Nonlocal Electron-phonon Coupling Research Articles

Roles of nonlocal electron-phonon coupling on the electrical conductivity and Seebeck coefficient: A time-dependent DMRG study

Roles of nonlocal electron-phonon coupling on the electrical conductivity and Seebeck coefficient: A time-dependent DMRG study

Large polarons in two-dimensional fullerene networks: the crucial role of anisotropy in charge transport.

The recent synthesis of a two-dimensional quasi-hexagonal-phase monolayer network of C60 molecules, known as qHPC60, holds significant promise for future semiconductor applications. However, the mechanism behind charge transport in these networks remains unknown. In this study, we developed a Holstein-Peierls Hamiltonian model to investigate charge transport in qHPC60, incorporating both local and non-local electron-phonon couplings. Our computational approach involved identifying suitable semi-empirical parameters to realize the formation of stable polarons in this material. The results unveiled the formation of stable large polarons as the primary carriers in the charge transport throughout qHPC60. To explore polaron transport properties, we conducted dynamic simulations within the picosecond time scale while subjecting the system to an external electric field. Our analysis emphasized the substantial influence of anisotropy on shaping mobile polarons, with an anisotropy coefficient of at least 50%. The polarons exhibited velocities within the acoustic regime ranging from 0.5-1.5 nm ps-1. While these velocities are comparable to those observed in high-end organic molecular crystals, they are considerably lower than those in graphene and conducting polymers. With qHPC60 possessing a semiconducting band gap of approximately 1.6 eV, our findings shed light on its potential application in flat electronics, overcoming the null-gap predicament of graphene.

Dynamic Disorder Drives Exciton Dynamics in Diketopyrrolopyrrole–Thiophene-Containing Molecular Crystals

There is a growing interest in controllable molecular materials for potential nanophotonic and quantum information applications where excitons move beyond the incoherent transport regime. Thus, the ability to identify the key parameters that correlate with the efficiency of the transport of the excitation energy is highly desirable. In this work, we investigate the effects of the dynamic disorder on the transport of the exciton in molecular crystals of several mono- and dialkylated 1,4-diketo-3,6-dithiophenylpyrrolo[3-4-c]pyrrole derivatives. These systems exhibit great potential for photovoltaic applications due to their broad optical absorption and efficient charge transport. The exciton dynamics are studied using a model Hamiltonian, in which the thermal fluctuations of the excitonic coupling (nonlocal electron–phonon coupling), as well as the local exciton–phonon couplings, have been appropriately taken into account. The computed reorganization energies for the most feasible transport pathway (π–π stacking) for the excitons in UBEQUQ and UBEQOK molecular crystals are 0.366 and 0.357 eV, respectively. These values are comparable with the magnitude of the average excitonic coupling ⟨J⟩ (≈ 0.1 eV) for these two molecular crystals. In this instance, the local exciton–phonon coupling is not large enough to form a small exciton-polaron. In addition, substantial coherences are observed on a time scale of less than 100 fs, which indicates that the dynamic disorder is sufficient to overcome quantum dephasing and help drive exciton transport in this class of organic semiconductors. On the other hand, the diffusion of the excitons reduces significantly when the thermal fluctuations of the excitonic coupling are omitted. Thus, dynamic disorder plays a vital role in the transport of the exciton, and the ability to control this inherent property in molecular aggregates will provide valuable tools for the design and development of efficient organic semiconductors.

A general charge transport picture for organic semiconductors with nonlocal electron-phonon couplings

The nonlocal electron-phonon couplings in organic semiconductors responsible for the fluctuation of intermolecular transfer integrals has been the center of interest recently. Several irreconcilable scenarios coexist for the description of the nonlocal electron-phonon coupling, such as phonon-assisted transport, transient localization, and band-like transport. Through a nearly exact numerical study for the carrier mobility of the Holstein-Peierls model using the matrix product states approach, we locate the phonon-assisted transport, transient localization and band-like regimes as a function of the transfer integral (V) and the nonlocal electron-phonon couplings (ΔV), and their distinct transport behaviors are analyzed by carrier mobility, mean free path, optical conductivity and one-particle spectral function. We also identify an “intermediate regime” where none of the established pictures applies, and the generally perceived hopping regime is found to be at a very limited end in the proposed regime paradigm.

