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

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

The "normal" state of superconducting cuprates might really be normal after all

High magnetic field studies of cuprate superconductors revealed a non-BCS temperature dependence of the upper critical field $H_{c2}(T)$ determined resistively by several groups. These determinations caused some doubts on the grounds of both the contrasting effect of the magnetic field on the in-plane and out-of-plane resistances reported for large Bi2212 sample and the large Nernst signal \emph{well above} $T_{c}$. Here we present both $\rho_{ab}(B)$ and $\rho_{c}(B)$ of tiny Bi2212 crystals in magnetic fields up to 50 Tesla. None of our measurements revealed a situation when on the field increase $\rho_c$ reaches its maximum while $\rho_{ab}$ remains very small if not zero. The resistive %upper critical fields estimated from the in-plane and out-of-plane $H_{c2}(T)$ estimated from $\rho_{ab}(B)$ and $\rho_{c}(B)$ are approximately the same. Our results support any theory of cuprates that describes the state above the resistive phase transition as perfectly normal with a zero off-diagonal order parameter. In particular, the anomalous Nernst effect above the resistive phase transition in high-$T_{c}$ cuprates can be described quantitatively as a normal state phenomenon in a model with itinerant and localised fermions and/or charged bosons

Nernst effect in poor conductors and the cuprate superconductors

We calculate the Nernst signal in disordered conductors with the chemical potential near the mobility edge. The Nernst effect originates from interference of itinerant and localised-carrier contributions to the thermomagnetic transport. It reveals a strong temperature and magnetic field dependence, which describes quantitatively the anomalous Nernst signal in high-Tc cuprates.Comment: 4 pages, 2 figures, thermopower is discussed, Fig.1 change

How normal is the "normal" state of superconducting cuprates?

High magnetic field studies of the cuprate superconductors revealed a non-BCS temperature dependence of the upper critical field $H_{c2}(T)$ determined resistively by several groups. These determinations caused some doubts on the grounds of the contrasting effect of the magnetic field on the in-plane, $\rho_{ab}$, and out-of-plane, $\rho_{c}$ resistances reported for large sample of Bi2212. Here we present careful measurements of both $\rho_{ab}(B)$ and $\rho_{c}(B)$ of tiny Bi2212 crystals in magnetic fields up to 50 Tesla. None of our measurements revealed a situation when on field increase $\rho_c$ reaches its maximum while $\rho_{ab}$ remains very small if not zero. The resistive $H_{c2}(T)$ estimated from $\rho_{ab}(B)$ and $\rho_{c}(B)$ are approximately the same. We also present a simple explanation of the unusual Nernst signal in superconducting cuprates as a normal state phenomenon. Our results support any theory of cuprates, which describes the state above the resistive phase transition as perfectly 'normal' with a zero off-diagonal order parameter

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

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

C-axis negative magnetoresistance and upper critical field of Bi2Sr2CaCu2O8

The out-of-plane resistance and the resistive upper critical field of BSCCO-2212 single crystals with Tc=91-93 K have been measured in magnetic fields up to 50 T over a wide temperature range. The results are characterised by a positive linear magnetoresistance in the superconducting state and a negative linear magnetoresistance in the normal state. The zero field normal state c-axis resistance, the negative linear normal state magnetoresistance, and the divergent upper critical field Hc2(T)are explained in the framework of the bipolaron theory of superconductivity.Comment: 4 pages (REVTeX), 4 figures, submitted to Physical Review Letters 6 April 1999, rejected in February 2000, accepted for publication in Europhysics Letters on 31 May 200

Polaron and bipolaron transport in a charge segregated state of doped strongly correlated 2D semiconductor

The 2D lattice gas model with competing short and long range interactions is appliedused for calculation of the incoherent charge transport in the classical strongly-correlated charge segregated polaronic state. We show, by means of Monte-Carlo simulations, that at high temperature the transport is dominated by hopping of the dissociated correlated polarons, where with thetheir mobility is inversely proportional to the temperature. At the temperatures below the clustering transition temperature the bipolaron transport becomes dominant. The energy barrier for the bipolaron hopping is determined by the Coulomb effects and is found to be lower than the barrier for the single-polaron hopping. This leads to drastically different temperature dependencies of mobilities for polarons and bipolarons at low temperatures