Photoinduced Switching of the Current through a Single Molecule

Letter pubs.acs.org/NanoLett

Photoinduced Switching of the Current through a Single Molecule: Effects of Surface Plasmon Excitations of the Leads Yaroslav Zelinskyy†,‡ and Volkhard May*,† †

Institut für Physik, Humboldt−Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Metrologichna street, 14-b, UA-03143, Kiev, Ukraine

‡

ABSTRACT: The photoinduced switch of the current through a single molecule is studied theoretically by including plasmon excitations of the leads. A molecule weakly linked to two spherical nanoelectrodes is considered resulting in sequential charge transmission scheme. Taking the molecular charging energy (relative to the equilibrium lead chemical potential) to be comparable to the molecular excitation energy, an efficient current switch in a low voltage range becomes possible. A remarkable enhancement of the current is achieved due to simultaneous plasmon excitations in the electrodes. The behavior is explained by an increased molecular absorbance due to oscillator strength transfer from the electrode plasmon excitations and by a net excitation energy motion from the electrodes to the molecule. KEYWORDS: Molecular junction, photoinduced current switch, plasmon enhancement, current−voltage characteristics, density matrix theory

I

t is of ongoing interest to design experiments that enable laser pulse control of the electric current through a single molecule attached to nanoelectrodes.1−11 Also, when using techniques of nano-optics the excitation of the pair of leads bridged by a molecule of 1 or 2 nm extension cannot be circumvented. While this effect has been often ignored, recent work took advantage of lead plasmon excitations and resulting local field enhancement.12−16 Respective theoretical studies have been in the focus of some groups for a couple of years. The interaction of a molecule sandwiched between two leads with the electron−hole pair excitations in the leads has been already considered.17,18 Later, the used nonequilibrium Green’s function approach was combined with the computation of a local field caused by plasmon excitations in the leads.19,20 However, the simulations of the response of the junction to an external laser pulse had to be restricted to a 100 fs time interval. In contrast, emphasis has been put on mirror charge effects due to the presence of leads in ref 21 (similar studies can be also find in the older work of refs 22 and 23). In ref 24, two metal nanoshells connected by a cylindrical medium of given conductivity have been considered. A transition could be demonstrated with increasing conductivity of the connecting medium from shell localized plasmons to a charge transfer plasmon covering both shells. The present work combines our approach on the photoinduced switching of the current through a single molecule (cf., e.g., refs 25−28) with our recent studies on coupled molecule metal nanoparticle (MNP) systems.29,30 Therefore, we suggest a scheme where pyramidal leads are completed by spheres which contact the molecule (cf. Figure 1). This has been inspired by experiments already reported in ref 13. Optical © 2011 American Chemical Society

Figure 1. Single molecule attached to two spherical gold nanoparticles (20 nm diameter, 1 nm gap between both) forming a left and a right lead (both continued by a pyramidal electrode). An applied voltage may result in a net current that can be altered by optical excitation of the nanoparticle−molecule complex (photon energy ℏω). Upper right corner: Excitation energy scheme of the molecule−lead system. The excited state energy E0e of the neutral molecule is positioned between the upper and the lower hybrid plasmon level E+ and E−, respectively, which are formed by the two spherical leads (shaded areas indicate the strong life−time broadening of the hybrid levels).

excitation of the junction should be dominated by surface plasmons of the spheres and by their coupling to the molecule. Since plasmon excitations of metal spheres are well understood, the chosen scheme removes any complication related to plasmon excitations of a MNP with a more complex geometry. The extension of the junction is small compared to optical wavelengths. Therefore, the coupling of the molecule to the Received: October 28, 2011 Revised: November 29, 2011 Published: December 7, 2011 446

