We compare localization properties of one-dimensional Frenkel excitons with Gaussian and Lorentzian uncorrelated diagonal disorder. We focus on the states of the Lifshits tail, which dominate the optical response and low-temperature energy transport in molecular J-aggregates. The absence of exchange narrowing in chains with Lorentzian disorder is shown to manifest itself in the disorder scaling of the localization length distribution. Also, we show that the local exciton level structure of the Lifshits tail differs substantially for these two types of disorder: In addition to the singlets and doublets of localized states near the bare band edge, strongly resembling those found for Gaussian disorder, for Lorentzian disorder two other types of states are found in this energy region as well, namely multiplets of three or four states localized on the same chain segment and isolated states localized on short segments. Finally, below the Lifshits tail, Lorentzian disorder induces strongly localized exciton states, centered around low energy sites, with localization properties that strongly depend on energy. For Gaussian disorder with a magnitude that does not exceed the exciton bandwidth, the likelihood to find such very deep states is exponentially small.
We present results of numerical simulations of the kinetics of exciton-exciton annihilation of weakly localized one-dimensional Frenkel excitons at low temperatures. We find that the kinetics is represented by two well-distinguished components: a fast short-time decay and a very slow long-time tail. The former arises from excitons that initially reside in states belonging to the same localization segment of the chain, while the slow component is caused by excitons created on different localization segments. We show that the usual bi-molecular theory fails in the description of the behavior fou…
A method is proposed for calculating the absorption spectrum of a long one-dimensional closed-into-a-ring chain with Frenkel's exciton under diagonal disorder. This disorder is represented by the hyperbolic singularities of atomic fission. These defects are shown to lead to a wing in the exciton zone of a chain without defects. The form of the wing does not depend on the relative positions or number of defects and its value is proportional to the sum of the amplitudes of the defects. The proposed method uses only the continual approximation.
We study a one-dimensional Frenkel Hamiltonian with off-diagonal disorder, focusing our attention on the physical nature of the zero-energy peak of the density of states. The character of excitonic states (localized or delocalized) is also examined in the vicinity of this peak. It is shown that the state being responsible for the peak is localized. A detailed comparison of the nearest-neighbor approach with the long-range dipole-dipole coupling is performed.
On the optical absorption and the density of states of Frenkel exciton systems on square, rectangular, and triangular lattices with nearest-neighbor interactions and a Gaussian distribution of transition frequencies. The analysis is based on an elliptic integral approach that gives results over the entire spectrum. It is found that the absorption is weakly affected by the anisotropy in contrast to the density of states where the effects can be much stronger. The results for the square lattice are in good agreement with the finite array calculations of Schreiber and Toyozawa. Our findings sugge…
We analyze the effects of intersite energy correlations on the linear optical properties of one-dimensional disordered Frenkel exciton systems. The absorption line width and the factor of radiative rate enhancement are studied as a function of the correlation length of the disorder. The absorption line width monotonously approaches the seeding degree of disorder on increasing the correlation length. On the contrary, the factor of radiative rate enhancement shows a non-monotonous trend, indicating a complicated scenario of the exciton localization in correlated systems. The concept of coherentl…
A method is proposed for manipulating with diagrammatic expansion of Green's function of Frenkel's exciton random walks on the perfect lattice. The method allows one to select diagrams, to supply diagrams with factors containing information about the number of sites the diagram has passed through, etc. Simple problems related to the defect lattices are considered using the proposed method. The new criterion of localization of Frenkel exciton - the number of sites covered by the wave function - is established. The number of sites covered by the zero state of 1D non-diagonally disordered chain i…
The standard one-parameter scaling theory predicts that all eigenstates in two-dimensional random lattices are weakly localized. We show that this claim fails in two-dimensional dipolar Frenkel exciton systems. The linear energy dispersion at the top of the exciton band, originating from the long-range inter-site coupling of dipolar nature, yields the same size-scaling law for the level spacing and the effective disorder seen by the exciton. This finally results in the delocalization of those eigenstates in the thermodynamic limit. Large scale numerical simulations allow us to perform a detail…
