Strong-coupling Polaron Research Articles

Polarons in axial transport in single-layer high-Tc superconductors

AbstractThe temperatureT dependencies ρ(T) of normal state electric resistivitiesρ c (axial) andρ ab (in plane) of single-layer high-T c superconductors show common trends: AsT is raised, the resistivity first drops steeply before it starts rising αT above an apparent semiconductor-to-metal crossoverT cross. To analyze ρ(T) we plottT/ρ againstT at various dopingsx for bothρ c andρ ab.T/ρ is inversely proportional to the traversal time across a potential barrier as an ionic particle drifts in an electric field. We findT/ρ in good agreement with theT dependence of the quantum rate of migrating particles: AsT is raised, a zero-point rate at the lowestT is extended to a nearly flat plateau before a thermally activated branch sets in. We also find evidence for the admixture of 1- & 2-phonon absorptions below the Arrhenius range. These features shape the semiconductor-like branch below Tcross. AboveT cross a metallic-like branch sets in, its αT character deriving from the field coupling of the migrating particle. Our analysis suggests that metal physics may not suffice if ionic features play a role in transport. We attribute our conclusions to the drift of strong-coupling polarons along Cu−O bonds. These “bond polarons” originate from carrier scattering by double-well potentials associated with the bonds. A bond polaron dissociates to a free hole as it passes onto a neighboring O-O link.

Temperature Dependence of the Properties of the Strong-Coupling Polaron in a Slab of Polar Crystal

In this paper, the temperature dependence of the properties of polaron, which is weakly coupled with bulk LO phonons and strongly coupled with SO phonons, in a slab of polar crystal is studied by means of a modified second LLP transformation for the first time. An expressions for the self-trapping energy and the effective mass of the polaron in a slab of polar crystal as a function of the temperature and slab thickness are derived by using a linear combination operator and two modified LLP variational method. Our numerical results of the self-trapping energy and the effective mass for KCl show that the polaron self-trapping energy and effective mass in a polar crystal are strongly related to the slab thickness and the temperature. The self-trapping energy and the effective mass will decrease with increasing slab thickness and temperature.

Theory of bound polarons in oxide compounds

We present a multilateral theoretical study of bound polarons in oxide compounds MgO and \alpha-Al_2O_3 (corundum). A continuum theory at arbitrary electron-phonon coupling is used for calculation of the energies of thermal dissociation, photoionization (optically induced release of an electron (hole) from the ground self-consistent state), as well as optical absorption to the non-relaxed excited states. Unlike the case of free strong-coupling polarons, where the ratio \kappa of the photoionization energy to the thermal dissociation energy was shown to be always equal to 3, here this ratio depends on the Froehlich coupling constant \alpha and the screened Coulomb interaction strength \beta. Reasonable variation of these two parameters has demonstrated that the magnitude of \kappa remains usually in the narrow interval from 1 to 2.5. This is in agreement with atomistic calculations and experimental data for hole O^- polarons bound to the cation vacancy in MgO. The thermal dissociation energy for the ground self-consistent state and the energy of the optically induced charge transfer process (hops of a hole between O^{2-} ions) have been calculated using the quantum-chemical method INDO. Results obtained within the two approaches for hole O$^-$ polarons bound by the cation vacancies (V^-) in MgO and by the Mg^{2+} impurity (V_{Mg}) in corundum are compared to experimental data and to each other. We discuss a surprising closeness of the results obtained on the basis of independent models and their agreement with experiment.

Optical absorption from a nondegenerate polaron gas

We apply the dynamical mean field theory to calculate the low-density limit of the optical conductivity in the Holstein model. This nonperturbative treatment allows continuous spanning from the weak-coupling quasi-free-electron behavior to the strong-coupling small polaron picture. Different features arise in the intermediate coupling regime: (i) a noticeable transfer of spectral weight toward low frequencies occurs at low temperatures, when coherent processes acquire importance; (ii) thermally activated polaron interband transitions appear at nonzero temperature, whose spectral weight has a nonmonotonic temperature dependence. We propose an interpretation of the infrared active vibrations observed in the optical spectra of underdoped superconducting cuprates in terms of small polarons in the intermediate coupling regime.

