On the Fano Line Shape of Single Molecule Electroluminescence

Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX

pubs.acs.org/NanoLett

On the Fano Line Shape of Single Molecule Electroluminescence Induced by a Scanning Tunneling Microscope Lei-Lei Nian,† Yongfeng Wang,‡ and Jing-Tao Lü*,† †

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School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, 430074 Wuhan, People’s Republic of China ‡ Key Laboratory for the Physics and Chemistry of Nanodevices, Department of Electronics, Peking University, 100871 Beijing, People’s Republic of China S Supporting Information *

ABSTRACT: The coupling between molecular exciton and gap plasmons plays a key role in single molecular electroluminescence induced by a scanning tunneling microscope (STM). But it has been difficult to clarify the complex experimental phenomena. By employing the nonequilibrium Green’s function method, we propose a general theoretical model to understand the light emission spectrum of single molecule and gap plasmons from an energy transport point of view. The coherent interaction between gap plasmons and molecular exciton leads to a prominent Fano resonance in the emission spectrum. We analyze the dependence of the Fano line shape on the system parameters, based on which we provide a unified account of several recent experimental observations. Moreover, we highlight the effect of the tip−molecule electronic coupling on the spectrum. KEYWORDS: Scanning tunneling microscope, light emission, Fano resonance, molecular exciton

S

the system parameters is important for further development and application of this technique. Here, we propose a general theoretical model that is able to account for all these experimental results. We first demonstrate that the coherent optical coupling between molecular exciton and gap plasmons leads to a pronounced Fano resonance, whose line shape depends sensitively on the system parameters. Using the parameters extracted from experiment, the simulated spectrum shows quantitative agreement with the experimental results. This is an essential step to predict or control the dynamic energy transfer process in STML experiments. Model and Theory. We consider a model system schematically shown in Figure 1a. The voltage bias applied between the tip and the substrate generates a flowing electrical current between them, which is used to excite the localized gap plasmons. A single molecule is represented by two electronic

ingle molecular electroluminescence (EL) induced by the inelastic electron tunneling from a scanning tunneling microscope (STM) has attracted renewed interest, yielding many fascinating behavior and potential applications1−7 In such STM-induced luminescence (STML) experiments, light emission from gap plasmon modes is a universal phenomenon,8−14 which in turn can dominate, accompany, or influence the luminescence of single molecules positioned nearby STM tip.3,4,15,16 The resulting coupling between the molecular exciton and gap plasmons has revealed its importance in recent experiments,17−30 through, for example, prominent Fano31 line shapes in the emission spectrum. Vibrational signal has also been observed, which can be used for single molecule detection.27−29 Statistical property of the emitted photon reveals single photon antibunching behavior, which is characteristic of single photon source.32 Despite its scientific importance and potential applications, a systematic theoretical model to account for all these experimental results is so far lacking. Revealing the connection between the line shape and © XXXX American Chemical Society

Received: July 3, 2018 Revised: October 16, 2018 Published: October 16, 2018 A

DOI: 10.1021/acs.nanolett.8b02706 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters

Figure 1. (a) Schematic picture of the experimental setup in STM-induced light emission and single molecule luminescence. (b) Effective model to study the energy transfer in the experimental setup in (a). The nonequilibrium electron bath includes the STM tip, the substrate, and the single molecule under certain voltage bias. The gap plasmon is represented by a photon mode with angular frequency ωp, whereas that of molecular exciton is ω0 = (εl − εh)/ℏ. There is a direct coupling whose magnitude depends on the relative position of the STM tip and the molecule x (see (a)). The emitted light is collected by the photon detector. There are also nonradiative channels into which the two photon modes can dissipate their energy, denoted by the environment.

