Lifetime dynamics of plasmons in the few-atom limit

• plasmonics
• excited-state dynamics
• molecular plasmons
• plasmonicity
• lifetime

The collective electronic resonances—surface plasmons—of nanometer-scale structures provide a mechanism for light confinement on length scales far shorter than the wavelength of light (1⇓–3), giving rise to a host of well-studied transformational applications, which include energy harvesting (4), enhanced spectroscopies (5⇓–7), photocatalysis (8), and new types of devices (9). While many properties of nanoscale plasmons are well described by classical electromagnetic theory, in the few-atom quantum limit this description breaks down for the systems that still exhibit plasmonic behavior (10, 11), thus requiring a fully quantum treatment. From a quantum-mechanical perspective, plasmons can be described as coherent superpositions of individual electron–hole pair transitions that emerge when the Coulomb interaction between excited states is switched on (12⇓⇓–15).

Plasmons in metallic, semiconductor, and graphene-based systems all present unique excited-state dynamics, a key experimental observable that can empirically distinguish plasmonic (collective electronic) from excitonic (single-electron) behavior. Noble metal plasmon dephasing times are typically ∼10 fs (16⇓–18), due to their rapid electron–electron and electron–phonon damping rates resulting from high carrier concentrations (19). Doped semiconductor plasmons undergo less damping due to their relatively low carrier concentrations, which typically results in longer plasmon lifetimes than in metals (20). Graphene exhibits extremely high electron mobilities, greatly reducing the damping rate due to electron–electron scattering (21). Graphene plasmons are therefore predicted to have lifetimes of tens of picoseconds or longer (22), although recent experimental studies report substantially faster graphene plasmon dephasing times due to additional relaxation channels brought about by the presence of impurities and coupling to phonons (23, 24). Plasmon excitations in all of these systems are experimentally characterized by ultrafast, subpicosecond dynamics with a trend toward longer lifetimes with decreasing damping scattering rates.

Reducing the dimensionality of graphene to quasi–one-dimensional nanoribbons, and further, to quasi–zero-dimensional nanoscale islands, modifies its electronic and plasmonic properties dramatically. For narrow graphene nanoribbons, the extreme electron confinement in the transverse dimension opens a large bandgap, accompanied by the presence of high-energy excitonic states (25). Adding an additional dimension of confinement reduces graphene to the length scale of molecules, known as polycyclic aromatic hydrocarbons (PAHs), consisting of a few fused benzene rings where the carbon edge atoms are each bound to a hydrogen atom (i.e., H-passivated). In their charge-neutral state, these molecules possess large highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps and have been very well studied (26). However, with the addition or removal of as little as a single electron, plasmon-like features known as molecular plasmons have been experimentally verified (27⇓–29). This behavior warrants a critical examination of the question: can few-atom systems support collective oscillations? If so, how would their behavior differ from plasmons in larger systems with a continuum of states? Recent theoretical focus has been placed on rigorously quantifying to what extent an excitation supported by few-atom systems shows collective, plasmon-like character (13⇓–15, 28, 30, 31). A metric called the generalized plasmonicity index (GPI) has been introduced to rigorously distinguish between single-electron and collective excitations in quantum systems (32). For example, calculations involving silver nanoclusters with as few as 20 atoms have shown resonances with appreciable plasmonicity (32, 33). This type of analysis supports the idea that few-atom systems are capable of supporting incipient plasmon-like collective resonances. Theoretical studies into the nature of small doped graphene nanoislands (27) and charged PAHs (28) have similarly found excitations strongly dependent on the electron–electron Coulomb interaction and the charge state of the system. When coupled with transition densities showing oscillating dipolar charge distributions (13, 30, 31), this is indicative of resonances exhibiting collective electron motion.

