A density functional theory study of polarons on different TiO_(2) surfaces

Polarons are widely considered to play a crucial role in the charge transport and photocatalytic performance of materials,but the mechanisms of their formation and the underlying driving factors remain a matter of controversy.This study delves into the formation of polarons in different crystalline forms of TiO_(2) and their connection with the materials'structure.By employing density functional theory calculations with on-site Coulomb interaction correction(DFT+U),we provide a detailed analysis of the electronic polarization behavior in the anatase and rutile forms of TiO_(2).We focus on the polarization properties of defect-induced and photoexcited excess electrons on various TiO_(2) surfaces.The results reveal that the defect electrons can form small polarons on the anatase TiO_(2)(101)surface,while on the rutile TiO_(2)(110)surface,both small and large polarons(hybrid-state polarons)are formed.Photoexcited electrons are capable of forming both small and large polarons on the surfaces of both crystal types.The analysis indicates that the differences in polaron distribution are primarily determined by the intrinsic properties of the crystals;the structural and symmetry differences between anatase and rutile TiO_(2) lead to the distinct polaron behaviors.Further investigation suggests that the polarization behavior of defect electrons is also related to the arrangement of electron orbitals around the Ti atoms,while the polarization of photoexcited electrons is mainly facilitated by the lattice distortions.These findings elucidate the formation mechanisms of different types of polarons and may contribute to understanding the performance of TiO_(2)in different fields.

Bound Polaron in a Quantum Well Under an Electric Field

We conduct a theoretical study on the properties of a bound polaron in a quantum well under an electric field using linear combination operator and unitary transformation methods, which are valid in the whole range of electron-LO phonon coupling. The changing relations between the ground-state energy of the bound polaron in the quantum well and the Coulomb bound potential, the electric field strength, and the well width are derived. The numerical results show that the ground-state energy increases with the increase of the electric field strength and the Coulomb bound potential and decreases as the well width increases.

Influence of the Interaction Between Phonons and Coulomb Potential on the Properties of a Bound Polaron in a Quantum Dot

The properties of a bound polaron in a parabolic quantum dot with weak electron-LO-phonon coupling under a Coulomb field are studied. The ground state energy of the bound polaron is derived by using a linear combination operator and the perturbation method. The influence of the interaction between phonons with different wave vectors in the recoil process on the ground state energy of the bound polaron is discussed. Numerical calculations are performed,and the results show that the ground state energy increases significantly as the effective confinement length of the quantum dot decreases,considering of the interaction between phonons. When l0〉1.0, the influence of the interaction between phonons on the ground state energy cannot be ignored.

A Fractional-Dimension Variational Approach for the Bound Polaron in Parabolic Quantum Wells

The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional- dimensional variational method. The numerical results for the binding energies of the bound polaron and longitudinal-optical phonon contributions in GaAs/Al0.3 Ga0.7 AS parabolic quantum well structures are obtained as functions of the well width. It is shown that the binding energies of the bound polaron are obviously reduced by the electron-phonon interaction and the phonon contribution is observable and cannot be neglected.

Influence of Coulomb Potential on the Properties of a Polaron in a Quantum Dot

The ground-state energy and the average number of virtual phonons around the electron of a hydrogenic impurity confined in a parabolic quantum dot are calculated using the squeezed-state variational approach,which is based on two successive canonical transformations and uses a displaced-oscillator type unitary transformation to deal with the bilinear terms,which are usually neglected.Numerical calculations are carried out in order to study the relation between the ground-state energy and the average number of virtual phonons around the electron of a bound polaron in a parabolic quantum dot with the Coulomb binding parameter.The electron-phonon coupling constant and the confinement length are derived.

