Subdiffusive exciton motion in systems with heavy-tailed disorder

Spatial Correlations Drive Long-Range Transport and Trapping of Excitons in Single H-Aggregates: Experiment and Theory

Describing long-range energy transport is a crucial step, both toward deepening our knowledge on natural light-harvesting systems and toward developing novel photoactive materials. Here, we combine experiment and theory to resolve and reproduce energy transport on pico- to nanosecond time scales in single H-type supramolecular nanofibers based on carbonyl-bridged triarylamines (CBT). Each nanofiber shows energy transport dynamics over long distances up to ∼1 μm, despite exciton trapping at specific positions along the nanofibers. Using a minimal Frenkel exciton model including disorder, we demonstrate that spatial correlations in the normally distributed site energies are crucial to reproduce the experimental data. In particular, we can observe the long-range and subdiffusive nature of the exciton dynamics as well as the trapping behavior of excitons in specific locations of the nanofiber. This trapping behavior introduces a net directionality or asymmetry in the exciton dynamics as observed experimentally.

Negative diffusion of excitons in quasi-two-dimensional systems

We show how two different mobile-immobile type models explain the observation of negative diffusion of excitons reported in experimental studies in quasi-two-dimensional semiconductor systems. The main reason for the effect is the initial trapping and a delayed release of free excitons in the area close to the original excitation spot. The density of trapped excitons is not registered experimentally. Hence, the signal from the free excitons alone includes the delayed release of not diffusing trapped particles. This is seen as the narrowing of the exciton density profile or decrease of mean-squared displacement which is then interpreted as a negative diffusion. The effect is enhanced with the increase of recombination intensity as well as the rate of the exciton-exciton binary interactions.

Directed Gradients in the Excited-State Energy Landscape of Poly(3-hexylthiophene) Nanofibers

Funneling excitation energy toward lower energy excited states is a key concept in photosynthesis, which is often realized with at most two chemically different types of pigment molecules. However, current synthetic approaches to establish energy funnels, or gradients, typically rely on Förster-type energy-transfer cascades along many chemically different molecules. Here, we demonstrate an elegant concept for a gradient in the excited-state energy landscape along micrometer-long supramolecular nanofibers based on the conjugated polymer poly(3-hexylthiophene), P3HT, as the single component. Precisely aligned P3HT nanofibers within a supramolecular superstructure are prepared by solution processing involving an efficient supramolecular nucleating agent. Employing hyperspectral imaging, we find that the lowest-energy exciton band edge continuously shifts to lower energies along the nanofibers' growth direction. We attribute this directed excited-state energy gradient to defect fractionation during nanofiber growth. Our concept provides guidelines for the design of supramolecular structures with an intrinsic energy gradient for nanophotonic applications.

Non-Markovian diffusion of excitons in layered perovskites and transition metal dichalcogenides

The diffusion of excitons in perovskites and transition metal dichalcogenides shows clear anomalous, subdiffusive behaviour in experiments. In this paper we develop a non-Markovian mobile-immobile model which provides an explanation of this behaviour through paired theoretical and simulation approaches. The simulation model is based on a random walk on a 2D lattice with randomly distributed deep traps such that the trapping time distribution involves slowly decaying power-law asymptotics. The theoretical model uses coupled diffusion and rate equations for free and trapped excitons, respectively, with an integral term responsible for trapping. The model provides a good fitting of the experimental data, thus, showing a way for quantifying the exciton diffusion dynamics.

All-optical manipulation of singlet exciton transport in individual supramolecular nanostructures by triplet gating

Directed transport of singlet excitation energy is a key process in natural light-harvesting systems and a desired feature in assemblies of functional organic molecules for organic electronics and nanotechnology applications. However, progress in this direction is hampered by the lack of concepts and model systems. Here we demonstrate an all-optical approach to manipulate singlet exciton transport pathways within supramolecular nanostructures via singlet-triplet annihilation, i.e., to enforce an effective motion of singlet excitons along a predefined direction. For this proof-of-concept, we locally photo-generate a long-lived triplet exciton population and subsequently a singlet exciton population on single bundles of H-type supramolecular nanofibres using two temporally and spatially separated laser pulses. The local triplet exciton population operates as a gate for the singlet exciton transport since singlet-triplet annihilation hinders singlet exciton motion across the triplet population. We visualize this manipulation of singlet exciton transport via the fluorescence signal from the singlet excitons, using a detection-beam scanning approach combined with time-correlated single-photon counting. Our reversible, all-optical manipulation of singlet exciton transport can pave the way to realising new design principles for functional photonic nanodevices.