Evaluations of nonlocal electron-phonon couplings in tetracene, rubrene, and C10−DNBDT−NW based on density functional theory

In organic molecular semiconductors (OSCs), fluctuation of transfer integrals originating from thermally induced molecular vibrations is suggested to cause large scatterings of carriers, and to be a most important factor for the suppression of their carrier mobility. The intrinsic carrier mobility under such a fluctuation of transfer integrals is calculated using the transient localization theory, in which the estimation of transfer-integral fluctuation depending on each OSC is indispensable. In the present study, we provide a methodology to evaluate nonlocal electron-phonon couplings in OSCs using the density functional theory, which enables us to evaluate precisely the fluctuation magnitude of transfer integrals. Our method is based upon the combination of the frequency correction to reduce numerical inaccuracies in normal-mode frequencies, the extraction of tight binding parameters using maximally localized Wannier functions, and the explicit consideration of anharmonicity of phonons. We apply this method to classical OSCs, tetracene and rubrene, and a recently developed high-mobility OSC, $3,11\text{\ensuremath{-}}\text{didecyl-dinaphtho}[2,3\text{\ensuremath{-}}d:2\ensuremath{'},3\ensuremath{'}\text{\ensuremath{-}}d\ensuremath{'}]\mathrm{benzo}[1,2\text{\ensuremath{-}}b:4,5\text{\ensuremath{-}}b\ensuremath{'}]\mathrm{dithiophene}$ $({\mathrm{C}}_{10}\text{\ensuremath{-}}\mathrm{DNBDT}\text{\ensuremath{-}}\mathrm{NW})$. We succeeded in identifying the low-frequency vibrations dominating the fluctuation of transfer integrals at room temperature, which we consider to be the main factors to limit the intrinsic mobility.

Modeling nonlocal electron-phonon coupling in organic crystals using interpolative maps: The spectroscopy of crystalline pentacene and 7,8,15,16-tetraazaterrylene.

Electron-phonon coupling plays a central role in the transport properties and photophysics of organic crystals. Successful models describing charge- and energy-transport in these systems routinely include these effects. Most models for describing photophysics, on the other hand, only incorporate local electron-phonon coupling to intramolecular vibrational modes, while nonlocal electron-phonon coupling is neglected. One might expect nonlocal coupling to have an important effect on the photophysics of organic crystals because it gives rise to large fluctuation in the charge-transfer couplings, and charge-transfer couplings play an important role in the spectroscopy of many organic crystals. Here, we study the effects of nonlocal coupling on the absorption spectrum of crystalline pentacene and 7,8,15,16-tetraazaterrylene. To this end, we develop a new mixed quantum-classical approach for including nonlocal coupling into spectroscopic and transport models for organic crystals. Importantly, our approach does not assume that the nonlocal coupling is linear, in contrast to most modern charge-transport models. We find that the nonlocal coupling broadens the absorption spectrum non-uniformly across the absorption line shape. In pentacene, for example, our model predicts that the lower Davydov component broadens considerably more than the upper Davydov component, explaining the origin of this experimental observation for the first time. By studying a simple dimer model, we are able to attribute this selective broadening to correlations between the fluctuations of the charge-transfer couplings. Overall, our method incorporates nonlocal electron-phonon coupling into spectroscopic and transport models with computational efficiency, generalizability to a wide range of organic crystals, and without any assumption of linearity.

Two-dimensional electronic and charge-transport properties of a monolayer organic crystal: Impacts of the collinear transfer-integral correlations

Abstract Electronic transfer integrals between the frontier orbitals of adjacent molecules represent the most important parameter governing charge transport in organic crystals. Different transfer integrals may be significantly modulated by the same modes of molecular vibrations as a result of nonlocal electron-phonon couplings, leading to spatial correlations between the transfer integrals. Here, by employing a multiscale modeling approach, we investigate theoretically the impacts of transfer-integral correlations (TICs) on the two-dimensional electronic and charge-transport properties of a monolayer pentacene crystal. In particular, we focus on the collinear TICs that are present between molecular pairs along the same direction of molecular packings in the crystal. We reveal that the interplay of the collinear TICs along different directions leads to diverse landscapes of nonlocal electron-phonon couplings in reciprocal space, of which the impacts explicitly manifest themselves in the band structures at finite temperatures. We also evaluate the anisotropic hole mobility of the pentacene monolayer and demonstrate that the consequence of the collinear TICs can be reflected in the behaviors of the temperature-dependent band-like mobility observed in experiment. These findings provide an insight into how nonlocal electron-phonon couplings operate through TICs to impact the electronic and electrical properties of organic crystals in two dimension.