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leads plasmon excitations as well as the coupling of the two leads among each other can be described by a restriction to the (nonretarded) Coulomb interaction. Such an approach circumvents the computation of the lead-induced local field influencing the molecule and its absorption. Instead, this effect is considered by a consequent (nonperturbative) account of the molecule−lead Coulomb coupling that is responsible for electronic excitation energy transfer. Accordingly, the degree of photoexcitation of the molecule and thus the efficiency of the current switch is influenced by the lead plasmons and by their short lifetime. As a main result of the present considerations, it is demonstrated that the current switch is promoted by an increased molecular absorption due to oscillator strength transfer from the leads plasmon excitations and by a net excitation energy motion from the leads to the molecule. As indicated in Figure 1, we consider a molecular junction formed by two spherical leads with the same diameter and with a single molecule in between. An applied voltage across the leads initiates charge transmission through the molecule. The molecule−lead coupling should be weak enough to stay in the regime of sequential charge transmission. Accordingly, the used states are those of the isolated molecule. Some changes are possible due to the bonding to the leads and due to mirror charge effects (those can be covered by the definition of the molecular energies; what, however, will not be indicated explicitly). We assume that in the considered voltage range only the singly negatively charged state of the molecule is involved in the current formation. The molecular Hamiltonian takes the form Hmol = ∑N,aεNa|φNa⟩⟨φNa|. The molecular energies are εNa and the molecular states are denoted as φNa. Both are labeled by the charging number N (number of excess electrons in the molecule), and the electronic quantum number a referring to the ground-state a = g and an excited state a = e. The difference ε1g − ε0g gives the so-called charging energy. In the absence of an applied voltage, charging is impossible if ε1g − ε0g is larger than the chemical potential μ0 of the leads. Therefore, we introduce the relative charging energy ΔE10 = ε1g − ε0g − μ0 as a basic parameter. Furthermore, we assume that ε2g − ε1g ≫ μ0 but ε0g − ε − 1g ≪ μ0. If these inequalities stay valid for all applied voltages, it is guaranteed that double charging and hole transfer, respectively, can be ignored, that is, charging only appears via the presence of a single excess electron (N = 0,1). To include the plasmon excitations of the leads in a proper way we follow ref 32. There, the electron motion in a single MNP has been studied by introducing a separation of the electron coordinates into those of the center of mass of all electrons and into relative coordinates. The related center of mass motion (collective electron motion) corresponds to plasmon excitations of the MNP and the electron motion relative to the center of mass forms a reservoir for fast plasmon energy dissipation, that is, it causes a finite plasmon lifetime. Reference 33 suggested to interpret the introduction of a collective and relative electron motion as a separation into an active system and a reservoir what is common in dissipative quantum dynamics.34 This will be utilized below when formulating a density matrix description of current formation through the junction. The plasmon Hamiltonian of the two lead system is

Hpl =

∑ (ℏΩX 0|X 0⟩⟨X 0| + ∑ ℏΩI |XI ⟩⟨XI |) X

+

I

∑ (VLI , RI ′|LI , R 0⟩⟨RI′, L0| + H.c.) I ,I′

(1)

It distinguishes between the left (X = L) and the right (X = R) lead, and includes the ground state energies ℏΩX0 and the dipole plasmon energies ℏΩXI. Those are three-fold degenerated. The quantum number I = x,y,z counts the possible excitations in the three spatial directions (cf., for example, ref 29). The VLI,RI′ are the energy exchange couplings (see below). The basic dipole plasmon excitation energy is denoted as Epl = ℏ(ΩXI − ΩX0). Finally, molecule lead−plasmon excitation energy exchange is included in

Hmol − pl =

∑ N ,X ,I

Ve , XI |φNe , X 0⟩⟨XI , φNg | + H.c. (2)

