Large Bipolarons Research Articles

Phonon-mediated attraction between large bipolarons: Condensation to a liquid.

The self-trapped carriers of large (multisite) bipolarons redistribute themselves among the sites of their molecular orbitals as their self-trapping potential wells are altered by changing atomic positions. Through this polarizability, large bipolarons reduce the phonon frequencies. The dependence of the lowering of the zero-point vibrational energy on the spatial distribution of large bipolarons produces an intermediate-ranged phonon-mediated attraction between large bipolarons that is comparable to a phonon energy. Coulomb repulsions that oppose the phonon-mediated attractions tend to be suppressed by the large static dielectric constants associated with large-bipolaron formation. However, a strong short-range repulsion between bipolarons, analogous to the hard-core repulsion between helium atoms, persists. With the dominance of the medium-range phonon-mediated attraction and the short-range repulsion, large bipolarons can condense into a liquid. The bipolaronic liquid might be the condensed fluid phase that has been suggested as a precursor to superconductivity in cuprates.

Phonon-mediated attraction between large bipolarons: Condensation to a liquid.

Self-trapped carriers of large bipolarons are redistributed among sites of their molecular orbitals in response to atomic motions. This effect lowers the phonon frequencies. The dependence of the zero-point energy on the spatial distribution of large bipolarons produces a phonon-mediated attraction between them. This dynamic quantum-mechanical effect fosters the condensation of large bipolarons into a liquid at sufficiently low temperatures.

STABILITY OF ALL-COUPLING LARGE OPTICAL SINGLET BIPOLARONS

A variational calculation is performed to obtain the stability criteria, effective mass and the size of a large optical singlet bipolaron for the entire range of the coupling parameters in both two and three dimensions. It is shown that the bipolaron binding is stronger in thin films than in bulk crystals. It is suggested that Cu 2 O and TiCl in the form of thin films might exhibit bipolaronic effects.

Optical properties of large and small polarons and bipolarons.

In systems that are two and three dimensional electronically, a large polaron and a small polaron are distinct types of quasiparticles. The type of polaron formed depends on which electron-lattice interaction is of primary importance. A large polaron forms when the electron-lattice interaction due to the long-range Coulombic interactions between an electronic carrier and a solid's ions are of paramount importance. Competing effects then determine the radius of a large polaron. By contrast, a small polaron can form when a short-range electron-lattice interaction, such as the deformation-potential interaction, is dominant. A small polaron forms as its self-trapped carrier shrinks without limit until it is confined to a single site. Fundamental differences between large and small polarons produce optical spectra with distinguishing features. The absorption due to photoionization of a large polaron depends on products of the matrix elements for exciting a carrier from its self-trapped states to a free-carrier state and the density of these free-carrier states. These matrix elements fall sharply with increasing free-carrier wave vector k when kRg1, where R is the large polaron's radius. A large polaron's photoionization produces a temperature-independent absorption band. This band is asymmetric with the absorption intensity on the high-energy side of the peak exceeding that on the low-energy side of the peak.By contrast, the small-polaron absorption arises as the self-trapped carrier is induced to transfer from its well-localized state to a localized state at an adjacent site. Phonon broadening of these local electronic energy levels produces the widths of these absorption bands. Small-polaron absorption bands are asymmetric with the absorption intensity below the peak energy exceeding that above the peak energy. With rising temperature the phonon broadening of the local electronic energy levels progressively broadens these absorption bands. In addition, the motion of a polaron in response to an ac field can produce a (Drude-like) free-carrier absorption. A large polaron's free-carrier absorption occurs at frequencies below the characteristic phonon frequency. By contrast, if the narrow bands that characterize small polarons did not result in their localization, their coherent motion would produce a free-carrier absorption that is restricted to frequencies far below the phonon frequency. The optical spectra of large and small bipolarons are similar to those for large and small polarons, respectively. Finally, carrier-induced absorption bands observed in semiconducting and superconducting cuprates are compared with the expectations of large- and small-polaronic absorptions. The high-frequency absorption bands are consistent with the existence of large-polaronic carriers. However, taken together, the free-carrier absorptions and the dc transport in the superconductors depart from expectations of independent polaronic carriers. It is suggested that if the carriers in the cuprates are polaronic, their transport in the superconductors' normal states is collective.

Stability criteria for a singlet magnetobipolaron

The stability of a strong-coupling large optical singlet bipolaron is studied for the first time in the presence of an externally applied magnetic field. It is shown that the magnetic field reduces the stability of the bipolaron.

Carrier-charge measurement test for the existence of large bipolarons in YBa 2Cu 3O z

The carrier-charge determination method suggested by Emin in the case of large bipolarons using simultaneous Seebeck coefficient and resistivity measurements in the semiconducting parents of the high-temperature superconductors has been used in the case of YBa 2Cu 3O z . It is shown that this method can only be applied in a limited composition range around z=6.2 and at temperatures higher than 600 K. In this range the carrier-charge is likely to be equal to one elementary charge.

Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials.

The effect of spatially periodic on-site potentials on solitons of the (1+1)-dimensional nonlinear Schr\"odinger equation depends not only on the amplitude of the perturbation but also on two length ratios---between the wavelength of the potential and either the spatial width of the soliton or its phase-modulation wavelength. For solitons which are slowly moving or at rest, only the first ratio is important: Solitons which are narrow compared to the wavelength of the potential move like particles in an effective potential; wide solitons move like ``renormalized'' particles; and for competing length scales, solitons are easily destabilized by the perturbation and break up into smaller localized excitations and radiation. For initially rapidly moving solitions in short-wavelength potentials, a different resonance effect is described which can inhibit soliton propagation. Away from this resonance the solitons can move in a ``dressed'' form radiating very slowly. Furthermore, it is shown numerically that two such ``dressed'' solitons reemerge after collision, essentially unchanged. We also comment on the structural stability of completely integrable dynamics under spatially periodic perturbations. Finally, we remark on the relevance of our results for the dynamical behavior of large polarons and bipolarons in disordered ionic lattices.

Electron-correlation effects in one-dimensional large-bipolaron formation.

We study the effects of electron correlation on the ground state of a one-dimensional large singlet bipolaron. The electron-lattice interaction is taken to be the short-range interaction of Holstein's molecular-crystal model. We represent the Coulomb repulsion with the Hubbard short-range repulsion. This adoption of the Hubbard model is equivalent to replacing a strict one-dimensional system that has a short-range logarithmic divergence of the Coulomb repulsion energy between overlapping charges, with a quasi-one-dimensional system of finite width. Two types of electronic correlation are considered. With ``in-out'' correlation, we permit one of the two self-trapped carriers of the bipolaron to have a larger radius than the other. With ``left-right'' correlation, we permit the centroids of the self-trapped carriers to be displaced from one another. For both types of correlation, variational calculations are performed to determine the magnitudes of the correlation effects in the ground state. There are three parameters in the model: the electronic bandwidth parameter t, the electron-lattice coupling strength ${\mathit{E}}_{\mathit{b}}$, and the Hubbard repulsion, ${\mathit{V}}_{\mathit{c}}$. The electron-lattice interaction provides an indirect intercarrier attraction that fosters the coalescence of the two carriers. In opposition, the carriers' Coulomb repulsion and the kinetic energy required for carrier confinement foster the carriers spreading. With bipolaron formation the intercarrier attraction dominates the Coulomb repulsion.The electron-correlation effect on the bipolaron's binding depends explicitly on only ${\mathit{V}}_{\mathit{c}}$/${\mathit{E}}_{\mathit{b}}$. The electron correlation also depends on the shape of the local functions presumed in the variational calculations. Of course, the effects of electron correlation on the bipolaron's ground state increase as the Coulomb repulsion between the carriers is increased. Strikingly, we also find that the dependence of the confinement energy on electronic correlation is critical to promoting electronic correlation in the bipolaron's ground state. This feature is discussed in detail. At a maximum ratio of ${\mathit{V}}_{\mathit{c}}$/${\mathit{E}}_{\mathit{b}}$ for which we have stable bipolarons, we find that electronic correlation can lower the ground-state energy of our bipolaron by up to 30%.

Comment on "Path-integral treatment of the large-bipolaron problem"

We show that the recent path-integral calculation of Khandekar et al. [Phys. Rev. B 43, 9750 (1991)] for the ground-state energy of a large optical bipolaron neglects the Coulomb correlation effects completely and therefore leads to an incorrect stability condition. We furthermore show that their calculation for the bipolaron effective mass also leads to erroneous results.

STABILITY OF LARGE OPTICAL SINGLET BIPOLARONS, MANY-PARTICLE EFFECTS AND HIGH TEMPERATURE SUPERCONDUCTIVITY

The stability criteria for large optical bipolarons are obtained variationally for the entire range of the coupling parameters in both two and three dimensions. The size and the effective mass of these bipolarons are calculated and their variations with the material parameters are discussed. Two compounds are suggested which in the form of thin films should be tested for large bipolaronic effects. The theory is finally applied to La 2 CuO 4 and some of its normal state and superconductive properties are explained using the large bipolaronic mechanism.

Extended stability region for large bipolarons through interaction with multiple phonon branches

Abstract The large (bi)polaron is investigated for the case where the electron interacts with multiple LO-phonon branches. Explicit expressions for the groundstate energy and the effective mass are obtained within the Feynman polaron model approximation and they are applied to the material SrTiO3. The results of an effective LO-phonon branch approximation are compared with the results in which all LO-phonon branches are explicitly included. We show how the stability region for large bipolaron formation is enlarged when the electrons interact with multiple LO-phonon branches. The possible relevance of this result for the high-Tc superconductors is pointed out.

