Polaron dynamics and bipolaron condensation in cuprates

Based on the exact cluster diagonalization and recent Quantum Monte Carlo simulations we analyze dynamic properties of small polarons and bipolarons formed by short-range (Holstein) and long-range (Fröhlich) electron-phonon interactions. We show that the exact results agree well with canonical Holstein theory for a cluster and with Lang-Firsov theory for a lattice. Lang-Firsov theory of a single polaron and our 1/λ perturbation expansion for a multipolaron system are practically exact in a wide range of the adiabatic parameter ω/t and the electron-phonon coupling λ for a long-range interaction. (Bi)polarons exist in the itinerant Bloch states at temperatures below the characteristic phonon frequency no matter which values the parameters of the system take. We show that recent claims by several authors with regards to a breakdown of Holstein-Lang-Firsov theory of a small polaron and the “impossibility” of bipolaronic superconductivity are the result of an erroneous interpretation of the electronic energy levels of the two-site Holstein model and a misunderstanding of the electron-phonon interaction in ionic solids with polaronic carriers. A “phase” diagram in t/ω-λ space is proposed to elucidate the BCS and (bi)polaronic domains. Bipolaron theory provides a parameter-free expression for the superconducting critical temperature of layered cuprates. Crystallization of the (bi)polaronic liquid is shown to be impossible in the range of the parameters typical for cuprates. The small Fröhlich polaron has spectral features compatible with single-particle tunneling and photoemission in cuprates

Unconventional pairing symmetry of layered superconductors caused by acoustic phonons

An inevitable anisotropy of sound velocity in crystals makes the phonon-mediated attraction of electrons nonlocal in space providing unconventional Cooper pairs with a nonzero orbital momentum. As a result of this anisotropy, quasi-two-dimensional charge carriers weakly coupled with acoustic phonons undergo a quantum phase transition from a conventional s-wave to an unconventional d-wave superconducting state with less carriers per unit cell. In the opposite strong-coupling regime, rotational symmetry breaking appears as a result of a reduced Coulomb repulsion between unconventional bipolarons dismissing thereby some constraints on unconventional pairing in the Bose-Einstein condensation limit. The conventional acoustic phonons, and not superexchange, are shown to be responsible for the d-wave symmetry of cuprate superconductors, where the on-site Coulomb repulsion is large

Bipolaron anisotropic flat bands, Hall mobility edge, and metal-semiconductor duality of overdoped high-Tc oxides

Hole bipolaron band structure with two flat anisotropic bands is derived for oxide superconductors. Strong anisotropy leads to one-dimensional localization in a random field which explains the metal-like value of the Hall effect and the semiconductorlike doping dependence of resistivity of overdoped oxides. Doping dependence of Tc and λH(0) as well as the low-temperature dependence of resistivity, of the Hall effect, Hc2(T) and robust features of angle-resolved photoemission spectroscopy of several high-Tc copper oxides are explained

Vortex in the charged Bose liquid

Equations describing a single vortex in the charged Bose liquid at zero temperature are derived. The zero-temperature coherence length, magnetic-field penetration depth, vortex structure and energy, and lower critical field are calculated. The vortex differs from that in type-II BCS superconductors or in neutral superfluids. Its core is charged, and there is an electric field inside the core

Hall-Lorenz number paradox in cuprate superconductors

Significantly different normal state Lorenz numbers have been found in two independent direct measurements based on the Righi-Leduc effect, one about 6 times smaller and the other one about 2 times larger than the Sommerfeld value in single cuprate crystals of the same chemical composition. The controversy is resolved in the model where charge carriers are mobile lattice bipolarons and thermally activated nondegenerate polarons. The model numerically fits several longitudinal and transverse kinetic coefficients providing a unique explanation of a sharp maximum in the temperature dependence of the normal state Hall number in underdoped cuprates

Theory of giant and nil proximity effects in cuprate semiconductors

A number of observations point to the possibility that high-Tc cuprate superconductors may not be conventional Bardeen-Cooper-Schrieffer superconductors but rather derive from the Bose-Einstein condensation of real-space pairs, which are mobile small bipolarons. A solution of the Gross-Pitaevskii equation describing Bose-condensate tunneling into a cuprate semiconductor is analytically found. It accounts qualitatively and quantitatively for nil and giant proximity effects discovered experimentally in cuprates