where tikν is the tunnel coupling between molecule and the tip or the substrate. We note that, the coupling to the tip could change or even go to zero, depending on the tip position. Meanwhile, the coupling to the substrate is always nonzero. To model the molecular coupling to tip and substrate, we use the wide band approximation, such that the level broadening parameters Γms and Γmt, instead of tikν, are used to characterize the coupling. Their relationships are given in Section I of the Supporting Information (SI). While all the electronic states in the electrodes affect the center molecular levels through Γms/ Γmt, only those that can couple to the gap plasmon are modified due to electron-plasmon interaction via the selfenergies. The photonic Hamiltonian includes the free propagating photon field Hfp, the localize gap plasmon Hgp, and their interaction Hfg

states l and h, representing the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO), respectively. If the molecule is present underneath the STM tip, under certain bias a molecular exciton may also be excited by the electrical current, that is, injecting an electron to the LUMO and a hole to the HOMO orbital. If the molecule is not far away from the tip, the molecular exciton can be excited by the gap plasmons, given its much wider frequency and larger spatial distribution. This requires a direct coupling between the gap plasmons and the molecular exciton, the coupling is characterized by the parameter tp(x), which depends on the tip−molecule distance x (see Figure 1a). The model Hamiltonian includes the electronic part Hel, the photonic part Hph and their interaction term He−p H = Hel + Hph + He − p

(1)

The electronic Hamiltonian further includes the following parts Hel = Hb + Hm + Hbm

=

(2)

∑

εkνck†νckν +

kν = t,s

∑

tνν ̅(ck†νck

kν , k ′ ν

′ν̅

+ ck† ν ̅ckν) ′

(3)

He − p =

i = h,l kν = s , t

α

mp(ck†νck ν ̅a p† + ck† ν ̅ckνa p) ′ ′

+ t p(x)(dh†dla p† + dl†dha p) +

∑ m0(dh†dlaα† + dl†dhaα) α

(7)

Here, the first term describes the emission/absorption of gap plasmon due to direct electron tunneling between the tip and the substrate, with kν and k′ν̅ states from two electrodes. It does not involve the molecule and the energy conservation relation becomes εk′ν̅ − εkν = ℏωp. The coupling between two electronic states kν and k′ν̅ is mediated by the gap plasmon in this case. This kind of coupling is explicitly included in our calculation. The second term in eq 7 describes the interaction between gap plasmon and molecular exciton. We note that the

∑ εidi†di

∑ ∑

∑ kν , k ′ ν

(4)

where di† (di) creates (annihilates) an electron on the molecular orbital i = h, l with energy εi. The coupling between molecule and baths is Hbm =

∑ tα(aα†ap + aαap†)

Here, ωp is the angular frequency of the gap plasmon, α is the free propagating mode index, and tα represents the coupling between the gap plasmon and the propagating mode α. In the calculations, the coupling is represented by a constant γdp in the spirit of wide band approximation. The relationship between tα and γdp is given in Section I of the SI. We introduce an extra γpe to characterize the nonradiative coupling to the environment. The electron−photon interaction is described within the rotating wave approximation33

where (ckν) creates (annihilates) an electron in reservoir ν (tip or substrate) with momentum k and energy εkν. The second term describes the direct elastic tunneling between tip and substrate. When a voltage bias is applied, the electrons can transport from the electrode with high chemical potential to the electrode with low chemical potential. For the elastic tunneling process, this does not involve any energy loss. Thus, energy conservation is satisfied εkν = εk′ν.̅ When the molecule lies away from the tip, electron transport occurs through this direct tunneling. These are considered explicitly in the calculation on discrete equal-spaced energy grids. Here ν̅ means electrode different from ν and we take tνν̅ = tν̅ν = 1.5 eV. Hamiltonian of the molecule is i = h,l

y i1 y + aα†aα zzz + ℏωpjjj + a p†a pzzz + { k2 {

(6)

c†kν

Hm =

k2

α

The electron bath Hamiltonian includes contributions from the tip (t) and substrate (s) electrons Hb =

