventional light emission spectra,8,15−18 the Fano line shape cannot be observed in this experiment. They attribute this phenomenon to the presence of two independent light emission channels, namely, exciton and plasmon emission. Meanwhile, the ratio between the two emission processes can be controlled precisely by adjusting the position of the STM tip. This allows one to control or characterize the contribution of exciton and gap plasmon to electroluminescence, which is important for the development of plasmonics and nanophotonics. However, a systematic theoretical model describing the new STML mechanism has not been established, especially determining the connection between bimodal emission and typical Fano-featured emission such a system. In this paper, we use a simple model to describe the STMinduced bimodal light emission observed on the surface of C60 films. The bimodal light emission induced by two independent emission channels from exciton and gap plasmon is identified. Moreover, the mechanisms for both bimodal and Fanofeatured emission were clarified. Taking the parameters from the experiment, our theory provides a consistent account of the evolution of the emission spectrum with the relative tip− molecule position, as observed in the experiment. Our results Received: January 6, 2019 Revised: July 3, 2019 Published: July 8, 2019 A

DOI: 10.1021/acs.jpcc.9b00132 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

field contains a continuum of modes. To characterize the light emission of molecule films, we only consider the modes around angular frequencies of excitons. In our model, the molecule films are modeled by two well-defined defect states (i.e., d1 and d2 in Figure 1a), such that the light emission from the exciton is centered around a single frequency. Correspondingly, only the mode at the corresponding frequency in the radiation field can be excited by the exciton. The Hamiltonian describing the coupling between the two defect states and electrodes (tip and substrate) takes the form

also present a direct theoretical evidence that the light emission spectra of the considered system is sensitive to the energy detuning, the bias voltage, and the molecule−substrate coupling.

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MODEL AND THEORY To simulate the light emission from C60 films in a STM junction (see Figure 1a), we model the system with two defect

Htun =

(Vkick†ci + h. c . )

∑

(3)

k = t , s;i

where Vki is the molecule−electrode coupling. By using the wide-band approximation, the parameters of tip−molecule coupling Vtm (= Vtd1 = Vtd2) and molecule−substrate coupling Vsm (= Vsd1 = Vsd2) can be represented in the theory by Γtm(ε) = 2π∑k ∈ t|Vtm|2δ(ε − εk) and Γms(ε) = 2π∑k ∈ s|Vsm|2δ(ε − εk). They characterize the level broadening. The elastic and inelastic tunneling of electrons between the tip and substrate can be expressed as Heit =

∑ m0(cd† cd aα† + h. c. ) 2

1

α

+

[(mpap† + tts)ck†c k′ + h. c . ]

∑ k , k ′= t , s

+ m0p(c d†2c d1ap† + h. c . )

Figure 1. (a) Schematics of the STM junction with two defect states (high d1 and low d2) connected to the STM tip and the substrate. Three light emission channels are present: (i) exciton, the εd2 is above the chemical potential of tip and εd1 is below the chemical potential of the substrate, a hole (⊕) and an electron (⊖) can be injected from the tip and substrate, and the recombination of them generates light emission; (ii) gap plasmon, an electron undergoes an inelastic process from the substrate to defect state d1, which is accompanied by the emission of a gap plasmon, whose radiative damping leads to light emission; and (iii) gap plasmon, similar to (ii), but an electron tunnels directly between the substrate and STM tip. (b) The electronic system including the electrodes (tip and substrate) and two defect states under a certain bias voltage can be regarded as a nonequilibrium electron bath, which is the energy source of the three emission channels. The emitted light can be detected by the photon detector, and part of the energy may be dissipated nonradiatively to the environment.

+ mp1(cs†c d1ap† + h. c . )