It transfers the excitation of a lead dipole plasmon to the molecule and vice versa. The interlead and molecule−lead energy exchange couplings shall be taken in the following in a form of a standard dipole− dipole coupling which is written here for two excitable units m and n as Vmn = ([dmdn*] − 3[ndm][ndn*])/|X|3 (the dm,dn are the transition dipole moments of the two units, |X| labels the distance between both and we introduced n = X/|X|). To specify Vmn to the interlead coupling VLI,RI′ we note that the MNP transition dipole moments reads as dXI = dpleXI. The magnitude dpl is identical for the two leads and according to the spherical shape of the leads I labels the components of a Cartesian coordinate system (I = x,y,z). So the eXI are respective unit vectors referring to lead X.29 Since the two spherical leads are placed along the x-axis (cf. Figure 1), only certain elements of VLI,RI′ remain finite: VLx,Rx = −2Vpl, VLy,Ry = VLz,Rz = Vpl (with 3 Vpl = dpl2 /Xlead , where Xlead is the distance between the center of masses of the two spherical leads). The possible strong coupling between the two leads may result in the formation of hybrid dipole plasmon states.31 Obviously, plasmon excitations of different orientation are decoupled, but those of the same orientation may hybridize. For further use we quote the plasmon hybrid levels of the pair of spherical leads: Exφ=± = Epl ± 2Vpl and Eyφ=± = Eyφ=± = Epl ± Vpl. Respective optical absorption becomes J-aggregate-like (the lower hybrid level takes all oscillator strength) if the radiation field as assumed here is polarized in x direction. Note, that the treatment described below does not require the introduction of hybrid states (they are accounted for directly by the chosen density matrix approach). Their introduction, however, supports a clear discussion of the results. The molecule lead coupling Ve,XI is obtained in the same manner by choosing for one dipole moment in the general expression Vmn that of the molecule. Quadrupole plasmon excitations and even higher lying multipole plasmons change the position of the hybrid levels31 and may open new channels of excitation energy exchange between the molecule and the leads (thereby introducing couplings beyond the dipole−dipole interaction form). By concentrating on molecular excitation energies near the lower hybrid level Ex−, however, we only expect minor changes of the IV-characteristics when going beyond the present restriction to dipole−plasmons. Optical excitation of the junction may result in a population of an excited molecular state either if the molecule is neutral or singly charged. This process is described in the standard 447

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dipole−form with molecular transition dipole moment dmol (a possible dependence on the molecular charging has been ignored). The electric−field strength is denoted by E(t) = nE0 exp(iω0t) + c.c. (the polarization is fixed by the unit vector n, E0 denotes the amplitude and ω0 is the carrier frequency). Moreover, optically induced population of a single dipole plasmon excitation of the left or right lead is governed by the MNP transition dipole moments dXI. Spill−out electrons generated in the course of lead excitation should not change the charging state of the molecule, and the presence of lead plasmon excitations should not alter the strength of molecule− lead transfer coupling responsible for molecular charging and discharge. While these assumptions simplify the subsequent considerations, so far there are no studies available which could confirm them. According to our assumptions the rule of the leads is 2-fold. They appear as an electron reservoir and additionally as an excitable medium forming collective plasmon states. To establish a density matrix description, we note that the related reservoir comprises the relative electron motion of the spherical leads (cf. ref 33) and the separately treated reservoir of lead electrons ready to be injected into the molecule what is well established in Molecular Electronics (see, for example, ref 25 and references therein). To include radiative plasmon damping we also have to account for a reservoir of photon states. The density matrix of interest is given as ραβ(t) where α and β label the states of the active system (molecular states and lead plasmon excitations). Related equations of motion are taken in a form where the dissipative part does not couple diagonal and off-diagonal elements26 (this is sufficient when focusing on steady state currents)

leads and the molecule, however, they do not couple different charging states Finally, we have to specify the rates entering the diagonal part of the density matrix eq 3. There is one rate kα→γ = kNXI = 2γpl that describes the decay of the various plasmon states (the reverse rate can be neglected). The other rates follow from the molecule−lead electron transfer coupling and are responsible for molecular charging and discharge (see ref 26). The assumed weak molecule−lead transfer coupling allows to compute these rates in the second order with respect to the coupling. Accordingly, the kα→γ and kγ→α comprise the rates

k 0a → 1b = Γ ∑ fF (ℏε1b ,0a − μX ) X

which describe charging of the neutral molecule being in electronic state φ0a and ending up in the charged state φ1b (a,b, = g,e). The Fermi distribution f F includes besides the various transition frequencies the chemical potential μX of lead X (in the presence of an applied voltage). For the present purpose, it suffices to use the model of a symmetrically applied voltage with μL = EF + |e|V/2 and μR = EF − |e|V/2 (the equilibrium Fermi energy is denoted by EF). The quantity Γ represents the uniform molecule−lead coupling function 4π/ℏ2 × N̅ |V̅ |2. It covers the electronic state independent mean transfer coupling V̅ and the mean lead electron density of states N̅ ,26 which are both identical for the left and the right lead. The charging rates, eq 4, have to be complemented by the rates (Y = R, L)

k 0YI → 1YI = Γ ∑ fF (ℏε1YI ,0YI − μX ) X

(5)