∑ ℏωαijjj 1

Hph = Hfp + Hgp + Hfg

tikν(di†ckν + ck†νdi) (5) B


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Nano Letters molecular exciton is described by d†hdl and d†l dh with the angular frequency ω0 = (εl − εh)/ℏ. Thus, d†hdla†p describes annihilation of molecular exciton accompanied by generation of a gap plasmon, and d†l dhap describes the opposite process. The last terms describe the coupling of molecular exciton to propagating radiation field. Because of energy conservation, the molecular exciton mainly couples to the propagating modes with the same frequency ωα = ω0. Moreover, we introduce two parameters γ0e and γpe to characterize the coupling between molecular exciton and gap plasmon to the nonradiative environment, see details in Section I of the SI. To study the energy transfer between the electron and photon fields, we use an effective model shown in Figure 1b. The biased electronic system acts as an effective nonequilibrium electron bath, which supplies energy to the gap plasmons and the molecular exciton. The energy absorbed by the two emission channels is either dissipated into the environment or radiated to the free space. The radiation then goes to the detector. Energy transport for this effective model can be studied using the nonequilibrium Green’s function (NEGF) method.34−37 The frequency-resolved energy flux going into bath α is written as Iα(ω)dω =

Figure 2. Energy detuning Δp0 dependence of emission spectrum (black lines). The red lines represent the spectrum of gap plasmon mode. In the calculations, the most important parameters are εl = −1.55 eV, εh = −3.45 eV, Γmt = 0, Γms = 1 meV, tp(x) = 0.01 eV, mp = 8 meV, m0 = 1 meV, γ0e = 5 meV, γd0 = 1 meV, γpe = 0.18 eV, and γdp = 18 meV. The temperature is T = 8 K and the applied bias is Vst = μs − μt = −2.5 V. The tip chemical potential is set to 0, and the substrate chemical potential changes with bias. Note that Γms, Γmt represent the molecule−substrate coupling, molecule−tip coupling, respectively. Also, γ0e (γpe), γd0 (γdp) represent the nonradiative and radiative damping of the molecular exciton (gap plasmon). The details are given in the Section I of SI.

ℏω Tr[Π(ω) − Π>α (ω)D

α (Π |eV|. It enters into our theory through the self-energy Πel on which the Green’s functions D> and D< in eq 8 depend. Meanwhile, the line shape of the spectrum is mainly determined by the two parameters describing the photon mode, which we consider in the following. The first important parameter that determines the line shape is the detuning Δp0 = ℏ(ωp − ω0). In the experiment, the resonant frequency of gap plasmon ωp can be tuned by adjusting the tip shape or modifying the dielectric properties of the substrate, that is, introducing dielectric layers. Figure 2

displays the evolution of the spectrum with different values of energy detuning Δp0. We note that the strong energy detuning dependence of the Fano line shape is in agreement with experimental findings27 and can be fitted by a standard model detailed in Section II of SI (eqs 22 and 23), where the magnitude of the Fano q factor is mainly determined by the detuning q ∝ −Δp0. The second parameter is the coupling between the gap plasmon and the molecular exciton tp(x), determined by the relative position of the tip and the molecule (x), according to which, we can define three regimes. They correspond to the tip apart from (I), slight aside from (II), and located on top of the molecule (III), respectively. The energy flux spectrum of different situations is plotted in Figure 3. In case I, a broadband emission in the STML spectra can be observed in Figure 3I. This comes from the radiative decay of the gap plasmon, whereas the molecular exciton does not participate to the transport. The other two cases are more interesting, which we focus in the following. In case II, the interaction between the molecular exciton and the gap plasmon occurs, which results in coherent energy transfer between them. This interaction generates a sharp dip in the broadband emission spectra, as shown in Figure 3II. The resulting asymmetric line-shape is a signature of the Fano resonance. Essentially, the single molecule only couples to the substrate in this case, no tunneling electrons excite the single molecule directly. But it can be excited by the gap plasmon indirectly. Also shown in the figure are the separate contributions of the flux from the gap plasmon and the molecular exciton. The spectrum of the molecular exciton is a C