Here, we report the excited collective-state dynamics of three charged PAH molecules: perylene, benzo[ghi]perylene, and anthanthrene, and compare the results to the single-electron relaxation dynamics of their neutral counterparts. In this work, we focus on the most intense excitations in the low-energy region of the spectra of the anion systems, and on the absorption edges, that is, the first electronic excited states, of the neutral systems. Perylene was determined to have the main anion peak at 574 nm and the neutral absorption edge at 437 nm. Anthanthrene showed similar anion and neutral peaks at 576 and 432 nm, respectively, while benzo[ghi]perylene has slightly shifted values at 544 and 385 nm, respectively (see Fig. 3 and SI Appendix, Fig. S2). By combining pump–probe spectroscopy with fluorescence emission measurements and time-dependent density functional theory (TDDFT) (34) analysis of both charged and neutral PAH molecules, we can begin to clearly discriminate between the molecular plasmons of charged PAH molecules and the single-electron excitations of the same molecules in their neutral state.

The calculated (35) ground and excited-state energies and transition densities of the anion and the neutral molecule help to illustrate the collective nature of the anion molecular plasmon and the single-electron nature of the considered neutral molecule excitation (Fig. 1). The primary low-energy excited-state transitions for anthanthrene, for both the anion (Fig. 1A) and the neutral (Fig. 1B) cases, are shown. Transition densities, representing the excitations in terms of oscillating positive (blue) and negative (red) induced modifications of the ground-state molecular charge densities, were calculated for the most intense peak in the absorption spectrum of the anion (measured at λ = 576 nm) (Fig. 1C) and the first electronic excitation of the neutral molecule (measured at λ = 432 nm) (Fig. 1D). Both transition densities show a dipolar character along the long axis of the molecule. We performed a single-particle component analysis (15, 36) based on the TDDFT results of those excitations, shown graphically on the energy level diagrams of the systems (Fig. 1 E and F). The nondegenerate splitting of the energy levels in the anion system arises from the inherent asymmetry the addition of an unpaired electron causes by breaking the spin symmetry. This asymmetry results in the different spins of each electron in an orbital having different energy levels, as opposed to the neutral system where the electron energy levels are spin-degenerate. The single-particle component analysis of the anionic excitation (Fig. 1E) shows at least six single electron–hole pair transitions of varying weight contribute to the overall excitation. In contrast, the single-particle component analysis of the neutral molecule excitation (Fig. 1F) shows one single-electron transition (HOMO–LUMO) contributing mainly to the excitation. To further support the classification of the considered anionic excitations as molecular plasmons, we utilized the GPI metric, which is able to quantify the plasmonicity of such excitations and contrast it against the surrounding nonplasmonic anionic excited states. (See SI Appendix, section S9, for the complete GPI analysis of anionic and neutral systems.)

• Download figure
• Open in new tab
• Download powerpoint

Fig. 1.

Overview of the PAH system. Molecular schematic of (A) anion and (B) neutral anthanthrene. Transition density plots of the (C) anion excitation (corresponding to λ = 576 nm in the experimental spectrum) and the (D) neutral HOMO–LUMO excitation (corresponding to λ = 432 nm in the experimental spectrum) of anthanthrene, at the TDDFT level of theory. Energy level diagrams and simplified transition schematics of the (E) anion excitation and the (F) neutral excitation. Colors correspond to different single-particle electron–hole pair transition contributions to the single-particle component analysis of the excitation. The colored arrows and numbers show the relative weight of each transition with the signs indicating their phases. For the anion energy level diagram, SOMO stands for singly occupied molecular orbital and SUMO for singly unoccupied molecular orbital. The dashed arrows represent formally occupied energy levels, and the dashed lines denote the nondegenerate split in the energy levels of electrons. Transition components with weights smaller than 0.12 in modulus are not shown.

The excited-state relaxation dynamics of the anions and neutral molecules were performed using degenerate pump–probe spectroscopy. The PAHs were suspended in an ion gel in an electrochromic device (37) with the applied voltage modulated to maintain constant optical absorption levels, providing a consistent method to investigate the PAH molecules in both their neutral and charged states. (See Materials and Methods for a more detailed description of the laser system and device fabrication and characterization.)