Magnetic polaron-related optical properties in Ni(Ⅱ)-doped Cd S nanobelts: Implication for spin nanophotonic devices

Emissions by magnetic polarons and spin-coupled d-d transitions in diluted magnetic semiconductors(DMSs)have become a popular research field due to their unusual optical behaviors.In this work,high-quality NiI_(2)(Ⅱ)-doped CdS nanobelts are synthesized via chemical vapor deposition(CVD),and then characterized by scanning electron microscopy(SEM),x-ray diffraction,x-ray photoelectron spectroscopy(XPS),and Raman scattering.At low temperatures,the photoluminescence(PL)spectra of the Ni-doped nanobelts demonstrate three peaks near the band edge:the free exciton(FX)peak,the exciton magnetic polaron(EMP)peak out of ferromagnetically coupled spins coupled with FXs,and a small higher-energy peak from the interaction of antiferromagnetic coupled Ni pairs and FXs,called antiferromagnetic magnetic polarons(AMPs).With a higher Ni doping concentration,in addition to the d-d transitions of single Ni ions at 620 nm and 760 nm,two other PL peaks appear at 530 nm and 685 nm,attributed to another EMP emission and the d-d transitions of the antiferromagnetic coupled Ni^(2+)-Ni^(2+)pair,respectively.Furthermore,single-mode lasing at the first EMP is excited by a femtosecond laser pulse,proving a coherent bosonic lasing of the EMP condensate out of complicated states.These results show that the coupled spins play an important role in forming magnetic polaron and implementing related optical responses.

On the possibility of self-trapping transition of acoustic polarons in two dimensions

A 2D electron-longitudinal-acoustic-phonon interaction Hamiltonian is derived and used to calculate the groundstate energy of the acoustic polarons in two dimensions. The numerical results for the ground-state energy of the acoustic polarons in two and three dimensions are obtained. The 3D results agree with those obtained by using the Feynman path-integral approach. It is found that the critical coupling constant of the transition from the quasifree state to the self-trapped state in the 2D case is much smaller than in the 3D case for a given cutoff wave-vector. The theory has been used to judge the possibility of the self-trapping for several real materials. The results indicate that the self-trappings of the electrons in AlN and the holes in AlN and GaN are expected to be observed in 2D systems.

Extended Holstein polaron model for charge transfer in dry DNA

The variational method is applied to the study of charge transfer in dry DNA by using an extended Holstein small polaron model in two cases： the site-dependent flnite-chain discrete case and the site-independent continuous one. The treatments in the two cases are proven to be consistent in theory and calculation. Discrete and continuous treatments of Holstein model both can yield a nonlinear equation to describe the charge migration in an actual long-range DNA chain. Our theoretical results of binding energy Eb, probability amplitude of charge carrier Ф and the relation between energy and charge-lattice coupling strength are in accordance with the available experimental results and recent theoretical calculations.

Polaron effect on the optical rectification in spherical quantum dots with electric field

The polaron effect on the optical rectification in spherical quantum dots with a shallow hydrogenic impurity in the presence of electric field is theoretically investigated by taking into account the interactions of the electrons with both confined and surface optical phonons. Besides, the interaction between impurity and phonons is also considered. Numerical calculations are presented for typical Zn1-xCdxSe/ZnSe material. It is found that the polaronic effect or electric field leads to the redshifted resonant peaks of the optical rectification coefficients. It is also found that the peak values of the optical rectification coefficients with the polaronic effect are larger than without the polaronic effect, especially for smaller Cd concentrations or stronger electric field.

Variational Path-Integral Study on Bound Polarons in Parabolic Quantum Dots and Wires

The expression of the ground-state energy of the electron coupled simultaneously with a Coulomb potential and a longitudinal-optical phonon field in parabolic quantum dots and wires is derived within the framework of Feynman variational path integral theory.We obtain a general result with arbitrary electron-phonon coupling constant,Coulomb binding parameters,and confining potential strength,which could be used for further numerical calculation of polaron properties.Moreover,it is shown that all the previous path-integral formulae for free polarons,bound polarons,and polarons confined in parabolic quantum dots and wires can be recovered in the present formalism.