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Figure 3. Photon energy flux calculated as the tip is (I) apart from the molecule, (II) slight aside from the molecule so that there is a coupling between gap plasmon and the molecular exciton, but no direct electronic coupling between the tip and the molecule, (III) located on top of the molecule, so that there is direct electronic coupling between the tip and the molecule. The separate contributions from the plasmon (Ip) and the molecular exciton (Im) are shown as dotted lines, while the sum of the two (It) is shown as red solid lines. The parameters producing the plots are the following: (I) m0= 0, γd0 = 0, γ0e = 0, ℏωp = 1.908 eV, and tp(x) = 0; (II) ωp = 1.908 eV and tp(x) = 0.01 eV; (III) εl = 1.5 eV, εh = −0.01 eV, Γmt = 0.01 eV, Γms = 5 meV, ωp = 1.41 eV, tp(x) = 0.02 eV, mp = 1 meV, m0 = 1 meV, γ0e = 35 meV, γd0 = 9 meV, γpe = 0.35 eV, γdp = 35 meV, T = 4.5 K, Vst = 1.6 eV. The other parameters for (I) and (II) are the same as in Figure 2.

Figure 4. (a) The photon energy flux for different values of the parameter L with other parameters fixed. The red line represents the spectrum of gap plasmon for Vst = −3 V. (b) The photon emission spectrum for different values of tp(x). (c) Similar to (b), with different parameters εl = −1.4 eV, εh = −3.2 eV, Γmt = 0, Γms = 0.1 meV, ℏωp = 2.0 eV, mp = 15 meV, m0 = 0.1 meV, γ0e = 0.1 meV, γd0 = 0.5 meV, γpe = 0.18 eV, γdp = 30 meV, T = 4.6 K, Vst = −2.3 eV. Other parameters for (a,b) are the same as in Figure 3III and II, respectively.

A Suspended Molecular Wire. STM-induced narrow-line emission from a single molecular emitter (Porphyrin molecule - H2P) connected to the tip and the substrate through oligothiophene linkers was reported in ref 42. The light spectra exhibits an asymmetric line shape in a broad background with the peak position closely associated with the emission energy of the isolated molecule. The oligothiophene wires decouple the H2P emitter from the substrate and the tip. The length of the linker can be adjusted by lifting the STM tip away from the substrate. Therefore, the distance between tip and substrate plays a key role in achieving molecular luminescence. Here, we simulate the evolution of tip−substrate distance by adjusting the parameter L, which characterizes the lifetime of the molecular exciton (LTME), that is, the large L for long LTME. In our system, we set Γms = 0.05 eV − 0.1 × L and γ0e = 0.1 eV − 0.8 × L, indicating the Γms and γ0e decrease with the L increases. Which means that the molecule−substrate coupling

normal Lorentzian-like peak, while that of the plasmon shows the typical Fano line shape and contributes dominantly to the total spectrum. In case III, the molecule is underneath the STM tip. Both molecular exciton and gap plasmon can be excited directly by the tunneling electrons. In this case, a sharp peak instead of dip is observed. The signature of the molecular exciton becomes dominant, that is, the magnitude of the broad plasmon background is much smaller than the exciton peak, although most of the power still comes from the gap plasmon channel. We now apply our theory to consider three recent experiments. We show that they fall into one of the abovediscussed three regimes. In the first experiment, the molecule is attached to the metallic electrodes (tip and substrate) through molecular linkers,42 corresponding to case III. In the other two, the molecule lies on thin insulating layer deposited on the metal substrate.27,28 The relative position of the tip and molecule can be adjusted to cover different regimes. D