They refer to charging of the neutral molecule staying in its electronic ground state, however, in the presence of a plasmon excitation in lead Y before and after charging. Rates of discharge k1b→0a and k1YI→0YI are obtained from k0a→1b and k0YI→1YI, respectively, in replacing the Fermi distribution by 1 − f F (note that the energy arguments do not change within this replacement). A convenient discussion of the process of charging and discharge becomes possible if we reintroduce electronic energies Eel. Noting eq 4, we replace f F(ℏε1b,0a − μX) by ∫ dEel δ(E1b − E0a − Eel)f F(Eel − μX) (remember the definition of transition frequencies). The relation indicates charging with energy conservation E1a = E0b + Eel, where the Fermi−distribution f F(Eel − μX) guarantees Eel ≤ μX. In the same way, we may consider discharge. The energy conservation relation remains identical with the relation for charging but the leads electron energy has to fulfill Eel ≥ μX (cf. also Figure 2). Having explained the density matrix equations ready to describe charge transmission through the molecule in the presence of optical excitation and energy exchange between the molecule and the leads it remains to offer formulas to determine the current. According to ref 26, we obtain in the present scheme of sequential charge transmission the current moving from lead X into the molecule as IX(t) = IX,0→1(t) + IX,1→0(t). The part IX,0→1(t) responsible for molecular charging is determined by populations (diagonal density matrix elements) of the neutral molecule while the discharge current IX,1→0(t) includes population of the charged molecule. Both populations refer to the electronic ground and excited state. The steady state current I follows as I = IL = −IR. It has been obtained by propagating the density matrix in the presence of a cw optical excitation up to a time where a steady state of the junction is reached. In order to discuss the IV-characteristics it

∂ i ραβ = − i ε̃αβραβ − ∑ (Vαγ(t )ργβ ∂t ℏ γ − Vγβ(t )ραγ) − δαβ ∑ (k α→γραα γ

− k γ→αργγ)

(4)

(3)

On the righthand side, we introduced complex transition frequencies ε̃αβ = εαβ − i(1−δαβ)γαβ where the real part is given by εαβ = εα − εβ including the ground-state energies ENg = ℏεNg = εNg + ∑XℏΩX0 and the excited state energies ENe = ℏεNe = εNe + ∑XℏΩX0 and ENXI = ℏεNXI = εNg + ℏΩXI + ℏΩY0 (X, Y = L, R, X ≠ Y). The imaginary part of the complex transition frequencies accounts for dephasing with the molecular contributions γNe,Ng = γmol, the molecule−lead contribution γNe,NI = γmol + γpl, and the lead plasmon contribution γNI,Ng = γpl and γNI,NI′ = 2γpl. The molecular damping γmol mainly accounts for nonradiative contributions (vibrational induced dephasing) and represents the only point where molecular vibrations enter the present description (the effect of radiative damping γphot is discussed later). Plasmon damping γpl is originated by radiative and nonradiative processes, where for the chosen radius of the spherical leads the latter dominate. They originate from the coupling of the MNP collective and intrinsic electron motion.33 Dephasing contributions due to the molecule−lead electron transfer coupling can be neglected since they only contribute in a marginal way (restriction to the sequential regime of charge transmission). The different coupling potentials Vαβ(t) entering eq 3 comprise the influence of optical excitation and contributions due to excitation energy exchange among the 448

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Table 1. Used Parameters (For Explanation See Text) dmol γmol Epl dpl γpl VLx,Rx Ex+ Ex− Ve,Lx = Ve,Rx ℏΓ kBT