Effects of electron–optical phonon interactions on the polaron energy in a wurtzite ZnO/Mg_xZn_(1-x)O quantum well

We investigated the properties of polarons in a wurtzite ZnO/MgxZn1-xO quantum well by adopting a modified Lee–Low–Pines variational method, giving the ground state energy, transition energy, and phonon contributions from various optical-phonon modes to the ground state energy as functions of the well width and Mg composition. In our calculations, we considered the effects of confined optical phonon modes, interface-optical phonon modes, and half-space phonon modes, as well as the anisotropy of the electron effective band mass, phonon frequency, and dielectric constant. Our numerical results indicate that the electron–optical phonon interactions importantly affect the polaronic energies in the ZnO/MgxZn1-xO quantum well. The electron–optical phonon interactions decrease the polaron energies. For quantum wells with narrower wells, the interface optical phonon and half-space phonon modes contribute more to the polaronic energies than the confined phonon modes. However, for wider quantum wells, the total contribution to the polaronic energy mainly comes from the confined modes. The contributions of the various phonon modes to the transition energy change differently with increasing well width. The contribution of the half-space phonons decreases slowly as the QW width increases, whereas the contributions of the confined and interface phonons reach a maximum at d ≈ 5.0 nm and then decrease slowly. However,the total contribution of phonon modes to the transition energy is negative and increases gradually with the QW width of d.As the composition x increases, the total contribution of phonons to the ground state energies increases slowly, but the total contributions of phonons to the transition energies decrease gradually. We analyze the physical reasons for these behaviors in detail.

Vibrational frequency of a strong-coupling polaron in a quantum rod at finite temperatures

The Hamiltonian of a quantum rod with a boundary is presented after a coordinate transformation that changes the original ellipsoidal boundary into a spherical one. We then study the effect of temperature on the vibrational frequency and the ground state binding energy of the strong-coupling polaron in the rod. The two quantities are expressed as functions of the aspect ratio of the ellipsoid, the transverse and the longitudinal effective confinement lengths, the temperature and the electron-phonon coupling strength by linear combination operator and unitary transformation methods. It is found that the vibrational frequency and the ground state binding energy will increase rapidly with decreasing transverse and longitudinal effective confinement lengths. They are increasing functions of the electron- phonon coupling strength but become decreasing ones of the temperature and the aspect ratio.

The ground-state lifetime of polaron in a parabolic quantum dot

This paper reports that the ground-state energy of polaron was obtained with strong electron-LO-phonon coupling by using a variational method of the Pekar type in a parabolic quantum dot. Quantum transition is occurred in the quantum system due to the electron-phonon interaction and the influence of temperature. That is the polaron transit from the ground-state to the first-excited state after absorbing a LO-phonon and it causes the change of the polaron lifetime. Numerical calculations are performed and the results illustrate that the ground-state lifetime of the polaron will increase with increasing the ground-state energy of polaron and decrease with increasing the electron-LO-phonon coupling strength, the confinement length of the quantum dot and the temperature.

Mechanism of Insulator-Metal Transition in La_(2/3)Ca_(1/3)MnO_(3):Collapse of Small Polaron

The insulator-metal(I-M)transition in colossal magnetoresistance material La_(2/3)Ca_(1/3)MnO_(3) has been studied by electrical transport,magnetization and electron spin resonance(ESR)measurements.Around the I-M transition,the ESR signal shows a crossover from paramagnetic resonance line to ferromagnetic resonance line,which implies a coexistence of localized small polarons and itinerant carriers during the I-M transition.Based on the concept of‘small polaron collapse’,a two-phase model is proposed to quantitatively describe the electrical transport behaviour across the insulator-metal transition.The calculations of resistivity in different applied magnetic fields have close trends with the experimental data,which strongly proves that the I-M transition results from the collapse of small polarons and two phases coexist during the transition.

Bound polarons in quantum dot quantum well structures

The problem of bound polarons in quantum dot quantum well （QDQW） structures is studied theoretically. The eigenfrequencies of bulk longitudinal optical （LO） and surface optical （SO） modes are derived in the framework of the dielectric continuum approximation. The electron-phonon interaction Hamiltonian for QDQW structures is obtained and the exchange interaction between impurity and LO-phonons is discussed. The binding energy and the trapping energy of the bound polaron in CdS/HgS QDQW structures are calculated. The numerical results reveal that there exist three branches of eigenfrequencies of surface optical vibration in the CdS/HgS QDQW structure. It is also shown that the binding energy and the trapping energy increase as the inner radius of the QDQW structure decreases, with the outer radius fixed, and the trapping energy takes a major part of the binding energy when the inner radius is very small.