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Nano Letters and the nonradiative damping of the molecular exciton decrease with increasing the distance from tip to substrate. Figure 4a plots the emission spectrum (photon energy flux versus frequency/energy ω) for several values of L. For the short distance case, that is, most part of the molecular linker is adsorbed on the substrate, it is difficult to observe a welldefined fluorescence from the molecular emitter because of the quenching of molecular luminescence. In this case, the spectrum observed is similar to most STM-induced light emission experiments, showing a broad gap plasmon spectra (see L = −0.3 eV in Figure 4a). With increased tip−substrate distance, the molecule−substrate coupling and the nonradiative damping of the molecular exciton become smaller. EL from the molecule can then be observed as a peak in the spectrum. The intensity of the peak becomes stronger with further decoupling from the substrate. At the same time, the peak position shows a slight red shift and its width becomes smaller. These features are consistent with the experimental results. Single Molecule on Insulating Layer. In refs 27 and 28, STM-induced light emission from a single molecule decoupled from substrate by insulating NaCl layer was studied. It was found that the relative tip−molecule position modifies the emission spectrum significantly. This can be considered in our model by changing tp(x). Figure 4b,c shows the photon emission spectrum obtained from our theory to simulate results from refs 27 and 28. When the molecule and the tip are far apart (tp(x) = 0), the two emission channels do not couple directly, that is, the molecule can not be excited by the gap plasmon. Because the molecule does not participate the electron tunneling process, the molecular luminescence is not observed. Approaching the tip to the molecule generates a nonzero tp(x) ≠ 0, the coupling of the molecular exciton and gap plasmon mode opens the energy transfer channel between them. A sharp dip (Figure 4b) or peak (Figure 4c) develops due to the Fano interference. The interaction between the molecule exciton and the gap plasmons can be tuned by varying the tip position near molecule. This allows one to control their coupling. To provide a quantitative description that can be compared with the experimental data, we simulate the tip distance-dependent light spectra by adjusting the tp(x) ranging from 0 to 13 meV, all the main features of the experimental results are reproduced by our theory, for example, the dip/peak structure becomes more and more prominent as tp(x) increases. We note that although we consider only one exciton mode in Figure 4c, in the experiment two peaks are observed corresponding to transition dipoles along the two ligands axes of Phthalocyanine (H2Pc). The two dipoles are not degenerate due to the breaking of 4-fold rotational symmetry in H2Pc. Effect of Tip−Molecule Coupling. Encouraged by the good agreement between our results and the experimental data, we go one step further. We study here the effect of electronic coupling between tip and molecule on the spectrum. As we change the tip−molecule coupling strength while keeping other parameters fixed, the Fano dip in light spectra increases quickly with Γmt in the weak coupling regime and decreases gradually via further increasing the Γmt, as shown in Figure 5a. This change of the dip size is due to the change of tip− molecule coupling Γmt. When the tip approaches the molecule, Γmt increases. This makes the energy current flowing from the electronic to the photonic part grow larger. On the other hand, larger Γmt leads to larger nonradiative damping of the

Figure 5. (a) Change of the photon emission spectrum for different values of tip−molecule coupling Γmt. (b) The corresponding dip depth as a function of Γmt. Other parameters are the same as in Figure 3II.

molecular exciton. Quenching of molecular exciton luminescence occurs when Γmt reaches a certain value. This results in the broadening and gradually disappearance of the Fano dip. For a clear illustration, we plot in Figure 5b the corresponding dip depth as a function of Γmt. Our results are consistent with a recent experiment where the excitonic lifetime change with injected current from STM tip, displaying a nonmonotonic behavior, that is, the exciton quenching induced by charges can be observed.43 Our prediction can be verified in experiment by changing the vertical tip−molecule distance, which has been used in related studies.12,13 Summary. In summary, we have developed a general theoretical model based on NEGF to investigate the single molecule-mediated light emission from a STM junction inspired by the recent experiments. Three different regimes are highlighted to explain the experimental results. Our model provides a clear description of the evolution of the spectra line shapes that manifest the Fano resonance with the STM tip position and energy detuning between molecular exciton and gap plasmon. Moreover, this approach can also be used to study the light emission from other molecules such as DNA and RNA molecules, as the mismatch of base-pairs can be distinguished by the emission spectra.44−46 This may provide a novel opportunity to detect the gene mutation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.8b02706. Details of the theoretical model and method: (I) Details of the NEGF method, (II) Simple model for the Fano resonance (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yongfeng Wang: 0000-0002-8171-3189 E


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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank X. W. Chen for helpful discussions. J.T L. is supported by Program for HUST Academic Frontier Youth Team.

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On the Fano Line Shape of Single Molecule Electroluminescence

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