Polaron Mass Research Articles

Small polaron mass with a long range density–displacement type interaction

Abstract In this work renormalization of the effective mass of an electron due to a small polaron formation is studied within the framework of the extended Holstein model. It is assumed that an electron moves along the one-dimensional chain of ions and interacts with ions vibrations of a neighboring chain via a long-range density–displacement type force. By means of the exact calculations a renormalized mass of a nonadiabatic small polaron is obtained at strong coupling limit. The obtained results compared with the mass of small polaron of ordinary Holstein model. The effect of ions vibrations polarization on the small polaron mass is addressed.

Two-site model for a small polaron: Mass renormalization and optical conductivity

The renormalization of the mass of an electron interacting with many ions of a lattice via the long-range (Frohlich) electron-phonon interaction and optical absorption of electrons are studied at zero temperature. Ions are assumed to be isotropic three-dimensional oscillators. The optical conductivity and the renormalized mass of small adiabatic Frohlich polarons are calculated and compared with those of small adiabatic Holstein polarons.

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.

Effective Mass of Strong-Coupling Bound Polaron in a Triangular Quantum Well Induced by Rashba Effect

In this paper, on the basis of Huyhrechts' strong-coupling polaron model, the Tokuda modified linear-combination operator method and the unitary transformation method are used to study the properties of the strong-coupling bound polaron considering the influence of Rashba effect, which is brought by the spin-orbit (SO) interaction, in the semiconductor triangular quantum well (TQW). Numerical calculation on the RbCl TQW, as the example, is performed. The expressions for the effective mass of the polaron as a function of the vibration frequency, the velocity, the Coulomb bound potential and the electron areal density are derived. Numerical results show that the total effective mass of the polaron is composed of three parts. The interactions between the orbit and the spin with different directions have different effects on the effective mass of the bound polaron.

Solution of the Holstein polaron anisotropy problem

We study Holstein polarons in three-dimensional anisotropic materials. Using a variational exact diagonalization technique we provide highly accurate results for the polaron mass and polaron radius. With these data we discuss the differences between polaron formation in dimensions one and three and at small and large phonon frequencies. Varying the anisotropy we demonstrate how a polaron evolves from a one-dimensional to a three-dimensional quasiparticle. We thereby resolve the issue of polaron stability in quasi-one-dimensional substances and clarify to what extent such polarons can be described as one-dimensional objects. We finally show that even the local Holstein interaction leads to an enhancement of anisotropy in charge-carrier motion.

Density-of-state effective mass and non-parabolicity parameter of impurity doped ZnO thin films

The density-of-state effective masses of impurity doped polycrystalline ZnO thin films were measured by the method of four coefficients technique. By applying the first-order non-parabolicity approximation, the polaron effective mass and the bare band mass at the conduction band minimum, together with the corresponding non-parabolicity parameters, were analysed successfully. The determined perpendicular polaron mass of 0.29 me and the bare band mass of 0.247 me at the conduction band minimum corresponded very well to the previous results obtained for ZnO single crystals. The non-parabolicity parameter of 0.457 eV−1 derived for the polaron effective mass was larger than 0.33 eV−1 which was obtained for the bare band mass due to the increasing function of the Fröhlich coupling constant with respect to the bare band mass in polycrystalline ZnO films.

Polaronic self-trapped energy and effective mass of a cylindrical wurtzite GaN nanowire

The ground-state self-trapped energy and effective mass of the polaron in a freestanding wurtzite GaN nanowire (NW) are studied by employing the perturbation approach. Based on the dielectric continuum model and the Loudon uniaxial crystal model, the full polar optical phonon modes, i.e. quasi-confined (QC) phonon modes and surface optical (SO) phonon modes, in the one-dimensional (1D) wurtzite systems have been analyzed. The vibrating spectra of the two types of phonon modes and their electron–phonon coupling properties have been discussed and analyzed. The numerical results on the ground-state polaron self-trapped energy and correction of effective mass in the 1D GaN NWs reveal that these are far larger than those in 1D GaAs NW systems. The reasons resulting in this obvious difference in the two 1D structures can be attributed to the different electron–phonon coupling constants and electron effective masses of bulk materials constituted of the two types of 1D confined systems. Moreover, our calculated results regarding the polaronic self-trapped energy are consistent with the recent experimental observation in GaN NW systems.

The effective mass of strong-coupling polaron in a triangular quantum well induced by the Rashba effect

In this paper, on the basis of Huybrechts’ strong-coupling polaron model, the Tokuda modified linear-combination operator method and the unitary transformation method were used to study the properties of the strong-coupling polaron considering the influence of Rashba effect, which is brought by the spin–orbit (SO) interaction, in the semiconductor triangular quantum well (TQW). Numerical calculation on the RbCl TQW, as an example, is performed. The expressions for the effective mass of the polaron as a function of the vibration frequency, the velocity, the coupling constant and the electron areal density were derived. Numerical results show that the total effective mass of the polaron is composed of three parts. The interactions between the orbit and the spin with different directions have different effects on the effective mass of the polaron.

