Isotope effects in high-Tc cuprate superconductors: Ultimate proof for bipolaron theory of superconductivity

Developing a theory of high-temperature superconductivity in copper oxides is one of the outstanding problems in physics. Twenty-five years after its discovery, no consensus on the microscopic theory has been reached despite tremendous theoretical and experimental efforts. Attempts to understand this problem are hindered by the subtle interplay among a few mechanisms and the presence of several nearly degenerate and competing phases in these systems. Here we provide unified parameter-free explanation of the observed oxygen-isotope effects on the critical temperature, the magnetic-field penetration depth, and on the normal-state pseudogap for underdoped cuprate superconductors within the framework of the bipolaron theory compatible with the strong Coulomb and Froehlich interactions, and with many other independent observations in these highly polarizable doped insulators. Remarkably, we also quantitatively explain measured critical temperatures and magnitudes of the magnetic-field penetration depth. The present work thus represents an ultimate proof of the bipolaron theory of high-temperature superconductivity, which takes into account essential Coulomb and electron-phonon interactions.Comment: 8 pages, 2 figure

Decomposing CO2 emissions data into a pair of logistic growth pulses

Numerous scenarios of emissions growth presume that it can not grow infinitely: there are certain limits that may not or must not be exceeded. Applying the theory of pulsing logistic growth, I detected two pulses of logistic growth. This led me to the conclusion that constructing a scenario of emissions growth one should pay attention to the fact that limits to their growth do not remain constant

Key pairing interaction in layered doped ionic insulators

A controversial issue on whether the electron-phonon interaction (EPI) is crucial for high-temperature superconductivity or it is weak and inessential has remained one of the most challenging problems of contemporary condensed matter physics. We employ a continuum RPA approximation for the dielectric response function allowing for a selfconsistent semi-analytical evaluation of the EPI strength, electron-electron attractions, and the carrier mass renormalisation in layered high-temperature superconductors. We show that the Fr\"{o}hlich EPI with high-frequency optical phonons in doped ionic lattices is the key pairing interaction, which is beyond the BCS-Migdal-Eliashberg approximation in underdoped superconductors, and it remains a significant player in overdoped compounds.Comment: 4 pages, 4 figure

Theory of SIS tunnelling in cuprates

We show that the single-particle polaron Green's function describes SIS tunnelling in cuprates, including the absence of Ohm's law at high voltages, the dip/hump features in the first derivative of the current, a substantial incoherent spectral weight beyond quasiparticle peaks and unusual shape of the peaks. The theory allows us to determine the characteristic phonon frequencies, normal and superconducting gaps, impurity scattering rate, and the electron-phonon coupling from the tunnelling data.Comment: 10 pages, 2 figure

Green's and spectral functions of the small Frolich polaron

According to recent Quantum Monte Carlo simulations the small polaron theory is practically exact in a wide range of the long-range (Frohlich) electron-phonon coupling and adiabatic ratio. We apply the Lang-Firsov transformation to convert the strong-coupling term in the Hamiltonian into the form of an effective hopping integral and derive the single-particle Green's function describing propagation of the small Frohlich polaron. One and two dimensional spectral functions are studied by expanding the Green's function perturbatively. Numerical calculations of the spectral functions are produced. Remarkably, the coherent spectral weight (Z) and effective mass (Z') renormalisation exponents are found to be different with Z'>>Z, which can explain a small coherent spectral weight and a relatively moderate mass enhancement in oxides.Comment: RevTeX, 5 pages, 2 postscript figures, LaTeX processing problems correcte

Photoemission spectroscopy and sum rules in dilute electron-phonon systems

A family of exact sum rules for the one-polaron spectral function in the low-density limit is derived. An algorithm to calculate energy moments of arbitrary order of the spectral function is presented. Explicit expressions are given for the first two moments of a model with general electron-phonon interaction, and for the first four moments of the Holstein polaron. The sum rules are linked to experiments on momentum-resolved photoemission spectroscopy. The bare electronic dispersion and the electron-phonon coupling constant can be extracted from the first and second moments of spectrum. The sum rules could serve as constraints in analytical and numerical studies of electron-phonon models.Comment: 4 page

On choice of connection in loop quantum gravity

We investigate the quantum area operator in the loop approach based on the Lorentz covariant hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz connections giving rise to Wilson lines which are eigenstates of the area operator. For each connection the area spectrum is evaluated. In particular, the results of the su(2) approach turn out to be included in the formalism. However, only one connection from the family is a spacetime connection ensuring that the 4d diffeomorphism invariance is preserved under quantization. It leads to the area spectrum independent of the Immirzi parameter. As a consequence, we conclude that the su(2) approach must be modified accordingly to the results obtained since it breaks one of the classical symmetries.Comment: 11 pages, RevTEX; minor changes; a sign mistake correcte

High Temperature Superconductivity: the explanation

Soon after the discovery of the first high temperature superconductor by Georg Bednorz and Alex Mueller in 1986 the late Sir Nevill Mott answering his own question "Is there an explanation?" [Nature v 327 (1987) 185] expressed a view that the Bose-Einstein condensation (BEC) of small bipolarons, predicted by us in 1981, could be the one. Several authors then contemplated BEC of real space tightly bound pairs, but with a purely electronic mechanism of pairing rather than with the electron-phonon interaction (EPI). However, a number of other researchers criticized the bipolaron (or any real-space pairing) scenario as incompatible with some angle-resolved photoemission spectra (ARPES), with experimentally determined effective masses of carriers and unconventional symmetry of the superconducting order parameter in cuprates. Since then the controversial issue of whether the electron-phonon interaction (EPI) is crucial for high-temperature superconductivity or weak and inessential has been one of the most challenging problems of contemporary condensed matter physics. Here I outline some developments in the bipolaron theory suggesting that the true origin of high-temperature superconductivity is found in a proper combination of strong electron-electron correlations with a significant finite-range (Froehlich) EPI, and that the theory is fully compatible with the key experiments.Comment: 8 pages, 2 figures, invited comment to Physica Script