Friedel mechanism of formation of large bipolarons in high temperature superconductors

The interaction of large polarons in a degenerate gas of light electrons is investigated. Because of the Friedel oscillation of the electrostatic potential of large polarons these polarons may form a bipolaron molecule. Both the energy and the characteristic size of this bipolaron are calculated. The critical polaron density of the bipolaron liquid formation is presented.

Stability of large bipolarons

The problem of the stability of bipolarons is discussed under the assumption of the Frohlich electron-phonon interaction. A variational wavefunction for the bipolaron is proposed in a general form, which yields the translationally invariant wavefunction as a special case. A minimization of the expectation value of the Hamiltonian leads to the best estimates if the trial wavefunction is localized. In a broad range of material parameters, the upper bounds obtained for the ground-state energy of the bipolaron are better than those obtained with the help of methods fully exploiting the translational symmetry. A similar property has been observed for the free polarons for which the lowest upper bounds on the ground-state energy in the strong-coupling limit are obtained with the help of localized trial wavefunctions. This suggests that the stability of large bipolarons is connected with their self-trapping. Because of this tendency to localization the authors do not expect that the large bipolarons contribute to the bipolaronic mechanism of superconductivity in three-dimensional crystals.

Strong-coupling analysis of large bipolarons in two and three dimensions.

In the limit of strong electron-phonon coupling, we use either a Pekar-type or an oscillator wave function for the center-of-mass coordinate and either a Coulomb or an oscillator wave function for the relative coordinate, and are able to reproduce all the results from the literature for the large-bipolaron binding energy. Lower bounds are constructed for the critical ratio ${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$ of dielectric constants below which bipolarons can exist. It is found that, in the strong-coupling limit, the stability region for bipolaron formation is much larger in two dimensions (2D) than in 3D. We introduce a model that combines the averaging of the relative coordinate over the asymptotically best wave function with a path-integral treatment of the center-of-mass motion. The stability region for bipolaron formation is increased compared with the full path-integral treatment at large values of the coupling constant \ensuremath{\alpha}. The critical values are ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ensuremath{\approxeq}9.3 in 3D and ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ensuremath{\approxeq}4.5 in 2D. Phase diagrams for the presented models are also obtained in both 2D and 3D.

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.

A model of superconductivity in alkali-metal-carbon compounds

An empirical formula for T c is suggested for the alkali-metal-doped fulleride superconductors. The increase of T c with the size of the dopant alkali atoms and the decrease of T c with the external pressure are well-explained by the proposed formula. It is argued that large optical polarons and bipolarons are the natural quasi-particles of these systems in the normal phase and the superconductivity is induced by either the dynamical pairing of the polarons or the Bose-Einstein condensation of the singlet bipolarons.

Large bipolarons and superconductivity

With a strong electron-lattice interaction, charge carriers pair as bipolarons. In analogy with large (multisite) polarons, large bipolarons move itinerantly. Such mobile-charge bosons can condense into a superconducting state. Distinctive properties characterize large bipolarons.

Formation, motion and superconductivity of large bipolarons

Abstract Ferroelectric materials, characterized by very large ratios of the static to optical dielectric constants, are unique in fulfilling a requirement for the formation of a multidimensional large bipolaron. Unlike the very compact “small” bipolarons that are found in various transition-metal oxides, “large” bipolarons are not so massive that they readily localize. Thus, a large bipolaron is a mobile charged boson. As such, large bipolarons may manifest superconductivity analogous to the superfluidity of mobile neutral bosons. Distinctive electronic and magnetic properties of large bipolarons in the normal-state and superconducting states are described and compared to observations in high-temperature superconductors.

Path-integral treatment of the large-bipolaron problem.

We derive analytical expressions for the upper bound of the ground-state energy E0 and an estimate for the effective mass of a large bipolaron using path-integral methods.Received 27 November 1990DOI:https://doi.org/10.1103/PhysRevB.43.9750©1991 American Physical Society

Orbital magnetism of singlet large bipolarons.

Despite having no spin magnetism, a singlet large bipolaron in an anisotropic environment has a large anisotropic Van Vleck orbital paramagnetism. With the disklike large-bipolaron morphology envisioned for layered structures, the induced moment is aligned within the planes. The paramagnetic susceptibility and magnetic excitations of large bipolarons are suppressed in the condensate of interacting large bipolarons. Thus, carrier-related shifts of NMR frequencies and spin-lattice relaxation rates progressively fall as the temperature is lowered below ${\mathit{T}}_{\mathit{c}}$.