Breakdown of the Wiedemann-Franz law in strongly-coupled electron-phonon system, application to the cuprates

With the superconducting cuprates in mind, a set of unitary transformations was used to decouple electrons and phonons in the strong-coupling limit. While phonons remain almost unrenormalised, electrons are transformed into itinerent singlet and triplet bipolarons and thermally excited polarons. The triplet/singlet exchange energy and the binding energy of the bipolarons are thought to account for the spin and charge pseudogaps in the cuprates, respectively. We calculated the Hall Lorenz number of the system to show that the Wiedemann-Franz law breaks down due to the interference of the polaron and bipolaron contributions to heat flow. The model provides a quantitative fit to magnetotransport data in the cuprates. Furthermore we are able to extract the phonon component of the thermal conductivity with the use of experimental data and the model. Our results further validate the use of a charged Bose gas model to describe normal and superconducting properties of unconventional superconductors.Comment: 9 pages, 6 figures. Submitted to Physical Review

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

Coherent `ab' and `c' transport theory of high-TcT_{c} cuprates

We propose a microscopic theory of the `$c$'-axis and in-plane transport of copper oxides based on the bipolaron theory and the Boltzmann kinetics. The fundamental relationship between the anisotropy and the spin susceptibility is derived, $\rho_{c}(T,x)/\rho_{ab}(T,x)\sim x/\sqrt{T}\chi_{s}(T,x)$. The temperature $(T)$ and doping $(x)$ dependence of the in-plane, $\rho_{ab}$ and out-of-plane, $\rho_{c}$ resistivity and the spin susceptibility, $\chi_{s}$ are found in a remarkable agreement with the experimental data in underdoped, optimally and overdoped $La_{2-x}Sr_{x}CuO_{4}$ for the entire temperature regime from $T_{c}$ up to $800K$. The normal state gap is explained and its doping and temperature dependence is clarified.Comment: 12 pages, Latex, 3 figures available upon reques

R3R^3 index for four-dimensional N=2N=2 field theories

In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay across walls of marginal stability in the space of Coulomb branch parameters, leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a supersymmetric index $I$ which receives contributions from 1/2-BPS states, generalizing the familiar Witten index $Tr (-1)^F e^{-\beta H}$. We expect $I$ to be smooth away from loci where massless particles appear, thanks to contributions from the continuum of multi-particle states. Taking inspiration from a similar phenomenon in the hypermultiplet moduli space of $N=2$ string vacua, we conjecture a formula expressing $I$ in terms of the BPS indices $\Omega(\gamma,u)$, which is continuous across the walls and exhibits the expected contributions from single particle states at large $\beta$. This gives a universal prediction for the contributions of multi-particle states to the index $I$. This index is naturally a function on the moduli space after reduction on a circle, closely related to the canonical hyperk\"ahler metric and hyperholomorphic connection on this space.Comment: 7 pages; v2: introduction expanded, minor corrections, differs from published version in PRL in that supplemental material is included as an Appendi

A mechanism for pair formation in strongly correlated systems

We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved exactly. In the ground state, part of the electrons form bound pairs with opposite momentum and spin. The model also shows a gap in the kinetic energy of the fermions, but not in the spectrum of the full Hamiltonian. This gap is not of a mean-field nature, but is due to the Pauli exclusion principle.Comment: 13 pages, corrected some notations and made some clarification

Plebanski Theory and Covariant Canonical Formulation

We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert-Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed.Comment: 18 page

Diamagnetism of real-space pairs above Tc in hole doped cuprates

The nonlinear normal state diamagnetism reported by Lu Li et al. [Phys. Rev. B 81, 054510 (2010)] is shown to be incompatible with an acclaimed Cooper pairing and vortex liquid above the resistive critical temperature. Instead it is perfectly compatible with the normal state Landau diamagnetism of real-space composed bosons, which describes the nonlinear magnetization curves in less anisotropic cuprates La-Sr-Cu-O (LSCO) and Y-Ba-Cu-O (YBCO) as well as in strongly anisotropic bismuth-based cuprates in the whole range of available magnetic fields.Comment: 4 pages, 4 figure

Theory of Superconducting TcT_{c} of doped fullerenes

We develop the nonadiabatic polaron theory of superconductivity of $M_{x}C_{60}$ taking into account the polaron band narrowing and realistic electron-phonon and Coulomb interactions. We argue that the crossover from the BCS weak-coupling superconductivity to the strong-coupling polaronic and bipolaronic superconductivity occurs at the BCS coupling constant $\lambda\sim 1$ independent of the adiabatic ratio, and there is nothing ``beyond'' Migdal's theorem except small polarons for any realistic electron-phonon interaction. By the use of the polaronic-type function and the ``exact'' diagonalization in the truncated Hilbert space of vibrons (``phonons'') we calculate the ground state energy and the electron spectral density of the $C_{60}^{-}$ molecule. This allows us to describe the photoemission spectrum of $C_{60}^{-}$ in a wide energy region and determine the electron-phonon interaction. The strongest coupling is found with the high-frequency pinch $A_{g2}$ mode and with the Frenkel exciton. We clarify the crucial role of high-frequency bosonic excitations in doped fullerenes which reduce the bare bandwidth and the Coulomb repulsion allowing the intermediate and low-frequency phonons to couple two small polarons in a Cooper pair. The Eliashberg-type equations are solved for low-frequency phonons. The value of the superconducting $T_{c}$, its pressure dependence and the isotope effect are found to be in a remarkable agreement with the available experimental data.Comment: 20 pages, Latex, 4 figures available upon reques

Cut-and-Join operator representation for Kontsevich-Witten tau-function

In this short note we construct a simple cut-and-join operator representation for Kontsevich-Witten tau-function that is the partition function of the two-dimensional topological gravity. Our derivation is based on the Virasoro constraints. Possible applications of the obtained expression are discussed.Comment: 5 pages, minor correction

Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop Gravity

In the search for a covariant formulation for Loop Quantum Gravity, spin foams have arised as the corresponding discrete space-time structure and, among the different models, the Barrett-Crane model seems the most promising. Here, we study its boundary states and introduce cylindrical functions on both the Lorentz connection and the time normal to the studied hypersurface. We call them projected cylindrical functions and we explain how they would naturally arise in a covariant formulation of Loop Quantum Gravity.Comment: Latex, 15 page