Method for Fast Estimation of Lattice Distortion Energy in Organic Semiconductors

The efficient operation of organic electronic devices requires a high mobility of charge carriers in their active layers. According to modern concepts, the charge mobility in the best organic semiconductors is limited by dynamic disorder, i.e., fluctuations of intermolecular charge transfer integrals caused by the nonlocal electron–phonon coupling and thermal motion of molecules. However, the estimate of nonlocal electron–phonon coupling currently requires time- and resource-consuming methods, which complicates the search for high-mobility organic semiconductors among numerous candidates. In this work, a method has been proposed to rapidly estimate the lattice distortion energy, which is the main characteristic of the nonlocal electron–phonon coupling, by comparing the reorganization energies of molecules and molecular dimers. The determined lattice distortion energies are in good agreement with the values previously obtained by other methods. Furthermore, the proposed method has allowed addressing the effect of intermolecular delocalization on the nonlocal electron–phonon coupling. The results obtained indicate that the proposed approach is promising for the efficient search for organic semiconductors with a weak nonlocal electron–phonon coupling and a high charge mobility.

Polaron properties in 2D organic molecular crystals: directional dependence of non-local electron-phonon coupling.

In organic molecular crystals, the polaronic hopping model for the charge transport assumes that the carrier lies at one or a small number of molecules. Such a kind of localization suffers the influence of the non-local electron-phonon (e-ph) interactions associated with intermolecular lattice vibrations. Here, we developed a model Hamiltonian for numerically describing the role played by the intermolecular e-ph interactions on the stationary and dynamical properties of polarons in a two-dimensional array of molecules. We allow three types of electron hopping mechanisms and, consequently, for the nonlocal e-ph interactions: horizontal, vertical, and diagonal. Remarkably, our findings show that the stable polarons are not formed for isotropic arrangements of the intermolecular transfer integrals, regardless of the strengths of the e-ph interactions. Interestingly, the diagonal channel for the e-ph interactions changes the transport mechanism by sharing the polaronic charge between parallel molecular lines in a breather-like mode.

Rapid Evaluation of Dynamic Electronic Disorder in Molecular Semiconductors

One of the key factors limiting the charge mobility of molecular semiconductors is the fluctuation of transfer integrals, also known as dynamic disorder. This is a manifestation of the nonlocal electron–phonon coupling, a property that is computationally expensive to evaluate and, so far, prevented the study of this property on large datasets of molecules. In this article, we describe a methodology for the fast evaluation of the dynamic electronic disorder for molecular semiconductors from their crystalline structure. The computation is accelerated by (i) the evaluation of the Cartesian gradient of transfer integral and (ii) the use of approximate phonons evaluated within the rigid body approximation. The quality of the approximations is checked against less-approximated alternatives. This method is used to study a range of molecular crystals, and some general trends on the behavior of the nonlocal electron–phonon coupling are discussed. A strategy to find the optimal relative position between interacting...

Nonlocal Electron-Phonon Coupling in Prototypical Molecular Semiconductors from First Principles.

A substantial amount of evidence indicates a relevant role played by the nonlocal electron-phonon couplings in the mechanism of charge transport in organic semiconductors. In this work, we compute the nonlocal electron-phonon coupling for the prototypical molecular semiconductors rubrene and tetracene using the phonon modes obtained from ab initio methods. We do not make the rigid molecular approximation allowing a mixing of intra- and intermolecular modes, and we use a supercell approach to sample the momentum space. Indeed, we find that some low-frequency intramolecular modes are mixed with the rigid-molecule translations and rotations in the modes with the strongest electron-phonon coupling. To rationalize the results we propose a convenient decomposition of the delocalized lattice modes into molecular-based modes.