Comment on “Experimental and Theoretical Constraints of Bipolaronic Superconductivity in High Tc Materials: An Impossibility”

A Comment on the Letter by B. K. Chakraverty, J. Ranninger, and D. Feinberg, Phys. Rev. Lett. 81, 433 (1998). The authors of the Letter offer a Reply

d-Wave bipolaronic stripes and two energy scales in cuprates

There is strong experimental evidence for pairing of polaronic carriers in the normal state, two distinct energy scales, d-wave superconducting order parameter,and charge segregation in the form of stripes in several cuprates.All these remarkable phenomena might be unified in the framework of the bipolaron theory as a result of the formation of mobile bipolarons in the normal state and their Bose-Einstein condensation. Extending the BCS theory towards an intermediate and strong-coupling regime we show that there are two energy scales in this regime, a temperature independent incoherent gap and a temperature dependent coherent gap combining into one temperature dependent global gap. The temperature dependence of the gap and single particle (Giaver) tunnelling spectra in cuprates are quantitatively described. A framework for understanding of two distinct energy scales observed in Giaver tunnelling and Andreev reflection experiments is provided. We suggest that both d-wave superconducting order parameter and striped charge distribution result from the bipolaron (center-of-mass) energy band dispersion rather than from any particular interaction

Strong-coupling theory of high-temperature superconductivity and colossal magnetoresistance

We argue that the extension of the BCS theory to the strong-coupling regime describes the high-temperature superconductivity of cuprates and the colossal magnetoresistance (CMR) of ferromagnetic oxides if the phonon dressing of carriers and strong attractive correlations are taken into account. The attraction between carriers, which is prerequisite to high-temperature superconductivity, is caused by an almost unretarted electron-phonon interaction sufficient to overcome the direct Coulomb repulsion in the strong-coupling limit, where electrons become polarons and bipolarons (real-space electron or hole pairs dressed by phonons). The long-range Frohlich electron-phonon interaction has been identified as the most essential in cuprates providing ”superlight” lattice polarons and bipolarons. A number of key observations have been predicted and/or explained with polarons and bipolarons including unusual isotope effects, normal state (pseudo)gaps, upper critical fields, etc. Here some kinetic, magnetic, and more recent thermomagnetic normal state measurements are interpreted in the framework of the strong-coupling theory, including the Nernst effect and normal state diamagnetism. Remarkably, a similar strong-coupling approach offers a simple explanation of CMR in ferromagnetic oxides, while the conventional double-exchange (DEX) model, proposed half a century ago and generalised more recently to include the electron-phonon interaction, is in conflict with a number of modern experiments. Among these experiments are site-selective spectroscopies, which have shown that oxygen p-holes are current carriers rather than d-electrons in ferromagnetic manganites (and in cuprates) ruling out DEX mechanism of CMR. Also some samples of ferromagnetic manganites manifest an insulating-like optical conductivity at all temperatures contradicting the DEX notion that their ferromagnetic phase is metallic. On the other hand, the pairing of oxygen holes into heavy bipolarons in the paramagnetic phase and their magnetic pair-breaking in the ferromagnetic phase account for the first-order ferromagnetic phase transition, CMR, isotope effects, and pseudogaps in doped manganites. Here we propose an explanation of the phase coexistence and describe the shape of resistivity of manganites near the transition in the framework of the strong-coupling approach

Strings in charge-transfer Mott insulators: effects of lattice vibrations and the Coulomb interaction

Applying the canonical transformation with the 1/\lambda perturbation expansion in the nonadiabatic and intermediate regime and the discrete generalisation of Pekar's continuous nonlinear equation in the extreme adiabatic regime we show that there are no strings in narrow-band ionic insulators due to the Frohlich electron-phonon interaction alone. The multi-polaron system is a homogeneous state in a wide range of physically interesting parameters, no matter how strong correlations are. At the same time the Frohlich interaction allows the antiferromagnetic interactions and/or a short-range electron-phonon interactions to form short strings in doped antiferromagnetic insulators if the static dielectric constant is large enough