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.

Polaron Diffusion in Pentathienoacene Crystals

Molecular crystals have been used as prototypes for studying the energetic and dynamic properties of charge carriers in organic electronics. The growing interest in oligoacenes and fused-ring oligothiophenes in the last two decades is due, in particular, to the success achieved in conceiving pentacene-based organic photovoltaic devices. In the present work, a one-dimensional Holstein-Peierls model is designed to study the temperature-dependent polaron transport in pentathienoacene (PTA) lattices. The tight-binding Hamiltonian employed here takes into account intra and intermolecular electron-lattice interactions. Results reveal that polarons in PTAs can be stable structures even at high temperatures, about 400 K. During the dynamical process, these charge carriers present a typical 1D random walk diffusive motion with a low activation energy of 13 meV and a room temperature diffusivity constant of 1.07 × 10⁻³ cm² s⁻¹. Importantly, these critical values for the polaron diffusion and activation energy are related to the choice of model parameters, which are adopted to describe pristine lattices.

Translational-Invariant Bipolarons and Superconductivity

A translation-invariant (TI) bipolaron theory of superconductivity based, like Bardeen–Cooper–Schrieffer theory, on Fröhlich Hamiltonian is presented. Here the role of Cooper pairs belongs to TI bipolarons which are pairs of spatially delocalized electrons whose correlation length of a coupled state is small. The presence of Fermi surface leads to the stabilization of such states in its vicinity and a possibility of their Bose–Einstein condensation (BEC). The theory provides a natural explanation of the existence of a pseudogap phase preceding the superconductivity and enables one to estimate the temperature of a transition T * from a normal state to a pseudogap one. It is shown that the temperature of BEC of TI bipolarons determines the temperature of a superconducting transition T c which depends not on the bipolaron effective mass but on the ordinary mass of a band electron. This removes restrictions on the upper limit of T c for a strong electron-phonon interaction. A natural explanation is provided for the angular dependence of the superconducting gap which is determined by the angular dependence of the phonon spectrum. It is demonstrated that a lot of experiments on thermodynamic and transport characteristics, Josephson tunneling and angle-resolved photoemission spectroscopy (ARPES) of high-temperature superconductors does not contradict the concept of a TI bipolaron mechanism of superconductivity in these materials. Possible ways of enhancing T c and producing new room-temperature superconductors are discussed on the basis of the theory suggested.

Dynamical Mechanism of Polarons and Bipolarons in Poly(p-Phenylene Vinylene)

Studies on Poly(p-Phenylene Vinylene) (PPV) and derivatives have experienced enormous growth since they were successfully used to fabricate the first efficient prototypes of Polymer Light-Emitting Diodes in the 90s. Despite this rapid progress, understanding the relationship between charge transport and the morphology in these materials remains a challenge. Here, we shed light on the understanding of the transport mechanism of polarons and bipolarons in PPVs by developing a two-dimensional tight-binding approach that includes lattice relaxation effects. Remarkably, the results show that the PPV lattice loses the energy related to its conjugation during time by transferring this amount of energy to electrons. Such a process for energy transfer permits the quasiparticles to overcome the potential barrier imposed by the local lattice deformations, that are formed in the presence of an additional charge and, consequently, their electric field assisted transport takes place. Within the framework of this transport mechanism, a better insight into the origin of the carrier mobility in PPV and derivatives can be achieved and would be a useful guide for improving their chemical structures and morphologies.

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.

Stationary polaron properties in organic crystalline semiconductors

Polarons play a crucial role in the charge transport mechanism when it comes to organic molecular crystals. The features of their underlying properties - mostly the ones that directly impact the yield of the net charge mobility - are still not completely understood. Here, a two-dimensional Holstein-Peierls model is employed to numerically describe the stationary polaron properties in organic semiconductors at a molecular scale. Our computational protocol yields model parameters that accurately characterize the formation and stability of polarons in ordered and disordered oligoacene-like crystals. The results show that the interplay between the intramolecular (Holstein) and intermolecular (Peierls) electron-lattice interactions critically impacts the polaron stability. Such an interplay can produce four distinct quasi-particle solutions: free-like electrons, metastable polarons, and small and large polarons. The latter governs the charge transport in organic crystalline semiconductors. Regarding disordered lattices, the model takes into account two modes of static disorder. Interestingly, the results show that intramolecular disorder is always unfavorable to the formation of polarons whereas intermolecular disorder may favor the polaron generation in regimes below a threshold for the electronic transfer integral strength.

Polaron formation mechanisms in conjugated polymers

In semiconducting polymers, interactions with conformational degrees of freedom can localize charge carriers, and strongly affect charge transport. Polarons can form when charges induce deformations of the surrounding medium, including local vibrational modes or dielectric polarization. These deformations then interact attractively with the charge, tending to localize it. First we investigate vibrational polaron formation in poly(3-hexylthiophene) [P3HT], with a tight-binding model for charges hopping between adjacent rings, coupled to ring distortions. We use density functional theory (DFT) calculations to determine coupling constants, including the "spring constant" for ring distortions and the coupling to the charge carrier. On single chains, we find only broad, weakly bound polarons by this mechanism. In 2d crystalline layers of P3HT, even weak transverse hopping between chains destabilizes this polaron. Then, we consider polarons stabilized by dielectric polarization, described semiclassically with a polarizable continuum interacting with the carrier wavefunction. In contrast to vibrational polarons, we find dielectrically stabilized polarons in P3HT are narrower, more strongly bound, and stable in 2d crystalline layers.