Self-Trapping of Acoustic Polaron in One Dimension

The ground-state energy and effective mass of an acoustic polaron in onedimension are calculated by using anelectron–longitudinal-acoustic-phonon interaction Hamiltonian derivedhere. The self-trapping of the acoustic polaron is discussed. It isfound that the critical coupling constant shifts toward weakerelectron–phonon interaction with the increasing cutoff wave vector andthe products of the critical coupling constant by the cutoff wave vectortend to a certain value. The self-trapping of acoustic polarons in onedimension is easier to be realized than that in three- andtwo-dimensional systems. The self-trapping transition of acousticpolarons is expected to be observed in the one dimensional systems ofalkali halides and wide-band-gap semiconductors.

Influence of Zeeman splitting and thermally excited polaron states on magnetoelectrical and magnetothermal properties of magnetoresistive polycrystalline manganite La 0.8 Sr 0.2 MnO 3

Some possible connection between spin and charge degrees of freedom in magnetoresistive manganites is investigated through a thorough experimental study of the magnetic [alternating current susceptibility and direct current (dc) magnetization] and transport (resistivity and thermal conductivity) properties. Measurements are reported in the case of well characterized polycrystalline La0.8Sr0.2MnO3 samples. The experimental results suggest rather strong field-induced polarization effects in our material, clearly indicating the presence of ordered ferromagnetic regions inside the semiconducting phase. Using an analytical expression which fits the spontaneous dc magnetization, the temperature and magnetic field dependences of both electrical resistivity and thermal conductivity data are found to be well reproduced through a universal scenario based on two mechanisms: (i) a magnetization dependent spin polaron hopping influenced by a Zeeman splitting effect and (ii) properly defined thermally excited polaron states which have to be taken into account in order to correctly describe the behavior of the less conducting region. Using the experimentally found values of the magnetic and electron localization temperatures, we obtain L=0.5 nm and mp=3.2me for estimates of the localization length (size of the spin polaron) and effective polaron mass, respectively.

Spin-orbit interaction enhanced polaron effect in two-dimensional semiconductors

It is shown that in two-dimensional semiconductors, the electron-phonon interaction and polaron mass correction are both significantly enhanced by the Rashba spin-orbit coupling. The mass correction is positive for the upper Rashba branch and negative for the lower Rashba branch. Both Rashba branches have the same polaron binding energy, which is higher than that for systems in the absence of spin-orbit interaction. To the leading order, the correction to the binding energy is proportional to the square of the spin-orbit coupling strength.

Low frequency ac conduction and dielectric relaxation in pristine poly(3-octylthiophene) films

The ac conductivity σ(ω)m, dielectric constant ε′(ω) and loss ε″(ω) of pristine poly(3-octylthiophene) (P3OT) films (thickness ∼ 20 μm) have been measured in wide temperature (77–350 K) and frequency (100 Hz–10 MHz) ranges. At low temperatures, σ(ω)m can be described by the relation σ(ω)m = Aωs, where s is ∼ 0.61 at 77 K and decreases with increasing temperature. A clear Debye-type loss peak is observed by subtracting the contribution of σdc from σ(ω)m. The frequency dependence of conductivity indicates that there is a distribution of relaxation times. This is confirmed by measurement of the dielectric constant as a function of frequency and temperature. Reasonable estimates of various electrical parameters such as effective dielectric constant (εp), phonon frequency (νph), Debye temperature (θD), polaron radius (rp), small-polaron coupling constant , effective polaron mass (mp), the density of states at the Fermi level N(EF), average hopping distance (R) and average hopping energy (W) from dc conductivity measurements suggest the applicability of Mott's variable range hopping model in this system.

Polaron action for multimode dispersive phonon systems

Path-integral approach to the tight-binding polaron is extended to multiple optical phonon modes of arbitrary dispersion and polarization. The non-linear lattice effects are neglected. Only one electron band is considered. The electron-phonon interaction is of the density-displacement type, but can be of arbitrary spatial range and shape. Feynman's analytical integration of ion trajectories is performed by transforming the electron-ion forces to the basis in which the phonon dynamical matrix is diagonal. The resulting polaron action is derived for the periodic and shifted boundary conditions in imaginary time. The former can be used for calculating polaron thermodynamics while the latter for the polaron mass and spectrum. The developed formalism is the analytical basis for numerical analysis of such models by path-integral Monte Carlo methods.

Polaron transport in the paramagnetic phase of electron-doped manganites

The electrical resistivity, Hall coefficient, and thermopower as functions of temperature are reported for lightly electron-doped ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}\mathrm{Mn}{\mathrm{O}}_{3}$ $(0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.10)$. Unlike the case of hole-doped ferromagnetic manganites, the magnitude and temperature dependence of the Hall mobility $({\ensuremath{\mu}}_{H})$ for these compounds is found to be inconsistent with small-polaron theory. The transport data are better described by the Feynman polaron theory and imply intermediate coupling $(\ensuremath{\alpha}\ensuremath{\simeq}5.4)$ with a band effective mass ${m}^{*}\ensuremath{\sim}4.3{m}_{0}$ and a polaron mass ${m}_{p}\ensuremath{\sim}10{m}_{0}$.