The measured excited-state population as a function of pump–probe delay time for all three molecules in their neutral and anionic charge states is shown in Fig. 2. In a direct comparison of the dynamics of the anion (Fig. 2A) and its corresponding neutral molecule (Fig. 2B), it is apparent that the anion lifetimes are significantly shorter than their neutral counterparts by nominally two orders of magnitude. The most accurate description (SI Appendix, Fig. S5) of the charged PAH species is a biexponential decay, while the neutral molecules show far longer, monoexponential radiative lifetimes in the 1- to 3-ns range. In particular, the best lifetime parameters derived from the fits (SI Appendix, Fig. S5A) are 3433, 979, and 965 ps for neutral anthanthrene, benzo[ghi]perylene, and perylene, respectively. In the anionic species, the fastest decay time ranges from 0.5 to 6 ps (0.54, 6.3, and 3.5 ps for anionic anthanthrene, benzo[ghi]perylene, and perylene, respectively), while the longer decay time ranges from 7 to 15 ps (15.2, 11.6, and 7.3 ps, respectively). Benzo[ghi]perylene is unique among the PAH anions studied, where a third, far longer decay time is also observed (Fig. 2C). Likely mechanisms for the faster reaction times are internal conversion—the molecular plasmon “dephasing”—and vibrational relaxation, respectively, while the third decay term for benzo[ghi]perylene is due to a slower radiative decay channel (Fig. 2E).

• Download figure
• Open in new tab
• Download powerpoint

Fig. 2.

Summary of molecular plasmon dynamics. Excited-state decay curves of (A) the anion molecular plasmon excitation and (B) the neutral molecular HOMO–LUMO excitation of anthanthrene (blue), benzo[ghi]perylene (green), and perylene (red). (C) Comparative lifetime dynamics of benzo[ghi]perylene anion (green) and perylene anion (red) for long timescales (note shift in x-axis scale at gap). (D) Comparative fluorescence emission values between benzo[ghi]perylene anion (green) and perylene anion (red). (E) Proposed photoexcitation and relaxation dynamics of a molecular plasmon. The molecular plasmon mode (illustrated by the transition density) of the charged PAH is excited by light (green arrow), which couples to the vibrational modes of the molecule. The collective transition states of the molecular plasmon “dephases” roughly <6 ps after excitation, by the internal conversion nonradiative decay channel, followed shortly by vibrational relaxation on the order of 7 to 15 ps. In addition, a now uncoupled excited electron–hole pair may instead decay to a lower excited state and reach an energy level where radiative decay is possible, on the order of a nanosecond (red arrow).

To further investigate the decay pathways in the plasmonic molecules, fluorescence spectra from the perylene and benzo[ghi]perylene anions were monitored (anthanthrene did not exhibit measurable fluorescence; see SI Appendix). The fluorescence emission values (Fig. 2D) of the perylene anion is approximately one order of magnitude weaker than that of benzo[ghi]perylene. This agrees well with the assertion that the third decay term of the benzo[ghi]perylene anion, which the perylene anion does not appear to possess, is due to this radiative decay. However, larger Stokes shifts were also observed for the anions (>0.34 eV) compared with the neutral molecules (<0.16 eV), a trend consistent with the TDDFT calculations (Fig. 3 A–F). Indeed, calculations revealed a secondary set of lower-energy absorption peaks for the benzo[ghi]perylene (at around λ = 700 and 750 nm; Fig. 3D) and perylene (around λ = 710 nm; Fig. 3B) anions not readily observable in the experiment. These lower energy peaks may indicate that the fluorescence emission observed in the benzo[ghi]perylene anion at λ = 718 nm (Fig. 3C), and the shoulder around λ = 800 nm, are likely due to an initial nonradiative transition to a lower-energy excited state, which then decays radiatively. This two-step process is also observed in the lifetime dynamics. Similarly, the fluorescence response of the perylene anion (predicted at λ = 738 nm; Fig. 3B) originates from the lower-energy excited state (at around λ = 710 nm; Fig. 3B), and not directly from the main absorption peak (at λ = 540 nm; Fig. 3B). This process is noticeably weaker in perylene, compared with benzo[ghi]perylene. A Jablonski diagram illustrates this likely decay pathway (Fig. 3G).

• Download figure
• Open in new tab
• Download powerpoint

Fig. 3.

