Infrared optical absorption of Fr?hlich polarons in metal halide perovskites

The formation of Frohlich polarons in metal halide perovskites,arising from the charge carrier-longitudinal optical(LO)phonon coupling,has been proposed to explain their exceptional properties,but the effective identification of polarons in these materials is still a challenging task.Herein,we theoretically present the infrared optical absorption of Frohlich polarons based on the Huang-Rhys model.We find that multiphonon overtones appear as the energy of the incident photons matches the multiple LO phonons,wherein the average phonon number of a polaron can be directly evaluated by the order of the strongest overtone.These multiphonon structures sensitively depend on the scale of electronic distribution in the ground state and the dimensionality of the perovskite materials,revealing the effective modulation of competing processes between polaron formation and carrier cooling.Moreover,the order of the strongest overtone shifts to higher ones with temperature,providing a potential proof that the carrier mobility is affected by LO phonon scattering.The present model not only suggests a direct way to verify Frohlich polarons but also enriches our understanding of the properties of polarons in metal halide perovskites.

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.

The effect of interface hopping on inelastic scattering of oppositely charged polarons in polymers

The inelastic scattering of oppositely charge polarons in polymer heterojunctions is believed to be of fundamental importance for the light-emitting and transport properties of conjugated polymers. Based on the tight-binding SSH model, and by using a nonadiabatic molecular dynamic method, we investigate the effects of interface hopping on inelastic scattering of oppositely charged polarons in a polymer heterojunction. It is found that the scattering processes of the charge and lattice defect depend sensitively on the hopping integrals at the polymer/polymer interface when the interface potential barrier and applied electric field strength are constant. In particular, at an intermediate electric field, when the interface hopping integral of the polymer/polymer heterojunction material is increased beyond a critical value, two polarons can combine to become a lattice deformation in one of the two polymer chains, with the electron and the hole bound together, i.e., a self-trapped polaron-exciton. The yield of excitons then increases to a peak value. These results show that interface hopping is of fundamental importance and facilitates the formation of polaron-excitons.

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.

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.

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.

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.

Magnetic and electronic properties of La-doped hexagonal 4H-SrMnO_(3)

As typical strongly correlated electronic materials, manganites show rich magnetic phase diagrams and electronic structures depending on the doped carrier density. Most previous relevant studies of doped manganites rely on the cubic/orthorhombic structures, while the hexagonal structure is much less studied. Here first-principles calculations are employed to investigate the magnetic and electronic structures of La-doped 4H-SrMnO_(3). By systematically analyzing the two kinds of La-doped positions, our calculations predict that the doped electron with lattice distortion would prefer to form polarons, which contribute to the local magnetic phase transition, nonzero net magnetization, and semiconducting behavior. In addition, the energy gap decreases gradually with increasing doping concentration, indicating a tendency of insulator–metal transition.

Femtosecond tunneling of polarons in Pb_(5)Cr_(3)F_(19)

The complex dielectric constant/ac electrical conductivity was investigated as a function offrequency and temperature in Pb_(5)Cr_(3)F_(19).The system undergoes a ferroelectric phase transition at higher temperatures.At lower temperatures the real part of the complex ac electric conductivity was found to follow the universal dielectric response(UDR)σ′∝v^(s),typical for hopping or tunneling of localized charge carriers.A detailed analysis of the temperature dependence of the UDR parameter s in terms of the theoretical model for tunneling of small polarons revealed that,at low temperatures,this mechanism governs the charge transport in Pb_(5)Cr_(3)F_(19).The value of the inverse attempt frequency τ0 indicates the femtosecond tunneling of polarons in the system similar to the Büttiker-Landauer transversal time.

Repulsive Polarons in One-Dimensional Fermi Gases

Using the variational method, we study the properties of a spin-down impurity immersed in a onedimensional(1 D) spin-up Fermi sea. With repulsive interactions between them, the impurity is dressed up by surrounding particles in Fermi sea and forms a polaron. We clearly calculate the binding energy, effective mass, momentum distribution, Tan contact, and pair correlation. Even in strong repulsive regimes, the results can agree with the exact Bethe Ansatz results. The repulsive polaron energy E+ is below Fermi energy EF and no negative effective masses are found in whole interaction regimes, unequal masses polarons are also calculated. We show a clear momentum distribution and calculate the Tan contact from three different aspects. Furthermore, we explore the particle-hole excitation and find that the hole terms in Fermi sea have a great influence on the polaron energy and contact in repulsive regime. These results show that the variational method can still be used effectively in 1 D repulsive polaron system.

