Width effects on bilayer graphene nanoribbon polarons.

Recent progress in nanoelectronics suggests that stacking armchair graphene nanoribbons (AGNRs) into bilayer systems can generate materials with emergent quasiparticle properties. In this context, the impact of width changes is especially relevant. However, its effect on charged carriers remains elusive. In this work, we investigate the effect of width and interlayer interaction changes on polaron states via a hybrid Hamiltonian that couples the electronic and lattice interactions. Results show the rising of two interlayer polarons: the non-symmetric and the symmetric. The coupling strength needed to induce the transition between states depends on the nanoribbon width, being at the most extreme case of ≈174 meV. Electronic properties such as the coupling strength threshold, carrier size, and gap are shown to respect the AGNR width family 3p, 3p + 1, and 3p + 2 rule. The findings demonstrate that strong interlayer interaction simultaneously delocalizes the carriers and reduces the gap up to 0.6 eV. Additionally, it is found that some layers are more prone to share charge, indicating a potential heterogeneous stacking where a particular electronic pathway is favored. The results present an encouraging prospect for integrating AGNR bilayers in future flexible electronics.

Quasiparticle dynamics by effective [Formula: see text]-field distortion.

Modeling dynamical processes of quasiparticles in low dimensional [Formula: see text]-conjugated systems is challenging due to electron-phonon coupling. We show that this interaction leads to linear potential energy terms in the lattice Lagrangian similar to a local "gravitational" field. The presence of quasiparticles deforms this field in a way analogous to a low-dimension solution of general relativity. Our calculations with analytical expressions for effective [Formula: see text]-fields yield the correct band structure and deliver proper time evolution of the quasiparticle's properties. Furthermore, we report a sharp reduction in the dynamics computational time up to two orders of magnitude, a result that has major simulation implications.

Charge localization and hopping in a topologically engineered graphene nanoribbon.

Graphene nanoribbons (GNRs) are promising quasi-one-dimensional materials with various technological applications. Recently, methods that allowed for the control of GNR's topology have been developed, resulting in connected nanoribbons composed of two distinct armchair GNR families. Here, we employed an extended version of the Su-Schrieffer-Heeger model to study the morphological and electronic properties of these novel GNRs. Results demonstrated that charge injection leads to the formation of polarons that localize strictly in the 9-AGNRs segments of the system. Its mobility is highly impaired by the system's topology. The polaron displaces through hopping between 9-AGNR portions of the system, suggesting this mechanism for charge transport in this material.

Stability conditions of armchair graphene nanoribbon bipolarons.

Graphene nanoribbons are 2D hexagonal lattices with semiconducting band gaps. Below a critical electric field strength, the charge transport in these materials is governed by the quasiparticle mechanism. The quasiparticles involved in the process, known as polarons and bipolarons, are self-interacting states between the system charges and local lattice distortions. To deeply understand the charge transport mechanism in graphene nanoribbons, the study of the stability conditions for quasiparticles in these materials is crucial and may guide new investigations to improve the efficiency for a next generation of graphene-based optoelectronic devices. Here, we use a two-dimensional version of the Su-Schrieffer-Heeger model to investigate the stability of bipolarons in armchair graphene nanoribbons (AGNRs). Our findings show how bipolaron stability is dependent on the strength of the electron-phonon interactions. Moreover, the results show that bipolarons are dynamically stable in AGNRs for electric field strengths lower than 3.0 mV/Å. Remarkably, the system's binding energy for a lattice containing a bipolaron is smaller than the formation energy of two isolated polarons, which suggests that bipolarons can be natural quasiparticle solutions in AGNRs. Graphical Abstract Charge localization of bipolarons in armchair garphene nanoribbons.

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.

Tuning the electronic structure properties of MoS2 monolayers with carbon doping.

The structural and electronic properties of MoS2 sheets doped with carbon line domains are theoretically investigated through density functional theory calculations. It is primarily studied how the system's electronic properties change when different domain levels are considered. These changes are also reflected in the geometry of the system, which acquires new properties when compared to the pristine structure. We predict, both qualitative and quantitatively, how the energy gap changes as a function of domain types. Strikingly, the band structure for the doped system shows semiconducting behavior with an indirect-bandgap, which is narrower than the one for bulk MoS2. This is an important feature as far as gap tuning engineering is concerned. It has a profound impact on the applicability of these systems in electronic devices, where an indirect bandgap favors the quantum yield efficiency.

Same Charge Polaron and Bipolaron Scattering on Conducting Polymers.

We study the dynamics of scattering of two positive polarons moving toward each other with parallel spins and of a polaron and a bipolaron both with positive charges and different velocities, in single chains of cis-polyacetylene and polyparaphenylene. We use the Su-Schrieffer-Heeger model with Hubbard extensions solved within of the time-dependent Hartree-Fock approximation to account for electron-electron interactions, developed over a hexagonal lattice. The main results are elastic scattering in most cases. This behavior changes to transmission of the polaron through the bipolaron when the ratio of their velocities in the same direction is in the range of 3:1 to 5:1 when no external electric field is present. The velocities ratio changes to of 6:1 to 8:1 under external electric field. This suggests that these systems may present an abrupt increase in the charge transport, under specific conditions, in an otherwise smoothly and monotonically increasing relation to the applied field. Their effective masses in these systems are also determined: the polaron effective mass is 4-8 times the rest mass of a free electron, and that of the bipolaron is 15-30 times the electron mass.