Strong Electron–Phonon Interaction Effect in Quantum Dots**The project supported by Hong Kong Polytechnic Research Committee and the RGC of UPGC

Strong-coupling polaron in a parabolic quantum dot is investigated by the Landau–Pekar variational treatment. The polaron binding energy and the average number of virtual phonons around the electron as a function of the effective confinement length of the quantum dot are obtained in Gaussian function approximation. It is shown that both the polaron binding energy and the average number of virtual phonons around the electron decrease with increasing the effective confinement length. The results indicate that the polaronic effects are more pronounced in quantum dots than those in two-dimensional and three-dimensional cases.

The strong-coupling polaron in reduced dimensionality

Based on the LLP-H approach, a detailed study of the electron confinement in a polar semiconductor heterostructure has been made to derive analytically the ground state energy and the effective mass of the Fröhlich polaron in quasi-two-dimensional (Q2D) and quasi-one-dimensional (Q1D) systems.

Exact Ground State Energy of the Strong-Coupling Polaron

The polaron has been of interest in condensed matter theory and field theory for about half a century, especially the limit of large coupling constant. It was not until 1983, however, that a proof of the asymptotic formula for the ground state energy was finally given by using difficult arguments involving the large deviation theory of path integrals. Here we derive the same asymptotic result and with explicit error bounds, by simple, rigorous methods applied directly to the Hamiltonian. Our method is easily generalizable to other settings, e.g., the excitonic and magnetic polarons. This version of the article includes an erratum concerning the ultra-violet bound given in the published article. The erratum is to appear in the same journal.

Exact Ground State Energy of the Strong-Coupling Polaron

The polaron has been of interest in condensed matter theory and field theory for about half a century, especially the limit of large coupling constant, α. It was not until 1983, however, that a proof of the asymptotic formula for the ground state energy was finally given by using difficult arguments involving the large deviation theory of path integrals. Here we derive the same asymptotic result, , and with explicit error bounds, by simple, rigorous methods applied directly to the Hamiltonian. Our method is easily generalizable to other settings, e.g., the excitonic and magnetic polarons.

STRONG COUPLING POLARON WITHIN POLAR CRYSTAL SLAB IN A MAGNETIC FIELD

The strong coupling polaron in a slab of polar crystal in magnetic field is investigated by means of the extended the strong coupling variational theory of polaron. The energy and the effective mass of polaron are derived as functions of slab thickness and magnetic field. The numerical results of Cu2O slab show that the influence of magnetic field reduces the energy of polaron and enhances the energy shift of electron, and that the surface optical modes are important to polaronic effect in a thin slab and in the presence of magnetic field.

Strong Coupling Polaron in a Slab of Polar Crystal

By using the extensive Pekar's variational method, the strong coupling polaron energy and the effective mass in a slab of polar crystal including both LO- and SO-phonons are derived as a function of the thickness of slab and the coupling constant. When the slab is thin, the SO-phonons not only influence the ground state energy, but also make the polaronic effective mass become non-isotropic.

Strong coupling polaron in quantum well wire

With the use of variational method of Pekar type, we have calculated the polaron binding energies in quantum well wire (QWW) with strong electron-phonon interaction. Our results show that, with the increasing confinement strength of QWW, the polaron binding energy in the ground state and in the excited state increases, further more, the polaron binding energy of symmetric QWW increases faster than that of asymmetric QWW. The limiting case of bulk type, the strict two-dimensional type and the strict one-dimensional type is also discussed.

Magnetic field effects on strong-coupling polarons in quantum dots

Magnetic field effects om strong-coupling polarons in a parabolic quantum dot are investigated by the Landau-Pekr variational treatment. The polaron binding energy and the average number of virtual phonons around the electrons as functions of the magnetic field strength and the effective confinement length of the quantum dot are obtained in the Gaussian function approximation. It is shown that in the presence of magnetic fields, the polaron binding energy increases with the enhancement of the magnetic field strength. The magnetic field effects on the average number of virtual phonons around the electron are very small for strong electron-LO-phonon coupling.

Strong-coupling surface optical polaron in a magnetic field

A variational scheme of the Pekar type is employed to study the strong-coupling optical polaron on the outer surface of the polar crystal under the influence of a magnetic field. The ground state energy and the effective mass of the polaron are obtained as functions of the magnetic field strength and the electron-surface optical phonon coupling constant. It is shown that the effective mass of the surface polaron appears in nonisotropic nature due to the coupling between the electron and the surface optical phonon.

Large-bipolaron transport and cuprate superconductors.