Spin-Orbit Effects on the Dynamical Properties of Polarons in Graphene Nanoribbons

The dynamical properties of polarons in armchair graphene nanoribbons (GNR) is numerically investigated in the framework of a two-dimensional tight-binding model that considers spin-orbit (SO) coupling and electron-lattice (e-l) interactions. Within this physical picture, novel polaron properties with no counterparts to results obtained from conventional tight-binding models are obtained. Our findings show that, depending on the system’s width, the presence of SO coupling changes the polaron’s charge localization giving rise to different degrees of stability for the charge carrier. For instance, the joint action of SO coupling and e-l interactions could promote a slight increase on the charge concentration in the center of the lattice deformation associated to the polaron. As a straightforward consequence, this process of increasing stability would lead to a depreciation in the polaron’s motion by decreasing its saturation velocity. Our finds are in good agreement with recent experimental investigations for the charge localization in GNR, mostly when it comes to the influence of SO coupling. Moreover, the contributions reported here provide a reliable method for future works to evaluate spin-orbit influence on the performance of graphene nanoribbons.

Polaron dynamics in oligoacene stacks

The dynamical properties of polarons in organic molecular crystals are numerically studied in the framework of an one-dimensional Holstein-Peierls approach that includes lattice relaxation. Particularly, the present study is aimed at designing a tight-binding Hamiltonian that can address the charge transport mechanism in model oligoacene stacks. Our findings show that the definition of a particular oligoacene system depends strictly on the employed set of parameters. The usefulness of this methodology is highlighted by analyzing the polaron's saturation velocity and, consequently, its stability in the presence of a damping term and substantially high electric field strengths. Importantly, these results may be useful for the designing of novel materials to be employed in the field of molecular electronics.

Nonadiabatic dynamics of injected holes in conjugated polymers

The dynamics of injected holes in short transient times that precede polaron formation is numerically studied in the framework of a tight-binding electron-phonon interacting approach aimed at describing organic one-dimensional lattices. In particular, the direct impact of internal and external factors on the conversion of injected holes into polarons is carefully investigated. The results show that a hole injected at levels lower than the highest occupied molecular orbital forms self-trapped bound structures that can merge spontaneously to form a polaron after, at least, one picosecond. On the other hand, the life-time of such structures substantially decreases (up to a few hundreds of femtoseconds) when the influence of external electric fields, temperature effects and impurities is considered. Importantly, the critical values of the aforementioned factors in promoting the quenching of the self-trapped structures are obtained. These findings may enlighten the understanding of the mechanism of charge carrier generation in Polymer Light Emitting Diodes when several kinds of excitations are present.

Polaron dynamics in anisotropic Holstein-Peierls systems

Polaron dynamics in anisotropic organic molecular semiconductors is theoretically investigated and simulated in the framework of a semi-classical Holstein-Peierls model. Our computational protocol is presented and applied to studies of a two-dimensional molecular crystal. The intermolecular (Peierls) parameters for a particular crystal direction are systematically changed in order to study the effect of anisotropy in the system. The usefulness of this methodology is highlighted by studying the polaron dynamics on a picosecond timescale, which provides a microscopic insight into the influence of the interplay between different intramolecular parameters on the charge transport mechanism. Our results show that the polaron mobility is substantially reduced in going from an anisotropic to an isotropic relationship between the Peierls parameters for different directions in the crystal. Interestingly, the molecular charge distribution presents three different signatures corresponding to a one-dimensional polaron, a two-dimensional polaron, and an intermediate state for which the polaron localization depends on the degree of anisotropy. Importantly, the two-dimensional polaron, which is present in the essentially isotropic system, is immobile whereas the other two types of polarons are mobile. This, in order for polaron transport to occur in a two-dimensional molecular based system, this system has to be anisotropic.

Organic Optoelectronic Materials: Mechanisms and Applications

Organic (opto)electronic materials have received considerable attention due to their applications in thin-film-transistors, light-emitting diodes, solar cells, sensors, photorefractive devices, and many others. The technological promises include low cost of these materials and the possibility of their room-temperature deposition from solution on large-area and/or flexible substrates. The article reviews the current understanding of the physical mechanisms that determine the (opto)electronic properties of high-performance organic materials. The focus of the review is on photoinduced processes and on electronic properties important for optoelectronic applications relying on charge carrier photogeneration. Additionally, it highlights the capabilities of various experimental techniques for characterization of these materials, summarizes top-of-the-line device performance, and outlines recent trends in the further development of the field. The properties of materials based both on small molecules and on conjugated polymers are considered, and their applications in organic solar cells, photodetectors, and photorefractive devices are discussed.

Impact of the electron–phonon coupling symmetry on the polaron stability and mobility in organic molecular semiconductors

Schematic representation of a pentacene stack with two inter-molecular degrees of freedom.