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.

Influence of quasi-particle density over polaron mobility in armchair graphene nanoribbons.

An important aspect concerning the performance of armchair graphene nanoribbons (AGNRs) as materials for conceiving electronic devices is related to the mobility of charge carriers in these systems. When several polarons are considered in the system, a quasi-particle wave function can be affected by that of its neighbor provided the two are close enough. As the overlap may affect the transport of the carrier, the question concerning how the density of polarons affect its mobility arises. In this work, we investigate such dependence for semiconducting AGNRs in the scope of nonadiabatic molecular dynamics. Our results unambiguously show an impact of the density on both the stability and average velocity of the quasi-particles. We have found a phase transition between regimes where increasing density stops inhibiting and starts promoting mobility; densities higher than 7 polarons per 45 Å present increasing mean velocity with increasing density. We have also established three different regions relating electric field and average velocity. For the lowest electric field regime, surpassing the aforementioned threshold results in overcoming the 0.3 Å fs-1 limit, thus representing a transition between subsonic and supersonic regimes. For the highest of the electric fields, density effects alone are responsible for a stunning difference of 1.5 Å fs-1 in the mean carrier velocity.

Dynamic Formation of Bipolaron-Exciton Complexes in Conducting Polymers.

The recombination dynamics of two oppositely charged bipolarons within a single polymer chain is numerically studied in the scope of a one-dimensional tight-binding model that considers electron-electron and electron-phonon (e-ph) interactions. By scanning among values of e-ph coupling and electric field, novel channels for the bipolaron recombination were yielded based on the interplay between these two parameters. The findings point to the formation of a compound species formed from the coupling between a bipolaron and an exciton. Depending on the electric field and e-ph coupling strengths, the recombination mechanism may yield two distinct products: a trapped (and almost neutral) or a moving (and partially charged) bipolaron-exciton. These results might enlighten the understanding of the electroluminescence processes in organic light-emitting devices.

Charge Carrier Scattering in Polymers: A New Neutral Coupled Soliton Channel.

The dynamical scattering of two oppositely charged bipolarons in non-degenerate organic semiconducting lattices is numerically investigated in the framework of a one-dimensional tight-biding-Hubbard model that includes lattice relaxation. Our findings show that it is possible for the bipolaron pair to merge into a state composed of a confined soliton-antisoliton pair, which is characterized by the appearance of states within less than 0.1 eV from the Fermi level. This compound is in a narrow analogy to a meson confining a quark-antiquark pair. Interestingly, solitons are quasi-particles theoretically predicted to arise only in polymer lattices with degenerate ground state: in the general case of non-degenerate ground state polymers, isolated solitons are not allowed.

Bond length pattern associated with charge carriers in armchair graphene nanoribbons.

The geometry configuration of charged armchair graphene nanoribbons (AGNRs) is theoretically investigated in the framework of a two-dimensional tight-binding model that includes lattice relaxation. Our findings show that the charge distribution and, consequently, the bond length pattern is dependent on the parity of the nanoribbon width. In this sense, the lattice distortions decrease smoothly for increasingly wider GNRs. As should be expected, AGNRs belonging to a particular family present similar patterns for the bond lengths. The interplay between the electron-phonon coupling and band gap is also investigated. The results show that the electron-phonon coupling strength is fundamental to promote the transition from metallic towards semiconducting-like behavior for the band gap. Most important, such strength is crucial on defining the degree of lattice distortions in AGNRs.

Bloch oscillations in organic and inorganic polymers.

The transport of polarons above the mobility threshold in organic and inorganic polymers is theoretically investigated in the framework of a one-dimensional tight-binding model that includes lattice relaxation. The computational approach is based on parameters for which the model Hamiltonian suitably describes different polymer lattices in the presence of external electric fields. Our findings show that, above critical field strengths, a dissociated polaron moves through the polymer lattice as a free electron performing Bloch oscillations. These critical electric fields are considerably smaller for inorganic lattices in comparison to organic polymers. Interestingly, for inorganic lattices, the free electron propagates preserving charge and spin densities' localization which is a characteristic of a static polaron. Moreover, in the turning points of the spatial Bloch oscillations, transient polaron levels are formed inside the band gap, thus generating a fully characterized polaron structure. For the organic case, on the other hand, no polaron signature is observed: neither in the shape of the distortion-those polaron profile signatures are absent-nor in the energy levels-as no such polaron levels are formed during the simulation. These results solve controversial aspects concerning Bloch oscillations recently reported in the literature and may enlighten the understanding about the charge transport mechanism in polymers above their mobility edge.