Scaling relations of exciton diffusion in linear aggregates with static and dynamic disorder

Exciton diffusion plays an important role in many opto-electronic processes and phenomena. Understanding the interplay of intermolecular coupling, static energetic disorder, and dephasing caused by environmental fluctuations (dynamic disorder) is crucial to optimize exciton diffusion under various physical conditions. We report on a systematic analysis of the exciton diffusion constant in linear aggregates using the Haken-Strobl-Reineker model to describe this interplay. We numerically investigate the static-disorder scaling of (i) the diffusion constant in the limit of small dephasing rate, (ii) the dephasing rate at which the diffusion is optimized, and (iii) the value of the diffusion constant at the optimal dephasing rate. Three scaling regimes are found, associated with, respectively, fully delocalized exciton states (finite-size effects), weakly localized states, and strongly localized states. The scaling powers agree well with analytically estimated ones. In particular, in the weakly localized regime, the numerical results corroborate the so-called quantum Goldilocks principle to find the optimal dephasing rate and maximum diffusion constant as a function of static disorder, while in the strong-localization regime, these quantities can be derived fully analytically.

Exciton Diffusion in Highly-Ordered One Dimensional Conjugated Polymers: Effects of Back-Bone Torsion, Electronic Symmetry, Phonons and Annihilation

Many optoelectronic devices based on organic materials require rapid and long-range singlet exciton transport. Key factors controlling exciton transport include material structure, exciton-phonon coupling and electronic state symmetry. Here, we employ femtosecond transient absorption microscopy to study the influence of these parameters on exciton transport in one-dimensional conjugated polymers. We find that excitons with 2¹A_g^- symmetry and a planar backbone exhibit a significantly higher diffusion coefficient (34 ± 10 cm² s^-1) compared to excitons with 1¹B_u⁺ symmetry (7 ± 6 cm² s^-1) with a twisted backbone. We also find that exciton transport in the 2¹A_g^- state occurs without exciton-exciton annihilation. Both 2¹A_g^- and 1¹B_u⁺ states are found to exhibit subdiffusive behavior. Ab initio GW-BSE calculations reveal that this is due to the comparable strengths of the exciton-phonon interaction and exciton coupling. Our results demonstrate the link between electronic state symmetry, backbone torsion and phonons in exciton transport in π-conjugated polymers.

Energy transport and light propagation mechanisms in organic single crystals

Unambiguous information about spatiotemporal exciton dynamics in three-dimensional nanometer- to micrometer-sized organic structures is difficult to obtain experimentally. Exciton dynamics can be modified by annihilation processes, and different light propagation mechanisms can take place, such as active waveguiding and photon recycling. Since these various processes and mechanisms can lead to similar spectroscopic and microscopic signatures on comparable time scales, their discrimination is highly demanding. Here, we study individual organic single crystals grown from thiophene-based oligomers. We use time-resolved detection-beam scanning microscopy to excite a local singlet exciton population and monitor the subsequent broadening of the photoluminescence (PL) signal in space and on pico- to nanosecond time scales. Combined with Monte Carlo simulations, we were able to exclude photon recycling for our system, whereas leakage radiation upon active waveguiding leads to an apparent PL broadening of about 20% compared to the initial excitation profile. Exciton-exciton annihilation becomes important at high excitation fluence and apparently accelerates the exciton dynamics leading to apparently increased diffusion lengths. At low excitation fluences, the spatiotemporal PL broadening results from singlet exciton diffusion with diffusion lengths of up to 210 nm. Surprisingly, even in structurally highly ordered single crystals, the transport dynamics is subdiffusive and shows variations between different crystals, which we relate to varying degrees of static and dynamic electronic disorders.

Enhancing Long-Range Energy Transport in Supramolecular Architectures by Tailoring Coherence Properties

Efficient long-range energy transport along supramolecular architectures of functional organic molecules is a key step in nature for converting sunlight into a useful form of energy. Understanding and manipulating these transport processes on a molecular and supramolecular scale is a long-standing goal. However, the realization of a well-defined system that allows for tuning morphology and electronic properties as well as for resolution of transport in space and time is challenging. Here we show how the excited-state energy landscape and thus the coherence characteristics of electronic excitations can be modified by the hierarchical level of H-type supramolecular architectures. We visualize, at room temperature, long-range incoherent transport of delocalized singlet excitons on pico- to nanosecond time scales in single supramolecular nanofibers and bundles of nanofibers. Increasing the degree of coherence, i.e., exciton delocalization, via supramolecular architectures enhances exciton diffusivities up to 1 order of magnitude. In particular, we find that single supramolecular nanofibers exhibit the highest diffusivities reported for H-aggregates so far.