Hole polarons in poly(G)-poly(C) and poly(A)-poly(T) DNA molecules

The polaron might play an important role in the process of charge migration through duplex DNA stack. In the present work, we investigate properties of hole polarons in DNA molecules containing identical base pairs, such as poly(G)-poly(C) and poly(A)-poly(T), An extended tight-binding model (extended Su-Schrieffer-Heeger model), which involves the effect of an electric field in the direction of DNA stack, will be introduced. The transfer integral and electron-phonon coupling parameters in this model are obtained according to ab initio calculation for different base pair dimers. Calculations reveal that the polaron in poly(A)-poly(T) has a wider shape and a higher mobility under a specific electric field than that in poly(G)-poly(C) DNA stack.

Temperature effects on interface polarons in a strained(111)-oriented zinc-blende GaN/AlGaN heterojunction under pressure

The properties of interface polarons in a strained （111）-oriented zinc-blende GaN/AlxGa1-xN heterojunction at finite temperature under hydrostatic pressure are investigated by adopting a modified LLP variational method and a simplified coherent potential approximation. Considering the effect of hydrostatic pressure on the bulk longitudinal optical phonon mode, two branches interface-optical phonon modes and strain, respectively, we calculated the polaronic self-trapping energy and effective mass as functions of temperature, pressure and areal electron density. The numerical result shows that both of them near linearly increase with pressure but the self-trapping energies are nonlinear monotone increasing with increasing of the areal electron density. They are near constants below a range of temperature whereas decrease dramatically with increasing temperature beyond the range. The contributions from the bulk longitudinal optical phonon mode and one branch of interface optical phonon mode with higher frequency are important whereas the contribution from another branch of interface optical phonon mode with lower frequency is extremely small so that it can be neglected in the further discussion.

Ground-state energy of weak-coupling polarons in quantum rods

The Hamiltonian of the quantum rod （QR） with an ellipsoidal boundary is given after a coordinate transformation. Using the linear-combination operator and unitary transformation methods, the vibrational frequency and the ground-state energy of weak-coupling polarons are obtained. Numerical results illustrate that the vibrational frequency increases with the decrease of the effective radius R0 of the ellipsoidal parabolic potential and the aspect ratio e of the ellipsoid, and that the ground-state energy increases with the decrease of the effective radius R0 and the electron-LO-phonon coupling strength α. In addition, the ground-state energy decreases with increasing aspect ratio e within 0 〈 e 〈 1 and reaches a minimum when e = 1, and then increases with increasing e for e 〉 1.

Dynamics of interchain delocalized polarons in polymers

Polaron dynamics in a system of highly ordered conjugated polymer chains is investigated based on the tight binding model. With the interchain coupling enhancing,it takes longer time for the electron added to the system to induce a localized polaron state. Beyond a certain strength of the interchain coupling,the electron evolves into a two-dimensional delocalized polaron state. Dynamical simulations suggest that the well-ordered organic molecule systems with two-dimensional polarons exhibit higher mobilities than the systems with intrachain localized polarons,as also suggested by earlier experiments.

Property comparison of polarons in zinc-blende and wurtzite GaN/AlN quantum wells

The properties ofpolarons in zinc-blende and wurtzite GaN/AIN quantum wells with Frohlich interaction Hamiltonians are compared in detail. The energy shifts of polarons at ground state due to the interface （IF）, confined （CO） and half-space phonon modes are calculated by a finite-difference computation combined with a modified LLP variational method. It is found that the two Frohlich interaction Hamiltonians are consistent with each other when the anisotropic effect from the z-direction and the x-y plane is neglected. The influence of the anisotropy on the polaron energy shifts due to the IF phonon modes for a smaller well width or due to the CO phonon modes for a moderate well width is obvious. In addition, the built-in electric field has a remarkable effect on the polaron energy shifts contributed by the various phonon modes.

Photoinduced small electron polarons generation and recombination in hematite

Polarons generally affect adversely the photochemical and photophysical properties of transition metal oxides.However,the excited-state dynamics of polarons are not fully established to date and thus require an atomistic understanding.We focus onα-Fe_(2)O_(3)with photoexcitation,electron injection,and heterovalent doping as the small polaron models,and conduct simulations of ab initio adiabatic molecular dynamics(AIMD)and nonadiabatic molecular dynamics(NA-MD).The elaborately designed AIMD simulations show that localization of electron at a single Fe site is an adiabatic and ultrafast process within sub-15 fs.Fe_(2)O_(3)doping with an electron or a Si and Ti dopant forms a localized electron polaron while photoexcitation forms localized electron and hole polarons simultaneously,leading to diverse electron–hole recombination dynamics.NA-MD simulations demonstrate that recombination of an electron polaron created by doping with a delocalized hole at the valence band maximum ofα-Fe_(2)O_(3)takes place around 5 ps,while recombination between a pair of small electron and hole polarons in photoexcited Fe_(2)O_(3)delays to about 110 ps owing to weak NA coupling and fast decoherence process.The ultrafast formation of small electron polarons inα-Fe_(2)O_(3)impedes the accumulation of delocalized holes in the valence band that directly participate in water oxidation at photoanodes.The detrimental effect can be partially circumvented in photoexcited Fe_(2)O_(3)for slowing electron–hole recombination despite polarons may retain low charge mobility.These findings provide a fundamental understanding of the excited-state dynamics of small electron polaron inα-Fe_(2)O_(3)and may help design efficient transition metal oxides photoanodes.

