Self-trapped Electron States Research Articles

Two Types of Oscillations of the Holstein Polaron Uniformly Moving Along a Polynucleotide Chain in a Constant Electric Field

In connection with the development of molecular nanobioelectronics, the main task of which is the construction of electronic devices based on biological molecules, the problems of charge transfer in such extended molecules as DNA are of increasing interest. The relevance of studying the charges motion in one-dimensional molecular chains is primarily associated with the possibility of using these chains as wires in nanoelectronic devices. Current carriers in one-dimensional chains are self-trapped electronic states, which have the form of polaron formations. In this paper we investigate the motion of the Holstein polaron in the process of its uniform motion along the chain in a constant electric field. It is known that during uniform motion along the chain in a weak electric field, the polaron experiences small oscillations of its shape. These oscillations are associated with the discreteness of the chain and are due to the presence of the Peierls-Nabarro potential in the discrete chain. Previous investigations have shown that for certain parameters of the chain, there is the possibility of uniform charge motion in a constant electric field over very large distances. The charge motion with a constant velocity is possible for small values of the electric field intensity. With an increase in the electric field intensity, the charge goes into an oscillatory regime of motion with Bloch oscillations. The calculations performed in this work showed that the elements of Bloch oscillations also appear during stationary motion of the polaron along the chain. Thus, it is shown that the Holstein polaron, uniformly moving along the chain in a constant electric field, experiences not only Peierls-Nabarro oscillations, but also low-amplitude oscillations with a Bloch period.

Два типа осцилляций холстейновского полярона, равномерно движущегося в полинуклеотидной цепочке в постоянном электрическом поле

In connection with the development of molecular nanobioelectronics, the main task of which is the construction of electronic devices based on biological molecules, the problems of charge transfer in such extended molecules as DNA are of increasing interest. The relevance of studying the charges motion in one-dimensional molecular chains is primarily associated with the possibility of using these chains as wires in nanoelectronic devices. Current carriers in one-dimensional chains are self-trapped electronic states, which have the form of polaron formations. In this paper we investigate the motion of the Holstein polaron in the process of its uniform motion along the chain in a constant electric field. It is known that during uniform motion along the chain in a weak electric field, the polaron experiences small oscillations of its shape. These oscillations are associated with the discreteness of the chain and are due to the presence of the Peierls-Nabarro potential in the discrete chain. Previous investigations have shown that for certain parameters of the chain, there is the possibility of uniform charge motion in a constant electric field over very large distances. The charge motion with a constant velocity is possible for small values of the electric field intensity. With an increase in the electric field intensity, the charge goes into an oscillatory regime of motion with Bloch oscillations. The calculations performed in this work showed that the elements of Bloch oscillations also appear during stationary motion of the polaron along the chain. Thus, it is shown that the Holstein polaron, uniformly moving along the chain in a constant electric field, experiences not only Peierls-Nabarro oscillations, but also low-amplitude oscillations with a Bloch period.

Creation and mobility of self-trapped electronic states in nonlinear chains

We study the formation and mobility of self-trapped electronic states in a nonlinear one-dimensional lattice subjected to an electric-field. The nonlinearity arises from the electron-lattice coupling and the electric field is time-dependent. We show that the nonlinearity is a mechanism able to provide motion to the centroid of a delta-like wave-packet when subjected to an electric field, in contrast with the behavior of linear systems. With the co-existence of the electric field and electron-lattice interaction, the constitution of mobile self-trapped states is possible. The phase diagram reveals a rich phenomenology in which the mobility of self-trapped electronic states can exhibit an unidirectional branch migrating to the left or the right side of the chain. For weak nonlinearities, an analytical expression obtained from a semi-classical approach describes the dynamics of self-trapping states. In a strong electron-lattice regime, the wave-packet develops a self-trapped regime in which it remains fully localized at the initial site. Thus, we offer the proper tunning of electric field for the management of the creation and mobility of self-trapped electronic states through the lattice.