Fully Conjugated Porphyrin Glass: Collective Light-Harvesting Antenna for Near-Infrared Fluorescence beyond 1 μm

Expanded π-systems with a narrow highest occupied molecular orbital-lowest unoccupied molecular orbital band gap encounter deactivation of excitons due to the "energy gap law" and undesired aggregation. This dilemma generally thwarts the near-infrared (NIR) luminescence of organic π-systems. A sophisticated cofacially stacked π-system is known to involve exponentially tailed disorder, which displays exceptionally red-shifted fluorescence even as only a marginal emission component. Enhancement of the tail-state fluorescence might be advantageous to achieve NIR photoluminescence with an expected collective light-harvesting antenna effect as follows: (i) efficient light-harvesting capacity due to intense electronic absorption, (ii) a long-distance exciton migration into the tail state based on a high spatial density of the chromophore site, and (iii) substantial transmission of NIR emission to circumvent the inner filter effect. Suppression of aggregation-induced quenching of fluorescence could realize collective light-harvesting antenna for NIR-luminescence materials. This study discloses an enhanced tail-state NIR fluorescence of a self-standing porphyrin film at 1138 nm with a moderate quantum efficiency based on a fully π-conjugated porphyrin that adopts an amorphous form, called "porphyrin glass".

Information-Length Scaling in a Generalized One-Dimensional Lloyd's Model

We perform a detailed numerical study of the localization properties of the eigenfunctions of one-dimensional (1D) tight-binding wires with on-site disorder characterized by long-tailed distributions: For large ϵ , P ( ϵ ) ∼ 1 / ϵ 1 + α with α ∈ ( 0 , 2 ] ; where ϵ are the on-site random energies. Our model serves as a generalization of 1D Lloyd's model, which corresponds to α = 1 . In particular, we demonstrate that the information length β of the eigenfunctions follows the scaling law β = γ x / ( 1 + γ x ) , with x = ξ / L and γ ≡ γ ( α ) . Here, ξ is the eigenfunction localization length (that we extract from the scaling of Landauer's conductance) and L is the wire length. We also report that for α = 2 the properties of the 1D Anderson model are effectively reproduced.

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

The electronic excited states of molecular aggregates and their photophysical signatures have long fascinated spectroscopists and theoreticians alike since the advent of Frenkel exciton theory almost 90 years ago. The influence of molecular packing on basic optical probes like absorption and photoluminescence was originally worked out by Kasha for aggregates dominated by Coulombic intermolecular interactions, eventually leading to the classification of J- and H-aggregates. This review outlines advances made in understanding the relationship between aggregate structure and photophysics when vibronic coupling and intermolecular charge transfer are incorporated. An assortment of packing geometries is considered from the humble molecular dimer to more exotic structures including linear and bent aggregates, two-dimensional herringbone and "HJ" aggregates, and chiral aggregates. The interplay between long-range Coulomb coupling and short-range charge-transfer-mediated coupling strongly depends on the aggregate architecture leading to a wide array of photophysical behaviors.

Lévy Defects in Matrix-Immobilized J Aggregates: Tracing Intra-and Intersegmental Exciton Relaxation

One-dimensional J aggregates present narrow and intense absorption and emission spectra that are interesting for photonics applications. Matrix immobilization of the aggregates, as required for most device architectures, has recently been shown to induce a non-Gaussian (Lévy type) defect distribution with heavy tails, expected to influence exciton relaxation. Here we perform two-dimensional electronic spectroscopy (2DES) in one-dimensional J aggregates of the cyanine dye TDBC, immobilized in a gel matrix, and we quantitatively model 2DES maps by nonlinear optimization coupled to quantum mechanical calculations of the transient excitonic response. We find that immobilization causes strong non-Gaussian off-diagonal disorder, leading to a segmentation of the chains. Intersegmental exciton transfer is found to proceed on the picosecond time scale, causing a long-lasting excitation memory. These findings can be used to inform the design of optoelectronic devices based on J aggregates as they allow for control of exciton properties by disorder management.

Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems

We perform a detailed numerical study of the conductance G through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies ε of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large ε, P(ε)∼1/ε^{1+α} with α∈(0,2). Our model serves as a generalization of the 1D Lloyd model, which corresponds to α=1. First, we verify that the ensemble average 〈-lnG〉 is proportional to the length of the wire L for all values of α, providing the localization length ξ from 〈-lnG〉=2L/ξ. Then, we show that the probability distribution function P(G) is fully determined by the exponent α and 〈-lnG〉. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at G=0 and 1. In addition, we show that P(lnG) is proportional to G^{β}, for G→0, with β≤α/2, in agreement with previous studies.

Can Disorder Enhance Incoherent Exciton Diffusion?