Pressure influence on bound polarons in a strained wurtzite GaN/Al_xGa_(1_x)N heterojunction under an electric field

The binding energies of bound polarons near the interface of a strained wurtzite GaN/Al_xGa_（1-x）N het-erojunction are studied by using a modified LLP variational method and a simplified coherent potential approximation under hydrostatic pressure and an external electric field.Considering the biaxial strain due to lattice mismatch or epitaxial growth,the uniaxial strain effects and the influences of the electron-phonon interaction as well as impurity-phonon interaction including the effects of interface-optical phonon modes and half-space phonon modes,the binding energies as functions of pressure,the impurity position,areal electron density and the phonon effect on the Stark energy shift are investigated.The numerical result shows that the contributions from the interface optical phonon mode with higher frequency and the LO-like half space mode to the binding energy and the Stark energy shift are important and obviously increase with increasing hydrostatic pressure,whereas the interface optical phonon mode with lower frequency and the TO-like half space mode are extremely small and are insensitive to the impurity position and hydrostatic pressure.It is also shown that the conductive band bending should not be neglected.

Polarons in alkaline-earth-like atoms with multiple background Fermi surfaces

We study the impurity problem in a Fermi gas of 173Yb atoms near an orbital Feshbach resonance （OFR）, where a single moving particle in the 3p0 state interacts with two background Fermi seas of particles in different nuclear states of the ground 1S0 manifold. By employing wave function ansatz to molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. In comparison to the case where only one Fermi sea is populated, we find that the presence of an additional Fermi sea acts as an energy shift between the two channels of the OFR. In addition, quantum fluctuations near the Fermi level can also induce sizable effects to various properties of the attractive and repulsive polarons.

Electron engineering of metallic multiferroic polarons in epitaxial BaTiO_(3)

The coexistence of ferroelectricity,conductivity,and magnetism in a single-phase material has attracted considerable attention due to fundamental interest and tremendous technological potential.However,their mutually exclusive mechanisms hinder the discovery of multifunctional conducting multiferroics.Here,we propose a new material design approach for electron engineering to enable these conflicting properties to coexist.We use first principles calculations to demonstrate that appropriate mechanical strain can turn the excess electrons in doped BaTiO_(3) from a free-carrier configuration to a localized polaronic state by modulating the electron–phonon coupling.The resulting localized spin-polarized electron survives the host ferroelectricity and consequently manifests as a multiferroic polaron.The multiferroic properties coexist with the electronic conductivity arising from the highhopping mobility of the polaron,which enables the doped epitaxial BaTiO_(3) to act as a multiferroic conducting material.This mechanical control over the electron configuration is a potential path toward unusual coexisting properties.

Ab initio prediction of fast non-equilibrium transport of nascent polarons in SrI2: a key to high-performance scintillation

The excellent light yield proportionality of europium-doped strontium iodide(SrI2:Eu)has resulted in state-of-the-artγ-ray detectors with remarkably high-energy resolution,far exceeding that of most halide compounds.In this class of materials,the formation of self-trapped hole polarons is very common.However,polaron formation is usually expected to limit carrier mobilities and has been associated with poor scintillator light-yield proportionality and resolution.Here using a recently developed first-principles method,we perform an unprecedented study of polaron transport in SrI2,both for equilibrium polarons,as well as nascent polarons immediately following a self-trapping event.We propose a rationale for the unexpected high-energy resolution of SrI2.We identify nine stable hole polaron configurations,which consist of dimerised iodine pairs with polaron-binding energies of up to 0.5 eV.They are connected by a complex potential energy landscape that comprises 66 unique nearest-neighbour migration paths.Ab initio molecular dynamics simulations reveal that a large fraction of polarons is born into configurations that migrate practically barrier free at room temperature.Consequently,carriers created duringγ-irradiation can quickly diffuse away reducing the chance for nonlinear recombination,the primary culprit for non-proportionality and resolution reduction.We conclude that the flat,albeit complex,landscape for polaron migration in SrI2 is a key for understanding its outstanding performance.This insight provides important guidance not only for the future development of high-performance scintillators but also of other materials,for which large polaron mobilities are crucial such as batteries and solid-state ionic conductors.