Femtosecond dynamics of exciton localization: self-trapping from the small to the large polaron limit

We use femtosecond vibrational wavepacket techniques to time-resolve the coupled electronic and vibrational dynamics of exciton self-trapping in a series of materials in which the relative strength of the electron–phonon coupling can be compositionally tuned from the small to the large polaron limit. Transient absorption experiments are carried out in the quasi-one-dimensional halide-bridged mixed-valence transition metal linear chain complexes [Pt(en)2][Pt(en)2X2]⋅(ClO4)4 (en=ethylenediamine, C2H8N2) with X=Cl, Br and I. In each complex, we detect the formation of the self-trapped exciton through the appearance of its characteristic red-shifted optical absorption, and find that self-trapping occurs on a time scale of the order of a single vibrational period of the optical phonon mode that dominates the self-trapping dynamics. The associated optical phonon response, detected as wavepacket oscillations that modulate the exciton absorption, shows a significant softening of the optical phonon frequency compared to that of the unexcited system. The degree of softening is found to vary significantly with coupling strength, ranging from more than 40% in the strongly coupled chloride-bridged complex to less than 20% in the weakly coupled iodide-bridged complex. We relate these results to the extent of electronic delocalization by comparison with the electronic properties of the ground states of the materials and with the properties of their equilibrated self-trapped electronic states predicted by theoretical modeling.

Role of Geometric Distortion and Polarization in Localizing Electronic Excitations in Conjugated Polymers

Five different Density Functional Theory (DFT) models (ranging from pure GGA to long-range-corrected hybrid functionals) were used to study computationally the nature of the self-trapped electronic states in oligophenylene vinylenes. The electronic excitations in question include the lowest singlet (S1) and triplet (T1(†)) excitons (calculated using Time Dependent DFT (TD-DFT) method), positive (P(+)) and negative (P(-)) polarons, and the lowest triplet (T1) states (computed with the Self-Consistent Field (SCF) scheme). The polaron formation (spatial localization of excitations) is observed only with the use of range-corrected hybrid DFT models including long-range electronic exchange interactions. The extent of localization for all studied excitations is found to be invariant with respect to the size of the oligomer chain in their corresponding optimal geometries. We have analyzed the interdependence between the extent of the geometrical distortion and the localization of the orbital and spin density, and have observed that the localization of the P(+) and P(-) charged species is quite sensitive to solvent polarization effects and the character of the DFT functional used, rather than the structural deformations. In contrast, the localization of neutral states, S1 and T1(†), is found to follow the structural distortions. Notably, T1 excitation obtained with the mean field SCF approach is always strongly localized in range-corrected hybrid DFT models. The molecular orbital energetics of these excitations was further investigated to identify the relationship between state localization and the corresponding orbital structure. A characteristic stabilization (destabilization) of occupied (virtual) orbitals is observed in hybrid DFT models, compared to tight-binding model-like orbital filling in semilocal GGA functionals. The molecular and natural orbital representation allows visualization of the spatial extent of the underlying electronic states. In terms of stabilization energies, neutral excitons have higher binding energies compared to charged excitations. In contrast, the polaronic species exhibit the highest solvation energies among all electronic states studied.

Polaron-induced deformations in carbon nanotubes studied using the bicontinuum model

We compute for the first time full elastic deformations, as well as length, of self-trapped electronic states in carbon nanotubes of general radius and chirality, within the unifying framework of a recently introduced two field model for electromechanics of carbon nano-structures. We find that deformations are highly non monotonic in the chiral angle, whereas the length of the polaron is not. Applications include nano-mechanical devices as electrically or optically driven nano-actuators.

Self-trapped electron states in nanotubes

We study numerically self-trapped (polaron) states of quasiparticles (electrons or holes) in a deformable nanotube formed by a hexagonal lattice, wrapped into a cylinder (carbon- and boron nitride-type nanotube structures). We present a Hamiltonian for such a system taking into account an electron–phonon interaction, and determine conditions under which the lowest energy states are polarons. We compute a large class of numerical solutions of this model for a wide range of the parameters. We show that at not-too-strong electron–phonon coupling, the system admits ring-like localized solutions wrapped around the nanotube (the charge carrier is localized along the nanotube axis and is uniformly distributed with respect to the azimuthal coordinate). At stronger coupling, solutions are localized on very few lattice sites in both directions of the nanotube. The transition from one type of solution to the other one depends on the diameter of the nanotube. We show that for the values of the carbon nanotube parameters, the polarons have a ring-like structure wrapped around the nanotube, with a profile resembling that of the nonlinear Schrödinger soliton.