Recent experiments aimed at probing the dynamics of excitons have revealed that semiconducting films composed of disordered molecular subunits, unlike expectations for their perfectly ordered counterparts, can exhibit a time-dependent diffusivity in which the effective early time diffusion constant is larger than that of the steady state. This observation has led to speculation about what role, if any, microscopic disorder may play in enhancing exciton transport properties. In this article, we present the results of a model study aimed at addressing this point. Specifically, we introduce a general model, based upon Förster theory, for incoherent exciton diffusion in a material composed of independent molecular subunits with static energetic disorder. Energetic disorder leads to heterogeneity in molecule-to-molecule transition rates, which we demonstrate has two important consequences related to exciton transport. First, the distribution of local site-specific hopping rates is broadened in a manner that results in a decrease in average exciton diffusivity relative to that in a perfectly ordered film. Second, since excitons prefer to make transitions that are downhill in energy, the steady state distribution of exciton energies is biased toward low-energy molecular subunits, those that exhibit reduced diffusivity relative to a perfectly ordered film. These effects combine to reduce the net diffusivity in a manner that is time dependent and grows more pronounced as disorder is increased. Notably, however, we demonstrate that the presence of energetic disorder can give rise to a population of molecular subunits with exciton transfer rates exceeding those of subunits in an energetically uniform material. Such enhancements may play an important role in processes that are sensitive to molecular-scale fluctuations in exciton density field.

Quantum simulation of energy transport with embedded Rydberg aggregates

We show that an array of ultracold Rydberg atoms embedded in a laser driven background gas can serve as an aggregate for simulating exciton dynamics and energy transport with a controlled environment. Energetic disorder and decoherence introduced by the interaction with the background gas atoms can be controlled by the laser parameters. This allows for an almost ideal realization of a Haken-Reineker-Strobl-type model for energy transport. The transport can be monitored using the same mechanism that provides control over the environment. The degree of decoherence is traced back to information gained on the excitation location through the monitoring, turning the setup into an experimentally accessible model system for studying the effects of quantum measurements on the dynamics of a many-body quantum system.

Dynamics of the excitonic coupling in organic crystals

We show that the excitonic coupling in molecular crystals undergoes a very large fluctuation at room temperature as a result of the combined thermal motions of the nuclei. This observation dramatically affects the description of exciton transport in organic crystals and any other phenomenon (like singlet fission or exciton dissociation) that originates from an exciton in a molecular crystal or thin film. This unexpected result is due to the predominance of the short-range excitonic coupling mechanisms (exchange, overlap, and charge-transfer mediated) over the Coulombic excitonic coupling for molecules in van der Waals contact. To quantify this effect we develop a procedure to evaluate accurately the short-range excitonic coupling (via a diabatization scheme) along a molecular dynamics trajectory of the representative molecular crystals of anthracene and tetracene.

Single Lévy states-disorder induced energy funnels in molecular aggregates

Using fluorescence super-resolution microscopy we studied simultaneous spectral, spatial localization, and blinking behavior of individual 1D J-aggregates. Excitons migrating 100 nm are funneled to a trap appearing as an additional red-shifted blinking fluorescence band. We propose that the trap is a Frenkel exciton state formed much below the main exciton band edge due to an environmentally induced heavy-tailed Lévy disorder. This points to disorder engineering as a new avenue in controlling light-harvesting in molecular ensembles.

Localization in space and time in disordered-lattice open quantum dynamics

We study a two-dimensional tight-binding lattice for excitons with on-site disorder, coupled to a thermal environment at infinite temperature. The disorder acts to localize an exciton spatially, while the environment generates dynamics which enable exploration of the lattice. Although the steady state of the system is trivially uniform, we observe a rich dynamics and uncover a dynamical phase transition in the space of temporal trajectories. This transition is identified as a localization in the dynamics generated by the bath. We explore spatial features in the dynamics and employ a generalization of the inverse participation ratio to deduce an ergodic timescale for the lattice.

The structure and dynamics of molecular excitons

The photophysical behavior of organic semiconductors is governed by their excitonic states. In this review, I classify the three different exciton types (Frenkel singlet, Frenkel triplet, and charge transfer) typically encountered in organic semiconductors. Experimental challenges that arise in the study of solid-state organic systems are discussed. The steady-state spectroscopy of intermolecular delocalized Frenkel excitons is described, using crystalline tetracene as an example. I consider the problem of a localized exciton diffusing in a disordered matrix in detail, and experimental results on conjugated polymers and model systems suggest that energetic disorder leads to subdiffusive motion. Multiexciton processes such as singlet fission and triplet fusion are described, emphasizing the role of spin state coherence and magnetic fields in studying singlet ↔ triplet pair interconversion. Singlet fission provides an example of how all three types of excitons (triplet, singlet, and charge transfer) may interact to produce useful phenomena for applications such as solar energy conversion.