Crossover from Hopping to Band-Like Charge Transport in an Organic Semiconductor Model: Atomistic Nonadiabatic Molecular Dynamics Simulation.

The mechanism of charge transport (CT) in a 1D atomistic model of an organic semiconductor is investigated using surface hopping nonadiabatic molecular dynamics. The simulations benefit from a newly implemented state tracking algorithm that accounts for trivial surface crossings and from a projection algorithm that removes decoherence correction-induced artificial long-range charge transfer. The CT mechanism changes from slow hopping of a fully localized charge to fast diffusion of a polaron delocalized over several molecules as electronic coupling between the molecules exceeds the critical threshold V ≥ λ/2 (λ is the reorganization energy). With increasing temperature, the polaron becomes more localized and the mobility exhibits a “band-like” power law decay due to increased site energy and electronic coupling fluctuations (local and nonlocal electron–phonon coupling). Thus, reducing both types of electron–phonon coupling while retaining high mean electronic couplings should be part of the strategy toward discovery of new organics with high room-temperature mobilities.

Impact of Phonon Dispersion on Nonlocal Electron–Phonon Couplings in Organic Semiconductors: The Naphthalene Crystal as a Case Study

Recent studies point to the impact that the dispersion of both optical and acoustic phonons can have on the nonlocal electron–phonon couplings in organic molecular semiconductors. Here, in order to further elucidate the influence of phonon dispersion, we have calculated the phonon modes in the entire Brillouin zone of the naphthalene crystal. The results demonstrate that the overall nonlocal couplings are underestimated by calculations in which only the phonon modes derived at the Brillouin zone center are considered. Moreover, the contributions of acoustic phonons to the overall strength of nonlocal electron–phonon couplings are calculated to be quantitatively very significant for parallel-stacked dimers, as high as 40% for holes and 47% for electrons.

Ab initio study of electron-phonon coupling in rubrene

The use of ab initio methods for accurate simulations of electronic, phononic, and electron-phonon properties of molecular materials such as organic crystals is a challenge that is often tackled stepwise based on molecular properties calculated in gas phase and perturbatively treated parameters relevant for solid phases. In contrast, in this work we report a full first-principles description of such properties for the prototypical rubrene crystals. More specifically, we determine a Holstein-Peierls--type Hamiltonian for rubrene, including local and nonlocal electron-phonon couplings. Thereby, a recipe for circumventing the issue of numerical inaccuracies with low-frequency phonons is presented. In addition, we study the phenyl group motion with a molecular dynamics approach.

Charge transport in organic donor-acceptor mixed-stack crystals: the role of nonlocal electron-phonon couplings.

The charge-transport properties in C8BTBT-FnTCNQ and DMQtT-F4TCNQ mixed-stack crystals have been investigated by means of density functional theory, molecular dynamics and kinetic Monte Carlo simulations. The super-exchange nature of charge transport in these crystals is elucidated by the Larsson partition-based electronic coupling method that was developed recently by us. Compared with hole transport, in addition to the donor HOMO-acceptor LUMO interaction, the interaction between the donor HOMO-1 and the acceptor LUMO will also make an important contribution to electron transport. Moreover, this additional interaction plays an opposite role and results in electron-dominant and hole-dominant transport in the C8BTBT-FnTCNQ and DMQtT-F4TCNQ crystals, respectively. Most importantly, our calculations point out that the nonlocal electron-phonon couplings are very weak and much smaller than the electronic couplings in all the studied crystals. This implies that the nonlocal couplings have little influence on charge transport. In contrast to the experimental measurements, the external reorganization energies are thus expected to play an essential role in determining charge carrier mobilities. These findings pave the way for rational design of high performance organic donor-acceptor mixed-stack semiconductors.

Coherent dynamics of singlet fission controlled by nonlocal electron-phonon coupling

Based on the Frenkel-charge transfer (CT) mixing model of singlet fission (SF), we incorporate both the local and nonlocal phonon baths in the Hamiltonian and adopt the algorithm of time-dependent density matrix renormalization group to simulate the fission process in tetracene. The endergonic SF is found to be facilitated by the robust quantum coherence, which concurrently gives rise to a notable quantum beating effect. Controlled by the nonlocal electron-phonon coupling, the density of triplet yield manifests a nonlinear relationship with the singlet density. As a result, the fission rate in tetracene is explicitly obtained, which is in agreement with the experimental measurement.