Comparative lifetime dynamics and fluorescence in the radical anion state of perylene, benzo[ghi]perylene, and anthanthrene. (A) Experimental spectra of the normalized absorption (solid) and normalized fluorescence emission (dashed) of the neutral (black) and anionic (red) systems of perylene. (B) Theoretical simulations of the same quantities as in A. (C) Experimental spectra of the normalized absorption (solid) and normalized fluorescence emission (dashed) of the neutral (black) and anion (green) systems of benzo[ghi]perylene. (D) Theoretical simulations of the same quantities as in C. (E) Experimental spectra of the normalized absorption (solid) and normalized fluorescence emission (dashed) of the neutral (black) and anion (blue) systems of anthanthrene. (F) Theoretical simulations of the same quantities as in E. (A–F) Wavelength values for the main peaks and relative Stokes shifts for the neutral and anion cases are shown above the relevant peaks. The red lines connect the corresponding peaks in experimental and theoretical spectra for the neutral (dashed) and anion (solid) systems. (G) Jablonski diagram of the benzo[ghi]perylene anion decay pathways, radiative and nonradiative.

We can now present a conceptual framework for molecular plasmon excitation and decay in anionic PAH molecules. Initially, a collective oscillation of the charge density is excited optically, creating an excited state consisting of a superposition of multiple electron–hole pairs composed, with varying weight, of the delocalized π-band electrons. During photoexcitation, the plasmon also may couple strongly to the molecular vibrational modes (38). This molecular plasmon oscillation is weakly damped (compared with conventional plasmons) by electron–electron and electron–phonon interactions. After a certain time (0.5 to 6 ps), multiple excited electron–hole pairs recombine nonradiatively to the ground state. However, due to the discretized nature of its energy levels, the lifetime dynamics of the anion exhibits power-independent behavior (SI Appendix, Fig. S7), in contrast to plasmon resonances in larger metallic systems, but similarly with ultrasmall, molecular-scale (<2 nm) metal islands (10, 39). Such behavior typically appears in systems with discrete energy levels. Neither our measurements nor our simulations can disentangle the effects on the pump–probe dynamics of the open-shell electronic structure from that of the character (plasmonic or single particle) of the excited state itself. Being able to single out the latter effect would be a major achievement.

This framework differs from that of conventional metallic plasmonic systems where the plasmon interacts with a continuum of single electron–hole pair transitions. Instead, the decay results from nonradiative relaxations of the collectively excited electron–hole pairs by internal conversion. We attribute the initial fast 0.5- to 6-ps lifetime component to this decay mechanism and describe it as the molecular plasmon dephasing, in analogy to plasmon dephasing in metal nanoparticles. The rapid decay rates found in molecular plasmons are consistent with the trends for other materials and with typical internal conversion dynamics. The secondary decay time of 7 to 15 ps is attributable to the vibrational relaxation of the system. Molecular plasmons in PAHs couple strongly to the in-plane vibrational modes of the molecule (38); thus, a strong vibrational relaxation pathway would be expected. Past studies into the dynamics of PAH cations (40) have also shown biexponential decay, with the secondary term (also attributed to vibrational relaxation) exhibiting temperature-dependent behavior (decreased temperature corresponding to slower kinetics) that the first term, an electronic phenomenon, lacks. This decay results in an exchange of the excited-state energy with the surrounding media through phonon–phonon coupling. Any heating as a result of this is negligible, due to the extremely low anion concentration, and does not contribute to the relaxation dynamics.

For some molecular plasmons such as the benzo[ghi]perylene anion, an additional decay pathway exists. In this pathway, a small percentage of the excited electron–hole pairs, after the collapse of the collective state where most others have decayed nonradiatively, does not return to the ground state. Instead, they decay nonradiatively to a lower energy excited state capable of radiative decay (Fig. 3G). In molecular plasmons where this decay channel is strong, this transition to a lower radiative state is detected as fluorescence.

In summary, we have investigated the excited-state decay dynamics of molecular plasmons and identified the decay pathways for these few-atom systems. Their collective character together with the substantially shorter lifetimes and very different decay dynamics, in contrast to their neutral molecule counterparts, support a description of these systems as molecular plasmons. This study provides insight into collective excitations in few-atom quantum systems and can open the door to quantum-plasmon applications such as nonlinear plasmon-mediated optics, ultrafast electrochromic devices, and molecular-scale optoelectronic devices based on single-molecule or coupled-molecule collective effects.