The in-plane electronic transport of large bipolarons that move within parallel conducting sheets is considered. The Coulomb interactions between the heavy bipolarons in this planar system produce a distinctive spectrum for collective excitations. Transport of the quasiparticles associated with the collective excitations is treated via the conventional Boltzmann transport theory. However, the scattering of the heavy quasiparticles by acoustic phonons is taken to be analogous to the distinctive scattering of individual large polarons. In particular, as with strong-coupling (adiabatic) large polarons, the scattering time is taken to be proportional to the quasiparticle effective mass. The resistivity, the Hall effect, and the thermoelectric power are determined with this scheme. With a constant density of carriers, the resistivity is proportional to the temperature. The Hall number, the number of carriers deduced from the reciprocal of the Hall constant, exceeds the true carrier density by a ratio that rises linearly with temperature. In addition, the thermoelectric power falls in magnitude and ultimately changes sign as the temperature is raised. These unusual transport properties, as well as the ir conductivity, are consistent with the observed behaviors of the high-${\mathit{T}}_{\mathit{c}}$ cuprate superconductors.

The grounds-state description of the optical polaron versus the effective dimensionality in quantum-well-type systems

Within the framework of the strong-coupling polaron theory the ground-state binding energy and the effective mass of the electron-LO phonon system is retrieved as a function of the effective dimensionality in a quantum-well confinement. The geometry used is a three-dimensional parabolic potential box, the barrier slopes of which can be tuned so as to yield a unified characterization interpolating between the bulk, the quasi-two- and one-dimensional limits as well as the quantum-well box case.

The two-dimensional magneto-polaron in the strong-coupling regime

Within the framework of the strong-coupling polaron theory the problem of a two-dimensional electron coupled to LO phonons under an external magnetic field is studied. When a suitably modified coherent phonon state interrelating the magnetic field and the polaron counterparts of the problem is adopted, it is seen that the theory reproduces the desirable asymptotic limits attained by the perturbation or the usual adiabatic theories. Moreover, the theory indicates that an abrupt 'stripping transition' in the internal structure of the magneto-polaron with varying magnetic field intensity is favoured as investigated by Wu, Peeters and Devreese (1985).

Polaron effects on the binding energy of a hydrogenic impurity in a semiconductor quantum well

The polaron effect on the ground-state level of a hydrogenic impurity in a semiconductor quantum well is calculated as a function of the well thickness. The formulation is based on an extension of the strong-coupling polaron theory and covers the overall range of the electron-phonon coupling strength. It is observed that in a GaAs-based quantum structure the phonon-induced shift in the binding energy is smaller than that in the bulk case except for too narrow well sizes.

The Surface or Interface Polaron in Polar Crystals. II. Strong‐Coupling Limit

AbstractThe effective Hamiltonian and effective potential are given for the surface strong coupling polaron in polar crystals. Their binding energy and effective mass are also evaluated. When a piece of a polar crystal contacts with a piece of another non‐polar material, and the high frequency dielectric constant ε∞2 of the non‐polar material is larger than that (i.e. ε∞1) of the polar crystal, or is larger than a certain critical value (ε∞2)min, polarons can exist in the interface. Reversely, when ε∞2 < (ε∞2)min, the polaron is not able to exist near the interface. If the non‐polar material is metallic (i.e. ε∞2 = ∞), there is a deeper potential well near the interface in which the polaron may be trapped.

The regular perturbation theory in the strong-coupling polaron problem

The regular perturbation method in the strong coupling polaron theory is developed. It is shown that the law of conservation of momentum may be taken into account exactly and at the same time the high-order corrections for energy and other characteristics of the polaron may be calculated analytically.

Soliton excitations in polyacetylene and relativistic field theory models

A continuum model of a Peierls-dimerized chain, as described generally by Brazovskii and discussed for the case of polyacetylene by Takayama, Lin-Liu and Maki (TLM), is considered. The continuum (Bogliubov-de Gennes) equations arising in this model of interacting electrons and phonons are shown to be equivalent to the static, semiclassical equations for a solvable model field theory of self-coupled fermions-the N = 2 Gross-Neveu model. Based on this equivalence we note the existence of soliton defect states in polyacetylene that are additional to, and qualitatively different from, the amplitude “kinks” commonly discussed. The new solutions do not have the topological stability of kinks but are essentially conventional strong-coupling polarons in the dimerized chain. They carry spin ( 1 2 ) and charge (± e). In addition, we discuss further areas in which known field theory results may apply to a Peierls-dimerized chain, including relations between phenomenological φ 4 and continuum electron-phonon models, and the structure of the fully quantum versus mean field theories.