8D 3 meV 2.5949 eV 2893 D 28.5 meV −980 meV 3.60 eV 1.61 eV −21 meV 1 meV 25 meV

meV. To present signatures of photoinduced current switches in a low voltage range we consider a situation where ΔE10 becomes comparable to the molecular excitation energy. All calculations have been done at room-temperature conditions. We start with a brief discussion of the photoinduced current switch and choose a voltage regime where the transition from the neutral molecular ground state into the ground state of the charged molecule is impossible (in the present model the only mechanism for current formation in the absence of optical excitation). This situation is depicted in Figure 2 (the upper panel shows the steady state left−right current and the lower panel the right−left one). According to the small value of the applied voltage we have for both currents E0g + EF ± |e|V/2 < E1g and, as assumed, charging of the molecule without photoexcitation becomes impossible (it becomes possible only for V > 2ΔE10/|e| leading for the present choices of ΔE10 to voltages larger than 3 V). However, a left−right as well as a right−left current is formed if the excited state of the neutral molecule is populated via optical excitation. The situation shown in Figure 2 corresponds to the relation E0e + EF − |e|V/2 = E1g which defines the critical voltage Vcr = 2(Eeg − ΔE10)/|e|. For this voltage (and for lower values) a left−right and a right−left current appear. Moreover, discharge is always possible because E1g = E0g + Fel is valid (Fel > EF ± |e|V/2 is guaranteed, cf. also the lower panel of Figure 2). Since both currents coincide optical excitation does not result in a finite net current for V ≤ Vcr. In the contrary case V > Vcr, however, a right−left current cannot formed since E0e + EF − |e|V/2 < E1g. A finite net current appears. This current is absent without photoexcitation and thus a photoinduced current switch has been demonstrated. The thin black line in Figure 3 displays the photoinduced current in the absence of excitation energy exchange between the molecule and the two spherical leads. If the excitation energy exchange between the molecule and the leads is included one notices an enormous increase of the current. This results from the chosen configuration where the molecule is resonantly excited ℏω0 = Eeg and where its excitation energy coincides with the energy Ex− of the optically addressable lower MNP plasmon hybrid level. The increase of the current is caused by a net increase of the population of the excited molecular state compared to the case where the molecule−MNP excitation energy exchange has been neglected. Such an enlargement of the excited level population follows from the nonperturbative treatment of the molecule− MNP coupling which results in an increased molecular absorption (the molecule borrows oscillator strength from the MNP). But it is also originated from a net excitation energy transfer from the MNP to the molecule. This latter effect is not so obvious since one expects that excitation energy stored in

Figure 2. Energy level scheme and charge transmission steps for the left−right steady state current (upper panel) and the right−left current (lower panel). Shown are the energies E0a + Eel (a = g, e, transmission step 1), E1a (transmission step 2) and E0a + Fel (transmission step 3). The energies of occupied lead electron states are labeled by Eel and presented by dark blue areas located below the actual Fermi energy EF ± |e|V/2 (dotted lines: equilibrium Fermi energy). Energies of unoccupied lead electron states are labeled by Fel (light gray areas). Photoinduced left−right current: E0e + Eel → E1g → E0e + Eel, Fel = EF − |e|V/2 (final transition into E0g + Fel with Fel > EF − |e|V/2 is also possible but not shown). Photoinduced right−left current: E0e + EF − |e|V/2 → E1g → E0g + Fel.

is advisible to introduce the steady state left−right current IL→R = (IL,0→1 − IR,1→0)/2 and the steady state right−left current IR→L = (IR,0→1 − IL,1→0)/2 giving the net current as I = (IL − IR)/228 (cf. Figure 2). For our simulations, we took gold MNP with dipole plasmon parameters as listed in Table 1. The type of molecule will be not specified since essential parameters like the excitation energy Eeg = ENe − ENg (they are assumed to be independent of the charging state) and the relative charging energy ΔE10 are varied. However, we fix the line broadening and the transition dipole moment. The latter points in x-direction (cf. Table 1). This reduces the molecule−MNP couplings Ve,XI to their xcomponents Ve,Xx (X = L,R). To stay simple we also assume external field polarization in x-direction resulting in an exclusive optical excitation of the leads hybrid level with energy Ex−. Since our approach focuses on sequential charge transmission the molecule−lead coupling takes the small value of ℏΓ = 1 449