We report the amplitude scaling behavior of Frenkel exciton chains with nearest-neighbor correlated off-diagonal random interactions. The band center spectrum and its localization properties are investigated through the integrated density of states and the inverse localization length. The correlated random interactions are produced through a binary sequence similar to the interactions in spin glass chains. We produced sets of data with different interaction strength and "wrong" sign concentrations that collapsed after scaling to the predictions of a theory developed earlier for Dirac fermions …
Numerical study of the one-dimensional Frenkel Hamiltonian with on-site randomness is carried out. We focus on the statistics of the energy levels near the lower exciton band edge, i. e. those determining optical response. We found that the distribution of the energy spacing between the states that are well localized at the same segment is characterized by non-zero mean, i.e. these states undergo repulsion. This repulsion results in a local discrete energy structure of a localized Frenkel exciton. On the contrary, the energy spacing distribution for weakly overlapping local ground states (the …
We present a theoretical analysis of low-temperature quenching of one-dimensional Frenkel excitons that are localised by moderate on-site (diagonal) uncorrelated disorder. Exciton diffusion is considered as an incoherent hopping over localization segments and is probed by the exciton fluorescence quenching at point traps. The rate equation is used to calculate the temperature dependence of the exciton quenching. The activation temperature of the diffusion is found to be of the order of the width of the exciton absorption band. We demonstrate that the intra-segment scattering is extremely impor…
We calculate the temperature dependence of the fluorescence Stokes shift and the fluorescence decay time in linear Frenkel exciton systems resulting from the thermal redistribution of exciton population over the band states. The following factors, relevant to common experimental conditions, are accounted for in our kinetic model: (weak) localization of the exciton states by static disorder, coupling of the localized excitons to vibrations in the host medium, a possible non-equilibrium of the subsystem of localized Frenkel excitons on the time scale of the emission process, and different excita…
We study theoretically diffusion of one-dimensional Frenkel excitons in J-aggregates at temperatures that are smaller or of the order of the J-band width. We consider an aggregate as an open linear chain with uncorrelated on-site (diagonal) disorder that localizes the exciton at chain segments of size smaller than the full chain length. The exciton diffusion over the localization segments is considered as incoherent hopping. The diffusion is probed by the exciton fluorescence quenching which is due to the presence of point traps in the aggregate. The rate equation for populations of the locali…
Recent ultrafast experiments have implicated intrachain base-stacking rather than base-pairing as the crucial factor in determining the fate and transport of photoexcited species in DNA chains. An important issue that has emerged concerns whether or not a Frenkel excitons is sufficient one needs charge-transfer states to fully account for the dynamics. In we present an $SU(2)\otimes SU(2)$ lattice model which incorporates both intrachain and interchain electronic interactions to study the quantum mechanical evolution of an initial excitonic state placed on either the adenosine or thymidine sid…
We consider the dynamics of Frenkel excitons on quasiperiodic lattices, focusing our attention on the Fibonacci case as a typical example. We evaluate the absorption spectrum by solving numerically the equation of motion of the Frenkel-exciton problem on the lattice. Besides the main absorption line, satellite lines appear in the high-energy side of the spectra, which we have related to the underlying quasiperiodic order. The influence of lattice vibrations on the absorption line-shape is also considered. We find that the characteristic features of the absorption spectra should be observable e…
We model the optical dynamics in linear Frenkel exciton systems governed by scattering on static disorder and lattice vibrations, and calculate the temperature dependent fluorescence spectrum and lifetime. The fluorescence Stokes shift shows a nonmonotonic behavior with temperature, which derives from the interplay of the local band-edge level structure and thermal equilibration. The model yields excellent fits to experiments performed on linear dye aggregates.
1D diagonally disordered chain with Frenkel exciton and long range exponential intersite interaction is considered. It is shown that some states of this disordered system are delocalised contrary to the popular statement that all states in 1D disordered system are localised.
Using a model of Frenkel excitons coupled to a bath of acoustic phonons in the host medium, we study the temperature dependence of the dephasing rates and homogeneous line width in linear molecular aggregates. The model includes localization by disorder and predicts a power-law thermal scaling of the effective homogeneous line width. The theory gives excellent agreement with temperature dependent absorption and hole-burning experiments on aggregates of the dye pseudoisocyanine.