Charge and energy transfer by solitons in low-dimensional nanosystems with helical structure

We study the nonlinear mechanism of the energy and charge transfer in low-dimensional nanosystems with helical structure. We show that the helical symmetry is important for the formation, stability and dynamical properties of the soliton-like self-trapped electron states. We obtain several types of stationary soliton solutions, namely single-band and hybrid two-band solitons which possess different energies. The two-band hybrid soliton spontaneously breaks the local translational and helical symmetries. For the values of the parameters of α-helical proteins this soliton possesses the lowest energy as compared with other types of solitons. This soliton has an inner structure which is manifested by a modulated multi-hump amplitude distribution of excitations on the individual strands of hydrogen bonds, identified in the helix. The displacement of such a soliton along the helix reveals distinctly the complex and composite structure of the soliton and causes oscillations of the energy distributions between the strands of hydrogen bonds. We show that the frequency of these oscillations is proportional to the soliton velocity. The radiative life-time of this hybrid soliton is calculated and shown to exceed by several orders of magnitude the life-time of a soliton excitation in a three-strand macromolecule without helical structure. The other two soliton solutions are formed by single-band states. These solitons preserve the helical symmetry, but in the α-helix they are dynamically unstable: once initially formed, they transform into the ground hybrid soliton state when propagating along the chain.

Static solutions of a D-dimensional modified nonlinear Schrödinger equation

We study static solutions of a D-dimensional modified nonlinear Schrödinger equation (MNLSE) which was shown to describe, in two dimensions, the self-trapped (spontaneously localized) electron states in a discrete isotropic electron–phonon lattice [1, 2]. We show that this MNLSE, unlike the conventional nonlinear Schrödinger equation, possesses static localized solutions at any dimensionality when the effective nonlinearity parameter is larger than a certain critical value which depends on the dimensionality of the system under study. We investigate various properties of the equation analytically, using scaling transformations, within the variational scheme and numerically, and show that the results of these studies agree qualitatively and quantitatively. In particular, we prove that, for various values of D, when the coupling constant is larger than a certain critical value (which depends on D), this equation has two solutions, a stable (metastable) and an unstable one. We show that the solutions can be well approximated by a Gaussian ansatz and we also show that, in two dimensions, the equation possesses solutions with a nonzero angular momentum.

Polaronic signatures in mid-infrared spectra: Prediction forLaMnO3andCaMnO3

Hole-doped ${\mathrm{LaMnO}}_{3}$ and electron-doped ${\mathrm{CaMnO}}_{3}$ form self-trapped electronic states. The spectra of these states have been calculated using a two orbital (Mn ${e}_{\mathrm{g}}$ Jahn-Teller) model, from which the nonadiabatic optical conductivity spectra are obtained. In both cases the optical spectrum contains weight in the gap region, whose observation will indicate the self-trapped nature of the carrier states. The predicted spectra are proportional to the concentration of the doped carriers in the dilute regime, with coefficients calculated with no further model parameters.

Electron-phonon coupling on the ionic 60-atom carbon cluster buckminsterfullerene

Using a tight-binding model with electron-phonon coupling based on the modified SSH model Hamiltonian, we studied several ground states of the neutral and ionic 60-atom carbon cluster, buckminsterfullerene. The ground states of ionic structures are shown to consist of Jahn-Teller distortion and localized self-trapped electron states dependent upon the ratio of the electron-phonon coupling constant to the electron hopping constant.

Pi bonding in the icosahedral C60 cluster.

Using a tight-binding model with electron-phonon coupling, we have studied several ground and excited states of the neutral and ionic ${\mathrm{C}}_{60}$ cluster, hypothesized to have the structure of a soccer ball. We find that the presence of pentagons weakens the resonant \ensuremath{\pi}-bonding structure compared to graphite, and we present an analysis of this effect. The ionic ground state and low-lying neutral excited electronic states undergo Jahn-Teller instabilities which we classify. No localized self-trapped electronic states occur as excited states of the neutral structure or as ground states of singly ionic structures.

Self-trapped electron and hole states

The basic ideas and results of the theory of self-trapped electron and hole states are reviewed. The basic features of self-trapping as an important and quite general phenomenon as well as the basic types of self-trapped states (polarons, fluctuons, and electron pairs with a negative correlation energy) are studied. The characteristic features of self-trapping on defects in a crystal lattice, in disordered systems, and in amorphous structures are compared with self-trapping in regular crystals. Some pressing problems in the modern theory of self-trapped electron and hole states in solids are noted or briefly discussed.

Avtolokalizovannye sostoyaniya elektronov i dyrok

Avtolokalizovannye sostoyaniya elektronov i dyrok

Delocalized and self-trapped electron states in anisotropic continua

The localization behaviour of electron states due to interaction with acoustic and optical vibrations is studied for anisotropic continua. For extreme anisotropy our theory describes so-called one- or two-dimensional systems and yields results which differ from those of low-dimensional models.