Browsing by Author "Janković, Veljko"

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    Combination of Charge Delocalization and Disorder Enables Efficient Charge Separation at Photoexcited Organic Bilayers
    Janković, Veljko; Vukmirović, Nenad
    We study incoherent charge separation in a lattice model of an all-organic bilayer. Charge delocalization is taken into account by working in the basis of electron-hole pair eigenstates, and the separation is described as a series of incoherent hops between these states. We find that relatively weak energetic disorder, in combination with good charge delocalization, can account for efficient and weakly field- and temperature-dependent separation of the strongly bound charge transfer (CT) state. The separation efficiency is determined by the competition between the recombination from the initial CT state and the escape toward intermediate CT states, from which free-charge states can be reached with certainty. The separation of donor excitons also exhibits quite high yields, less bound excitons separating more efficiently. Overall, our results support the notion that efficient charge separation can be achieved even out of strongly bound pair states without invoking coherent effects.
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    Cumulant expansion in the Holstein model: Spectral functions and mobility
    Mitrić, Petar; Janković, Veljko; Vukmirović, Nenad; Tanasković, Darko
    We examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space, even in low dimensions. We find that in one dimension, the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law μ∝T−2 in the limit of weak coupling and μ∝T−3/2 for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.
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    Cumulant expansion in the Holstein model: Spectral functions and mobility
    Mitrić, Petar; Janković, Veljko; Vukmirović, Nenad; Tanasković, Darko
    We examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space, even in low dimensions. We find that in one dimension, the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law μ∞T-2 in the limit of weak coupling and μ∞T-3/2 for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.
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    Energy-Temporal Pathways of Free-Charge Formation at Organic Bilayers: Competition of Delocalization, Disorder, and Polaronic Effects
    Janković, Veljko; Vukmirović, Nenad
    We investigated the charge separation process in organic semiconductor bilayers from the moment of creation of a donor exciton to the time when all charge pairs have either recombined or reached external contacts. The system was modeled using a one-dimensional microscopic Hamiltonian that includes the effects of carrier delocalization, electron-hole interaction, static disorder, and carrier-phonon interaction. Transition rates between excitonic states were modeled using modified Redfield approach which takes into account polaronic effects by exact treatment of diagonal exciton-phonon interaction. An efficient numerical scheme was developed that enabled us to obtain the time dependence of energy-resolved populations of relevant exciton states on a time scale as long as 1 μs. Our results indicated that charge separation proceeds via the so-called cold pathway in which donor excitons convert to relaxed charge-transfer excitons which further transform to the states of separated charges. We found that for lower disorder strengths the time scale for conversion of donor excitons to charge transfer excitons is ∼(1-10) ps, while further separation to free charges takes place on the time scale reaching ∼1 ns. These time scales are extended for larger disorder strengths because diffusion of donor excitons to the interface and transport of separated charges toward external contacts are slowed down. We also found that charge separation yield has a rather weak dependence on electron-phonon interaction strength.
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    Exact description of excitonic dynamics in molecular aggregates weakly driven by light
    Janković, Veljko; Mančal, Tomáš
    We present a rigorous theoretical description of excitonic dynamics in molecular light-harvesting aggregates photoexcited by weak-intensity radiation of arbitrary properties. While the interaction with light is included up to the second order, the treatment of the excitation–environment coupling is exact and results in an exact expression for the reduced excitonic density matrix that is manifestly related to the spectroscopic picture of the photoexcitation process. This expression takes fully into account the environmental reorganization processes triggered by the two interactions with light. This is particularly important for slow environments and/or strong excitation–environment coupling. Within the exponential decomposition scheme, we demonstrate how our result can be recast as the hierarchy of equations of motion (HEOM) that explicitly and consistently includes the photoexcitation step. We analytically describe the environmental reorganization dynamics triggered by a delta-like excitation of a single chromophore and demonstrate how our HEOM, in appropriate limits, reduces to the Redfield equations comprising a pulsed photoexcitation and the nonequilibrium Förster theory. We also discuss the relation of our formalism to the combined Born–Markov–HEOM approaches in the case of excitation by thermal light.
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    Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice
    Janković, Veljko; Vučičević, Jakša
    Ultracold-atom simulations of the Hubbard model provide insights into the character of charge and spin correlations in and out of equilibrium. The corresponding numerical simulations, on the other hand, remain a significant challenge. We build on recent progress in the quantum Monte Carlo (QMC) simulation of electrons in continuous space and apply similar ideas to the square-lattice Hubbard model. We devise and benchmark two discrete-time QMC methods, namely the fermionic-propagator QMC (FPQMC) and the alternating-basis QMC (ABQMC). In FPQMC, the time evolution is represented by snapshots in real space, whereas the snapshots in ABQMC alternate between real and reciprocal space. The methods may be applied to study equilibrium properties within the grand-canonical or canonical ensemble, external field quenches, and even the evolution of pure states. Various real-space/reciprocal-space correlation functions are also within their reach. Both methods deal with matrices of size equal to the number of particles (thus independent of the number of orbitals or time slices), which allows for cheap updates. We benchmark the methods in relevant setups. In equilibrium, the FPQMC method is found to have an excellent average sign and, in some cases, yields correct results even with poor imaginary-time discretization. ABQMC has a significantly worse average sign, but also produces good results. Out of equilibrium, FPQMC suffers from a strong dynamical sign problem. On the contrary, in ABQMC, the sign problem is not time-dependent. Using ABQMC, we compute survival probabilities for several experimentally relevant pure states.