Electron-phonon coupling effects on intrachain polaron recombination in conjugated polymers.

Based on a one-dimensional Su-Schrieffer-Heeger (SSH) model with electron correlation considered within the extended Hubbard model (EHM), we investigate the role played by electron-phonon coupling constant on intrachain polaron recombination in conjugated polymers. Our results suggest that a competition between external electric field and electron-phonon coupling on defining the behavior of the charge distribution of the system takes place. Whereas increasing electric field plays the role of destabilizing the charge carriers, an increase of the electron-phonon coupling has the opposite effect. Therefore, a suitable balance of these properties can give rise to the correct description of charge carrier dynamics in conducting polymers.

Polaron and bipolaron stability on paraphenylene polymers.

Polyparaphenylene is the prototypical conjugated polymer containing phenyl rings and its properties are good references for a family of derived polymers. We investigate the structure, stability, and dynamics of polarons and bipolarons in polyparaphenylene chains under an applied electric field. To do this, we use a bidimensional SSH Hamiltonian model with the Hubbard extension, i.e., with local and nearest-neighbor Coulomb interaction, which has been designed to work with general hexagonal lattices, from which polyparaphenylene can be seen as a prominent case. Using the time-dependent Hartree-Fock approximation, we calculate the structural characteristics, the maximum field strength, supported before polarons and bipolarons gets unstable, and the maximum velocity achieved by these charge carriers. We obtained the polaron and bipolaron terminal velocity to be 0.51 Å/fs and 1.15 Å/fs, respectively. The maximum field strength determined by our calculations is 0.54 mV/Å and 0.80 mV/Å, respectively. Our results are in good agreement with other theoretical methods and experiments.

Impact of the Electron-Phonon Interactions on the Polaron Dynamics in Graphene Nanoribbons.

The influence of the electron-phonon (e-ph) interactions on the filed-included polaron dynamics in armchair graphene nanoribbons (GNRs) is theoretically investigated in the scope of a two-dimensional tight-binding model. The results show that the localization of the polaronic charge increases when the strength of e-ph coupling also increases. Consequently, the polaron saturation velocity decreases for higher e-ph coupling strengths. Interestingly, the interplay between the e-ph coupling strength and the GNR width changes substantially the polaron dynamics properties.

Low-Temperature Seebeck Coefficients for Polaron-Driven Thermoelectric Effect in Organic Polymers.

We report the results of electronic structure coupled to molecular dynamics simulations on organic polymers subject to a temperature gradient at low-temperature regimes. The temperature gradient is introduced using a Langevin-type dynamics corrected for quantum effects, which are very important in these systems. Under this condition we were able to determine that in these no-impurity systems the Seebeck coefficient is in the range of 1-3 µV/K. These results are in good agreement with reported experimental results under the same low-temperature conditions.

Transport of Polarons in Graphene Nanoribbons.

The field-induced dynamics of polarons in armchair graphene nanoribbons (GNRs) is theoretically investigated in the framework of a two-dimensional tight-binding model with lattice relaxation. Our findings show that the semiconductor behavior, fundamental to polaron transport to take place, depends upon of a suitable balance between the GNR width and the electron-phonon (e-ph) coupling strength. In a similar way, we found that the parameter space for which the polaron is dynamically stable is limited to an even narrower region of the GNR width and the e-ph coupling strength. Interestingly, the interplay between the external electric field and the e-ph coupling plays the role to define a phase transition from subsonic to supersonic velocities for polarons in GNRs.

Concentration effects on intrachain polaron recombination in conjugated polymers.

The influence of different charge carrier concentrations on the recombination dynamics between oppositely charged polarons is numerically investigated using a modified version of the Su-Schrieffer-Heeger (SSH) model that includes an external electric field and electron-electron interactions. Our findings show that the external electric field can play the role of avoiding the formation of excited states (polaron-exciton and neutral excitation) leading the system to a dimerized lattice. Interestingly, depending on a suitable balance between the polaron concentration and the electric field strength, the recombination mechanism can form stable polaron-excitons or neutral excitations. These results may provide guidance to improve the electroluminescence efficiency in Polymer Light Emitting Diodes.

Critical temperature and products of intrachain polaron recombination in conjugated polymers.

The intrachain recombination dynamics between oppositely charged polarons is theoretically investigated through the use of a version of the Su-Schrieffer-Heeger (SSH) model modified to include an external electric field, an extended Hubbard model, Coulomb interactions, and temperature effects in the framework of a nonadiabatic evolution method. Our results indicate notable characteristics concerning the polaron recombination: (1) it is found that there exists a critical temperature regime, below which an exciton is formed directly and (2) a pristine lattice is the resulting product of the recombination process, if the temperature is higher than the critical value. Additionally, it is found that the critical electric field regime plays the role of drastically modifying the system dynamics. These facts suggest that thermal effects in the intrachain recombination of polarons are crucial for the understanding of electroluminescence in optoelectronic devices, such as Polymer Light Emitting Diodes.