where these inelastic tunneling terms are obtained within the rotating wave approximation.35 The first term describes the coupling between exciton and radiation field, and the exciton is represented by c†d2cd1 (c†d1cd2) with the angular frequency ω0 = (εd1 − εd2)/ℏ. The second term describes two kinds of electron tunneling: (1) The process that leads to the excitation (deexcitation) of gap plasmon induced by the inelastic tunneling electrons from tip to substrate, or vice versa, where the energy conservation requires εk − εk′ ≈ ℏωp; (2) The elastic process that represents electron tunneling between the tip and substrate, in which the energy conservation requires εk = εk′. The third term is the coupling between exciton and gap plasmon. The last term also describes the excitation (deexcitation) of gap plasmon, in which the electrons injected from the substrate tunnel to the defect state d1 inelastically. In this case, the defect state d1 opens a new inelastic tunneling channel for the electrons injected from the substrate, while the defect state d2 does not participate in this inelastic tunneling process, as observed in experiments.34,36 The parameters m0, mp, m0p, and mp1 represent the coupling between exciton and radiation field, the coupling between electron (in electrodes) and plasmon, the exciton−plasmon coupling, and the coupling between electron (in substrate and defect state d1) and plasmon. The photon detector can be modeled by a far field, 1 Hd = ∑ν ℏων aν†aν + 2 , the radiative decay of gap plasmon is assumed to enter it. The coupling between gap plasmon and photon detector is

states d1 and d2 coupled to two electrodes tip (t) and substrate (s). The corresponding Hamiltonian is H = H0 + Htun + Heit + Hph − ph

(1)

where H0 describes the isolated electron and photon systems (including molecule, electrodes, radiation field, and gap plasmon) H0 =

∑

εici†ci +

+

∑

∑ ℏωαijjjaα†aα +

i = d1, d 2

α

k=t ,s

k

εkck†ck

1 yz 1y i zz + ℏωpjjjap†ap + zzz 2{ 2{ k

(4)

(

(2)

†

where c (c) denotes the creation (annihilation) operator of electrons, a† (a) is the corresponding operator for photons, εi is the energy of the defect state i = d1/d2, ωα is the radiation field angular frequency with the mode index α, and ωp is the angular frequency of the gap plasmon. Actually, the radiation

Hph − ph =

∑ Vνp(aν†ap + h. c. ) ν

B

)

(5) DOI: 10.1021/acs.jpcc.9b00132 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

This simplifies our calculation a lot, and the final results are not affected.

where the coupling Vνp can be represented by the parameter γdp(ω) = 2π∑ν|Vνp|2δ(ω − ων). This characterizes the radiative damping of gap plasmon. The nonradiative damping can be characterized by parameter γpe.22,37 Similarly, we assume that the photon mode with angular frequency ω0 in the radiation field strongly couples to the photon detector, and the radiative (nonradiative) damping of exciton can be represented by parameter γd0 (γ0e). In general, the nonradiative damping mechanisms (such as electron−hole pair excitations, vibrational excitation, and so on) could be of a different nature, and we do not model them explicitly. The parameters γdp, γpe, γd0, and γ0e enter our model through self-energies, such that the fluctuation−dissipation theorem is satisfied, that is, Π eVts, where ℏω is the photon energy. This is due to the fact that only the singleelectron tunneling events are considered in our model. We also note that the overbias light emission driven by higher-order quantum noise has been observed in a tunnel junction.65 Moreover, the intensity of the spectrum can be enhanced with increasing Vts. The behavior is clearly shown in the inset, in which we plot the intensities of the exciton and plasmon as a function of Vts. It is noted that there is an intersection between the curves of excitonic and plasmonic intensities, which indicates that the bias voltage is another optional way to control the ratio between the two emission channels.

Jing-Tao Lü: 0000-0001-8518-2816 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by the National Natural Science Foundation of China (Grant No. 21873033), the National Key Research and Development Program of China (Grant No. 2017YFA0403501) and the program for HUST academic frontier youth team.

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CONCLUSIONS In this paper, we theoretically studied the light emission from a C60 molecular film induced by a scanning tunneling microscope, as motivated by a recent experiment.34 We proposed a simple model for the molecular junction, simulating it by two well-defined defect states coupled to two electrodes. We took into account two channels of gap plasmonic excitation and their coupling with the exciton. By means of the nonequilibrium Green function method, the light emission spectra from molecule and gap plasmon driven by bias voltage was calculated. It is found that the bimodal emission is caused by two independent emission channels induced by exciton and gap plasmon, and the emission ratio between the two channels can be controlled by the tip position. We also demonstrated that the energy detuning and the bias voltage can be used to adjust the emission ratio between the excitonic and gap plasmonic channels. Interestingly, a stronger Purcell effect can be achieved by varying the molecule−substrate coupling. Our results can motivate further experimental and theoretical studies on coupled plasmon−exciton systems.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. F

DOI: 10.1021/acs.jpcc.9b00132 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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H

DOI: 10.1021/acs.jpcc.9b00132 J. Phys. Chem. C XXXX, XXX, XXX−XXX