We investigate the effects of disorder on Frenkel excitons in disordered conjugated polymers with allowed rotations about single bonds. In these materials, the principal effect of the disorder is to modify the transfer integrals appearing in the exciton Hamiltonian by changing the angle of rotation between single-bonded segments in a random manner. It is assumed the integrals have the form Jk,k+1 cos(qk-qk+1) where Jk,k+1 is taken to be a constant and qk denotes the orientation angle of the kth planar segment. Two types of disorder can be present: segmental disorder which is characterized by i…
The problem of the one-exciton absorption spectrum is considered for the lattice of two-level interacting atoms whose initial energy splitting depends on the coordinate. It is shown that for some types of interatomic interaction, this problem can be reduced to a differential equation of Schrodinger type, which, in some cases, can be solved in closed form. By way of example, problems on the one dimensional chain having an initial splitting jump and on the spherical cluster are solved. In both cases analitical solutions are obtained, which considerably reduce the time required for calculations o…
In their Letter "Excitons in Molecular Aggregates with Levy Disorder: Anomalous Localization and Exchange Broadening of Optical Spectra", Eisfeld et al. predicted the existence of exchange broadening and blue-shift of the absorption band and a non-universal disorder scaling of the localisation length of absorption band excitons in J-aggregates with heavy-tailed disorder, which they contrasted with the previously analysed Gaussian and Lorentzian case. The observations were explained by another localisation mechanism, the chain segmentation by outliers in heavy tails of the disorder distribution…
1D diagonally disordered chain with Frenkel exciton and long range exponential intersite interaction is considered. It is shown that some states of this disordered system are delocalised (extended) contrary to the popular statement that all states in 1D disordered system are localised. The theorem is established that for the Anderson's model of diagonal disorder one should expect the appearance of states with extended module. All statements are confirmed by computer simulations.
We study the dynamics of a single Frenkel exciton in a disordered molecular chain. The coherent-potential approximation (CPA) is applied to the situation when the single-molecule excitation energies as well as the transition dipole moments, both their absolute values and orientations, are random. Such model is believed to be relevant for the description of the linear optical properties of one-dimensional $J$ aggregates. We calculate the exciton density of states, the linear absorption spectra and the exciton coherence length which reveals itself in the linear optics. A detailed analysis of the…
We generalize our recent work on the optical bistability of thin films of molecular aggregates [J. Chem. Phys. 127, 164705 (2007); arXiv:0707.1264v1 [cond-mat.dis-nn]] by accounting for the optical transitions from the one-exciton manifold to the two-exciton manifold as well as the exciton-exciton annihilation of the two-exciton states via a high-lying molecular vibronic term. We also include the relaxation from the vibronic level back to both the one-exciton manifold and the ground state. By selecting the dominant optical transitions between the ground state, the one-exciton manifold, and the…
We theoretically study the efficiency of energy harvesting in linear exciton chains with an energy bias, where the initial excitation is taking place at the high-energy end of the chain and the energy is harvested (trapped) at the other end. The efficiency is characterized by means of the average time for the exciton to be trapped after the initial excitation. The exciton transport is treated as the intraband energy relaxation over the states obtained by numerically diagonalizing the Frenkel Hamiltonian that corresponds to the biased chain. The relevant intraband scattering rates are obtained …
We perform a theoretical study of the nonlinear optical response of an ultrathin film consisting of oriented linear aggregates. A single aggregate is described by a Frenkel exciton Hamiltonian with uncorrelated on-site disorder. The exciton wave functions and energies are found exactly by numerically diagonalizing the Hamiltonian. The principal restriction we impose is that only the optical transitions between the ground state and optically dominant states of the one-exciton manifold are considered, whereas transitions to other states, including those of higher exciton manifolds, are neglected…
In their Letter [Phys. Rev. Lett. 105, 137402 (2010)], Eisfeld et al. predicted the exchange broadening and blue-shift of the absorption band as well as a nonuniversal disorder scaling of the localization length of excitons in J-aggregates with Levy disorder, which they contrasted with the previously analyzed Gaussian and Lorentzian case [Phys. Rev. B, 79, 1 (2009)]. The observations were explained by chain segmentation due to outliers, and its interplay with localization of states in effective potential wells created by typical random site energies. We argue that the previously known theory d…