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    Holstein polaron transport from numerically “exact” real-time quantum dynamics simulations
    Janković, Veljko
    Numerically “exact” methods addressing the dynamics of coupled electron–phonon systems have been intensively developed. Nevertheless, the corresponding results for the electron mobility μdc are scarce, even for the one-dimensional (1d) Holstein model. Building on our recent progress on single-particle properties, here we develop the momentum-space hierarchical equations of motion (HEOM) method to evaluate real-time two-particle correlation functions of the 1d Holstein model at a finite temperature. We compute numerically “exact” dynamics of the current–current correlation function up to real times sufficiently long to capture the electron’s diffusive motion and provide reliable results for μdc in a wide range of model parameters. In contrast to the smooth ballistic-to-diffusive crossover in the weak-coupling regime, we observe a temporally limited slow-down of the electron on intermediate time scales already in the intermediate-coupling regime, which translates to a finite-frequency peak in the optical response. Our momentum-space formulation lowers the numerical effort with respect to existing HEOM-method implementations, while we remove the numerical instabilities inherent to the undamped-mode HEOM by devising an appropriate hierarchy closing scheme. Still, our HEOM remains unstable at too low temperatures, for too strong electron–phonon coupling, and for too fast phonons.
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    Nonequilibrium steady-state picture of incoherent light-induced excitation harvesting
    Janković, Veljko; Mančal, Tomáš
    We formulate a comprehensive theoretical description of excitation harvesting in molecular aggregates photoexcited by weak incoherent radiation. An efficient numerical scheme that respects the continuity equation for excitation fluxes is developed to compute the nonequilibrium steady state (NESS) arising from the interplay between excitation generation, excitation relaxation, dephasing, trapping at the load, and recombination. The NESS is most conveniently described in the so-called preferred basis in which the steady-state excitonic density matrix is diagonal. The NESS properties are examined by relating the preferred-basis description to the descriptions in the site or excitonic bases. Focusing on a model photosynthetic dimer, we find that the NESS in the limit of long trapping time is quite similar to the excited-state equilibrium in which the stationary coherences originate from the excitation–environment entanglement. For shorter trapping times, we demonstrate how the properties of the NESS can be extracted from the time-dependent description of an incoherently driven but unloaded dimer. This relation between stationary and time-dependent pictures is valid, provided that the trapping time is longer than the decay time of dynamic coherences accessible in femtosecond spectroscopy experiments.
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    Nonequilibrium Thermodynamics of Charge Separation in Organic Solar Cells
    Kaiser, Waldemar; Janković, Veljko; Vukmirović, Nenad; Gagliardi, Alessio
    This work presents a novel theoretical description of the nonequilibrium thermodynamics of charge separation in organic solar cells (OSCs). Using stochastic thermodynamics, we take realistic state populations derived from the phonon-assisted dynamics of electron-hole pairs within photoexcited organic bilayers to connect the kinetics with the free energy profile of charge separation. Hereby, we quantify for the first time the difference between nonequilibrium and equilibrium free energy profile. We analyze the impact of energetic disorder and delocalization on free energy, average energy, and entropy. For a high disorder, the free energy profile is well-described as equilibrated. We observe significant deviations from equilibrium for delocalized electron-hole pairs at a small disorder, implying that charge separation in efficient OSCs proceeds via a cold but nonequilibrated pathway. Both a large Gibbs entropy and large initial electron-hole distance provide an efficient charge separation, while a decrease in the free energy barrier does not necessarily enhance charge separation
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    Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations  of motion approach
    Janković, Veljko; Vukmirović, Nenad
    We develop a hierarchical equations of motion (HEOM) approach to compute real-time single-particle correlation functions and thermodynamic properties of the Holstein model at finite temperature. We exploit the conservation of the total momentum of the system to formulate the momentum-space HEOM whose dynamical variables explicitly keep track of momentum exchanges between the electron and phonons. Our symmetry-adapted HEOM enable us to overcome the numerical instabilities inherent to the commonly used real-space HEOM. The HEOM method is then used to study the spectral function and thermodynamic quantities of chains containing up to ten sites. The HEOM results compare favorably to existing literature. To provide an independent assessment of the HEOM approach and to gain insight into the importance of finite-size effects, we devise a quantum Monte Carlo (QMC) procedure to evaluate finite-temperature single-particle correlation functions in imaginary time and apply it to chains containing up to twenty sites. QMC results reveal that finite-size effects are quite weak, so that the results on 5 to 10-site chains, depending on the parameter regime, are representative of larger systems. A detailed comparison between the HEOM and QMC data place our HEOM method among reliable methods to compute real-time finite-temperature correlation functions in parameter regimes ranging from low- to high-temperature, and weak- to strong-coupling regime.
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    Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions
    Mitrić, Petar; Janković, Veljko; Vukmirović, Nenad; Tanasković, Darko
    It is generally accepted that the dynamical mean field theory gives a good solution of the Holstein model, but only in dimensions greater than two. Here, we show that this theory, which becomes exact in the weak coupling and in the atomic limit, provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. To establish this, we make a detailed comparison with the spectral functions that we obtain using the newly developed momentum-space numerically exact hierarchical equations of motion method, which yields electronic correlation functions directly in real time. We crosscheck these conclusions with our path integral quantum Monte Carlo and exact diagonalization results, as well as with the available numerically exact results from the literature.