Effect of electron-phonon interaction range on lattice polaron dynamics: A continuous-time quantum Monte Carlo study

We present the numerically exact ground state energy, effective mass, and isotope exponents of a one-dimensional lattice polaron, valid for any range of electron-phonon interaction, applying a new continuous-time Quantum Monte Carlo (QMC) technique in a wide range of coupling strength and adiabatic ratio. The QMC method is free from any systematic finite-size and finite-time-step errors. We compare our numerically exact results with analytical weak-coupling theory and with the strong-coupling $1/\lambda$ expansion. We show that the exact results agree well with the canonical Fr\"ohlich and Holstein-Lang-Firsov theories in the weak and strong coupling limits, respectively, for any range of interaction. We find a strong dependence of the polaron dynamics on the range of interaction. An increased range of interaction has a similar effect to an increased (less adiabatic) phonon frequency: specifically, a reduction in the effective mass.

SELF-TRAPPING ENERGY AND EFFECTIVE MASS OF POLARON IN WURTZITE NITRIDE SEMICONDUCTORS

A variational approach is used to study the intermediate-coupling polaron in bulk III-V nitride semiconductors with wurtzite crystal structure within the macroscopic dielectric continuum model and the uniaxial model. The polaronic self-trapping energy and effective mass are theoretically derived for the LO and TO polarizations mixing due to the anisotropy effect. The numerical computation has been performed for the polaronic self-trapping energy and effective mass for wurtzite nitrides GaN , AlN and InN . The results show that the self-trapping energies of the wurtzite nitrides are bigger than the zinc-blende structures above calculated materials. It is also found that the structure anisotropy increases the electron–phonon interaction in wurtizte nitride semiconductors. It indicates that the LO-like phonon influence on the polaronic effective mass and self-trapping energy are dominant and anisotropy effect is obvious.

Polaron properties in ternary group-III nitride mixed crystals

Polaron properties are studied in bulk wurtzite nitride ternary mixed crystals AxB1-xN (A, B = Al, Ga, In) with the use of a dielectric continuum Frohlich-like electron-phonon interaction Hamiltonian. The polaronic self-trapping energy and effective mass are analytically derived by taking the mixing properties of the LO and TO polarizations due to the anisotropy effect into account in the mono-phonon approximation. The numerical computation has been performed for the wurtzite ternary mixed crystal materials InxGa1-xN, AlxGa1-xN, and AlxIn1-xN as functions of the composition x. The results show that the polaronic self-trapping energies in the wurtzite structures are bigger than that in zinc-blende structures for the materials calculated. It is also found that the structure anisotropy increases the electron-phonon interaction in wurtizte nitride semiconductors. The results indicate that the LO-like phonon influence on the polaronic self-trapping energy and effective mass is dominant, and the anisotropy effect is obvious.

Polaron in a Quasi 0D Nanocrystal

Polaron states in a spherical quantum dot with a spherical symmetric parabolic confinement potential are investigated applying the Feynman variational principle. Effects of the dot radius on the polaron ground state energy level, the self-action potential energy, the mass and the Fröhlich electron–phonon-coupling constant are obtained for a spherical quantum dot.The electron–phonon-coupling amplitude derived from the Maxwell equation in a material medium is used. This yields a better upper bound for strong coupling polaron energy in a spherical quantum dot.The polaron mass, energy and self-action potential energy are found to have a monotonous decrease as the structures' radius increases. As the spherical quantum dot radius is reduced the regimes of weak and intermediate coupling polaron shorten and the strong coupling polaron region broadens and extends into weak and intermediate ones. The main contribution to polaron energy and mass comes from the self-action potential.

Electron‐phonon coupling effects in quasi‐2D ternary mixed crystals of polar semiconductors

The interaction between a quasi-two-dimensional confined electron and two branches of LO-phonon modes in a ternary mixed crystal of polar semiconductors is studied. The energies of intermediate coupling polarons are numerically calculated for several systems of III-V compounds. The obvious non-linearity of the phonon energies and polaron masses relative to their compositon is also theoretically found, in special for the systems composed of nitride-bases compounds. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Polaron crossover in molecular solids

An analytical variational method is applied to the molecular Holstein Hamiltonianin which the dispersive features of the dimension dependent phonon spectrumare taken into account by a force constant approach. The crossover between alarge and a small size polaron is monitored, in one, two and three dimensionsand for different values of the adiabatic parameter, through the behaviour of theeffective mass as a function of the electron–phonon coupling. By increasing thestrength of the intermolecular forces the crossover becomes smoother and occurs athigher e–ph couplings. These effects are more evident in three dimensions. Weshow that our modified Lang–Firsov method starts to capture the occurrence of apolaron self-trapping transition when the electron energies become of order of thephonon energies. The self-trapping event persists in the fully adiabatic regime. Atthe crossover we estimate polaron effective masses of order times the bare band mass according to the dimensionality and the value of the adiabaticparameter. Modified Lang–Firsov polaron masses are substantially reduced intwo and three dimensions. There is no self-trapping in the antiadiabatic regime.