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Accordingly, the finite current obtained in the rate equation approach is larger than that obtained in the absence of the molecule−MNP energy exchange coupling. So, we may conclude that already second-order energy exchange coupling rates describe a net energy transfer from the MNP to the molecule. But the inclusion of oscillator strength transfer from the MNP to the molecule (and a nonperturbative account for the energy exchange coupling) as included in the density matrix description further increases the photoinduced steady state current (black solid curve in Figure 4). Figure 4 also indicates that a total resonance is not necessary between the molecular excitation energy and the lower hybrid plasmon level to get a finite magnitude of the steady state current. This behavior is further illustrated in Figure 5 (upper Figure 3. IV-characteristics of the molecular junction in the presence of optical excitation resonant to the lower MNP hybrid level (dmol and field polarization point in x-direction, ℏω0 = Eeg = Ex−, ΔE10 = 1.36 eV, see also Table 1). Black solid curve, E0 = 106 V/m; red dashed curve, E0 = 5 × 105 V/m; blue chain-dotted curve, E0 = 105 V/m; thin black curve, neglect of molecule−MNP interaction and E0 = 106 V/m.

the MNP plasmon hybrid level is quickly dissipated due to the short plasmon lifetime. Noting, however, the data presented in Figure 4 it is possible to justify this conclusion.

Figure 4. IV-characteristics of the molecular junction in the presence of optical excitation (dmol and field polarization point in x-direction, E0 = 105 V/m, see also Table 1). Black solid curve, ℏω0 = Eeg = Ex−; red dashed curve, ℏω0 = Eeg = (Ex+ + Ex−)/2; blue chain-dotted curve, ℏω0 = Eeg = Ex+; thin black curve, use of rate equations and ℏω0 = Eeg = Ex− (to always achieve current formation around Vcr = 0.5 V, ΔE10 has been chosen as 1.36, 2.34, and 3.35 eV, respectively).

Figure 5. Current through the molecular junction (upper panel) and population of the lower MNP hybrid level (lower panel) for different detunings between the molecular excitation energy Eeg and the lower hybrid plasmon level Ex− and versus photon energy of optical excitation (dmol and field polarization point in x-direction, E0 = 5 × 105 V/m, applied voltage of 1.2 V). Choice of Eeg from the foreground to the background as Ex−, Ex− + 0.25 eV, Ex− + 0.5 eV, Ex− + 0.75 eV, and (Ex+ + Ex−)/2 (to always achieve current formation around Vcr = 0.5 V, ΔE10 has been chosen as 1.36, 1.61, 1.86, 2.01, and 2.36 eV, respectively).

Figure 4 compares results of the density matrix description (which guarantees an exact treatment of the molecule−MNP excitation energy exchange coupling) with an IV−curve obtained by a rate equation approach (thin black line). Within this treatment we introduced correct MNP plasmon hybrid levels but described the molecule hybrid level coupling via respective second-order rates (Förster−type rates). Also, optical excitation of the molecule and the lead hybrid levels was considered by independent rates exclusively defined either by the molecular transition dipole moment or the lead plasmon dipole moment (absence of oscillator strength transfer from the MNP). For a discussion, we compare the thin black curve of Figure 4 (rate equation approach) with the thin black curve of Figure 3. The latter ignores molecule−lead coupling but results from E0 = 106 V/m. If we change to E0 = 105 V/m as in Figure 4 (not shown), we obtain much smaller values for the current.

panel) where the current (at a given voltage) is plotted versus photon energy ℏω0 and for different detunings between the molecular excitation energy and the lower hybrid plasmon level (they are changed from the foreground to the background). As it has to be expected, the current shows a resonant behavior if the photon energy equals the molecular excitation energy. If the latter is close to the lower hybrid plasmon level, the current resonance is broad while it becomes sharper if the molecular excitation energy moves away from the hybrid plasmon level. 450

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electrode plasmon excitations and a net excitation energy transfer from the leads to the molecule. Some estimates on lead induced molecular radiative lifetime reductions and resulting current changes have been also offered.