Mixed quantum-classical dynamics for charge transport in organics.

Charge transport plays a crucial role in the working principle of most opto-electronic and energy devices. This is especially true for organic materials where the first theoretical models date back to the 1950s and have continuously evolved ever since. Most of these descriptions rely on perturbation theory to treat small interactions in the Hamiltonian. In particular, applying a perturbative treatment to the electron-phonon and electron-electron coupling results in the band and hopping models, respectively, the signature of which is conveyed by a characteristic temperature dependence of mobility. This perspective describes recent progress of studying charge transport in organics using mixed quantum-classical dynamics techniques, including mean field and surface hopping theories. The studies go beyond the perturbation treatments and represent the processes explicitly in the time-domain, as they occur in real life. The challenges, advantages, and disadvantages of both approaches are systematically discussed. Special focus is dedicated to the temperature dependence of mobility, the role of local and nonlocal electron-phonon couplings, as well as the interplay between electronic and electron-phonon interactions.

Effects of a metallic front gate on the temperature-dependent electronic property of pentacene films

The effect of a metallic front gate on the temperature-dependent electronic property of pentacene films was investigated in this study. The carrier mobility exhibits strong temperature dependence, implying the dominance of tunneling (hopping) at low (high) temperatures. The room-temperature mobility was drastically increased by capping an In (Au) layer on the pentacene front surface. However, the carrier concentration is not affected. An increase in the phonon energy occurs for In-capped or Au-capped pentacene samples, which corresponds to the abrupt transition to the nonlocal electron–phonon coupling. The enhanced mobility by capping a metal layer is attributed to a change in the electron–phonon coupling.

Transmon-based simulator of nonlocal electron-phonon coupling: A platform for observing sharp small-polaron transitions

We propose an analog superconducting quantum simulator for a one-dimensional model featuring momentum-dependent (nonlocal) electron-phonon couplings of Su-Schrieffer-Heeger and "breathing-mode" types. Because its corresponding vertex function depends on both the electron- and phonon quasimomenta, this model does not belong to the realm of validity of the Gerlach-L\"{o}wen theorem that rules out any nonanalyticities in single-particle properties. The superconducting circuit behind the proposed simulator entails an array of transmon qubits and microwave resonators. By applying microwave driving fields to the qubits, a small-polaron Bloch state with an arbitrary quasimomentum can be prepared in this system within times several orders of magnitude shorter than the typical qubit decoherence times. We demonstrate that in this system -- by varying the circuit parameters -- one can readily reach the critical coupling strength required for observing the sharp transition from a nondegenerate (single-particle) ground state corresponding to zero quasimomentum ($K_{\textrm{gs}}=0$) to a twofold-degenerate small-polaron ground state at nonzero quasimomenta $K_{\textrm{gs}}$ and $-K_{\textrm{gs}}$. Through exact numerical diagonalization of our effective Hamiltonian, we show how this nonanalyticity is reflected in the relevant single-particle properties (ground-state energy, quasiparticle residue, average number of phonons). The proposed setup provides an ideal testbed for studying quantum dynamics of polaron formation in systems with strongly momentum-dependent electron-phonon interactions.

Charge transport in organic semiconductors: Assessment of the mean field theory in the hopping regime

The performance of the mean field theory to account for charge transfer rate in molecular dimers and charge transport mobility in molecular stacks with small intermolecular electronic coupling and large local electron-phonon coupling (i.e., in the hopping regime) is carefully investigated against various other approaches. Using Marcus formula as a reference, it is found that mean field theory with system-bath interaction and surface hopping approaches yield fully consistent charge transfer rates in dimers. However, in contrast to the dimer case, incorporating system-bath interaction in the mean field approach results in a completely wrong temperature dependence of charge carrier mobility in larger aggregates. Although the mean field simulation starting from the relaxed geometry of a charged molecule and neglecting system-bath interaction can reproduce thermally activated transport, it is not able to characterize properly the role of additional nonlocal electron-phonon couplings. Our study reveals that the mean field theory must be used with caution when studying charge transport in the hopping regime of organic semiconductors, where the surface hopping approach is generally superior.