The energy-level and vibrational frequency properties of a polaron weak-coupled in a quantum well with asymmetrical Gaussian confinement potential

The vibrational frequency(VF), the ground state(GS) energy and the GS binding energy of the weak electron-phonon coupling polaron in a quantum well(QW) with asymmetrical Gaussian confinement potential are calculated. First we introduce the linear combination operator to express the momentum and coordinates in the Hamilton and then operate the system Hamilton using unitary transformation. The results indicate the relations of the quantities(the VF, the absolute value of GS energy and the GS binding energy) and the parameters(the QW barrier height and the range of Gaussian confinement potential in the growth direction of the QW).

A Polaron in a Quantum Dot quantum Well

The polaron effect in a quantum dot quantum well (QDQW)system is investigated by using the perturbation method. Both the bound electron states outside and inside the shell well are taken into account . Numerical calculation on the CdS/HgS QDQW shows that the phonon correction to the electron ground state energy is quite significant and cannot be neglected.

On Optical Polarons in One Dimensional Molecular-Crystal Chains

An improved solution for the optical polarons in the molecular-crystal model with the dispersion term in one dimensional chains is found.Under approximation neglecting the dispersion term,the improved solution tends to usual optical polarons solution.The self-trapped well of the electron is calculated.

Photothermal‐boosted polaron transport in Fe_(2)O_(3)photoanodes for efficient photoelectrochemical water splitting

Introduction of the photothermal effect into transition-metal oxide photoanodes has been proven to be an effective method to improve the photoelectrochemical(PEC)water-splitting performance.However,the precise role of the photothermal effect on the PEC performance of photoanodes is still not well understood.Herein,spinel-structured ZnFe_(2)O_(4)nanoparticles are deposited on the surface of hematite(Fe_(2)O_(3)),and the ZnFe_(2)O_(4)/Fe_(2)O_(3)photoanode achieves a high photocurrent density of 3.17 mA cm^(-2)at 1.23 V versus a reversible hydrogen electrode(VRHE)due to the photothermal effect of ZnFe_(2)O_(4).Considering that the hopping of electron small polarons induced by oxygen vacancies is thermally activated,we clarify that the main reason for the enhanced PEC performance via the photothermal effect is the promoted mobility of electron small polarons that are bound to positively charged oxygen vacancies.Under the synergistic effect of oxygen vacancies and the photothermal effect,the electron conductivity and PEC performance are significantly improved,which provide fundamental insights into the impact of the photothermal effect on the PEC performance of small polaron-type semiconductor photoanodes.

Effects of polarons on static polarizabilities and second order hyperpolarizabilities of conjugated polymers

According to the one-dimensional tight-binding Su-Schrieffer-Heeger model, we have investigated the effects of charged polarons on the static polarizability, axx, and the second order hyperpolarizabilities, γxxxx, of conjugated polymers. Our results are consistent qualitatively with previous ab initio and semi-empirical calculations. The origin of the universal growth is discussed using a local-view formalism that is based on the local atomic charge derivatives. Furthermore, combining the Su Schrieffer-Heeger model and the extended Hubbard model, we have investigated systematically the effects of electron-electron interactions on αxx and γxxxx of charged polymer chains. For a fixed value of the nearest-neighbour interaction V, the values of αxx and γxxxx increase as the on-site Coulomb interaction U increases for U 〈 Uc and decrease with U for U 〉 Uc, where Uc is a critical value of U at which the static polarizability or the second order hypcrpolarizability reaches a maximal value of αxx or γxxxx. It is found that the effect of the e-e interaction on the value of αxx is dependent on the ratio between U and V for either a short or a long charged polymer. Whereas, that effect on the value of γxxxx is sensitive both to the ratio of U to V and to the size of the molecule.