Note that the steady state value of the neutral molecule excited state population ρ0e,0e(t → ∞) behaves similar (not shown). Instead, the population of the lower hybrid plasmon level ρx−,x− (t → ∞) is depicted in the lower panel of Figure 5, again versus photon energy ℏω0 and for different detunings between the molecular excitation energy and the lower hybrid plasmon level. This population reflects the ability of the MNP pair coupled to the molecule to absorb photons. If the detuning is absent (front curve) or small the population versus photon energy shows a dip at the energetic position of the molecular absorbance. This behavior again illustrates oscillator strength redistribution and net energy transfer from the MNP to the molecule. The lower hybrid plasmon level population has been computed by noting the expansion of the hybrid states with respect to the single MNP plasmon excitations |I± ⟩ = ∑XCI±(X)|X I⟩, that is, we obtain ρx−,x− = ∑X,YCx−*(X)Cx−(Y)ρXx,Yx So far we indicated oscillator strength enhancement for the molecular absorbance. However, the same phenomenon takes place with respect to the radiative recombination of the molecule. Such an effect can be consistently accounted for if the excited molecular state and the plasmon excitations of the MNP are coupled to the reservoir of photon states.30,35 A lifetime reduction from some nanosecond to the subpicosecond range has to be expected. Here, we do not use results of a consequent theory but introduce a reasonable number of the molecular radiative decay rate (that of the MNP corrects the nonradiative decay rate in the range of 20−30% and will be neglected). Respective results are shown in Figure 6 with

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AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected].

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ACKNOWLEDGMENTS Financial support by the Deutsche Forschungsgemeinschaft through Sfb 951 is gratefully acknowledged.

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REFERENCES

(1) Yasutomi, S.; Morita, T.; Imanishi, Y.; Kimura, S. Science 2004, 304, 1944. (2) He, J.; Chen, F.; Liddell, P. A.; Andrasson, J.; Straight, S. D.; Gust, D.; Moore, T. A.; Moore, A. L.; Li, J.; Sankey, O. F.; Lindsay, S. M. Nanotechnology 2005, 16, 695. (3) Katzonis, N.; Kudernac, T.; Walko, M.; Jan van der Molen, S.; van Wees, B. J.; Ferinda, B. L. Adv. Mater. 2006, 18, 1397. (4) Nitahara, S.; Tarasaki, N.; Akijama, T.; et al. Thin Solid Films 2006, 499, 354. (5) Wu, S. W.; Ogawa, N.; Ho, W. Science 2006, 312, 1362. (6) Guhr, D. C.; Rettinger, D.; Boneberg, J.; Erbe, A.; Leiderer, P.; Scheer, E. Phys. Rev. Lett. 2007, 99, 086801. (7) Wu, S. W.; Nazin, G. V.; Ho, W. Phys. Rev. B 2008, 77, 205430. (8) Ward, D. R.; Scott, G. D.; Keane, Z. K.; Halas, N. J.; Natelson, D. J. Phys.: Condens. Matter 2008, 20, 374118. (9) van der Molen, S. J.; Liao, J.; Kudernac, T.; Agustsson, J. S.; Bernard, L.; Calame, M.; van Wees, B. J.; Feringa, B. L.; Schönenberger, C. Nano Lett. 2009, 9, 79. (10) Ittah, N.; Noy, G.; Yutsis, I.; Selzer, Y. Nano Lett. 2009, 9, 1615. (11) Battacharyya, S.; Kibel, A.; Kodis, G.; Liddell, P. A.; Gervaldo, M.; Gust, D.; Lindsay, S. Nano Lett. 2011, 11, 2709. (12) Mangold, M. A.; Weiss, C.; Calame, M.; Holleitner, A. W. Appl. Phys. Lett. 2009, 94, 161104. (13) Banerjee, P.; Conklin, D.; Nanayakkara, S.; Park, T.−H.; Therein, M. J.; Bonnell, D. A. ACS Nano 2010, 4, 1019. (14) Zang, Y.; Geng, F.; Gao, H. Y.; Liao, Y.; Dong, Z. C.; Hou, J. G. Appl. Phys. Lett. 2010, 97, 243101. (15) Noy, G.; Ophir, A.; Selzer, Y. Angew. Chem., Int. Ed. 2010, 49, 5734. (16) Arielly, R.; Ofarim, A.; Noy, G.; Selzer, Y. Nano Lett. 2011, 11, 2968. (17) Galperin, M.; Nitzan, A. Phys. Rev. Lett. 2005, 95, 206802. (18) Galperin, M.; Nitzan, A.; Ratner, M. Phys. Rev. Lett. 2006, 96, 166803. (19) Sukharev, M.; Galperin, M. Phys. Rev. B 2010, 81, 165307. (20) Fainberg, B. D.; Sukharev, M.; Park, T.−H.; Galperin, M. Phys. Rev. B 2011, 83, 205425. (21) Adamska, L.; Kozhushner, M. A.; Oleynik, I. I. Phys. Rev. B 2010, 81, 035404. (22) Persson, B. N.; Baratoff, A. Phys. Rev. B 1988, 38, 9616. (23) Petrov, E. G.; Tolokh, I. S.; Demidenko, A. A.; Gorbach, V. V. Chem. Phys. 1995, 193, 237. (24) Perez−Gonzalez, O.; Zabala, N.; Borisov, A. G.; Halas, N. J.; Nordlander, P.; Aizpurua, J. Nano Lett. 2010, 10, 3090. (25) May, V.; Kühn, O. Phys. Rev. B 2008, 77, 115439. (26) Wang, L.; May, V. Chem. Phys. 2010, 375, 252. (27) Wang, L.; May, V. Phys. Chem. Chem. Phys. 2011, 13, 8755. (28) Wang, L.; May, V. Phys. Rev. B 2011, 84, 205425. (29) Kyas, G.; May, V. J. Chem. Phys. 2011, 134, 034701. (30) Zelinskyy, Ya. R.; May, V. Chem. Phys. Lett. 2011, 511, 372. (31) Nordlander, P.; Oubre, C.; Prodan, E.; Li, K.; Stockman, M. I. Nano Lett. 2004, 4, 899.

Figure 6. IV-characteristics of the molecular junction in the presence of optical excitation resonant to the lower MNP hybrid level (dmol and field polarization point in x-direction, ℏω0 = Eeg = Ex−, ΔE10 = 1.36 eV, E0 = 5 × 105 V/m). Variation of the molecular radiative decay rate γphot, black solid curve, γphot = 0; red dashed curve, γphot = 5 meV; blue chain-dotted curve, γphot = 10 meV.

molecular radiative decay rate γphot as presented in ref 36. As obvious, the used values of γphot reduces the current somewhat but let survive a reasonable photoinduced steady state value. To summarize, we indicate that IV-curves have been computed utilizing a density matrix approach that offers an exact consideration of (i) the molecule−lead energy exchange coupling, (ii) the respective coupling among the leads, and (iii) the effect of a simultaneous photoexcitation of the molecule and the leads. The photoinduced current originated by an excited state population of the molecule is remarkably enhanced due to simultaneous plasmon excitations in the electrodes. It could be explained by an increased molecular absorbance due to oscillator strength transfer from the 451

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Nano Letters

Letter

(32) Gerchikov, L. G.; Guet, C.; Ipatov, A. N. Phys. Rev. A 2002, 66, 053202. (33) Weick, G.; Ingold, G.-L.; Jalabert, R. A.; Weinmann, D. Phys. Rev. B 2006, 74, 165421. (34) May, V.; Kühn, O. Charge and Energy Transfer Dynamics in Molecular Systems; Wiley-VCH: Weinheim, 2000 (35) Zelinskyy, Ya. R.; May, V. Unpublished work, 2011. (36) Johansson, P.; Xu, H.; Käll, M. Phys. Rev. B 2005, 72, 035427.

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