Enhanced stability of bound pairs at nonzero lattice momenta

A two-body problem on the square lattice is analyzed. The interaction potential consists of strong on-site repulsion and nearest-neighbor attraction. Exact pairing conditions are derived for s-, p-, and d-symmetric bound states. The pairing conditions are strong functions of the total pair momentum K. It is found that the stability of pairs increases with K. At weak attraction, the pairs do not form at the $\Gamma$-point but stabilize at lattice momenta close to the Brillouin zone boundary. The phase boundaries in the momentum space, which separate stable and unstable pairs are calculated. It is found that the pairs are formed easier along the $(\pi,0)$ direction than along the $(\pi,\pi)$ direction. This might lead to the appearance of ``hot pairing spots" on the Kx and Ky axes.Comment: 7 RevTEX pages, 5 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

Isotope effect on the electron band structure of doped insulators

Applying a continuous-time quantum Monte-Carlo algorithm we calculate the exact coherent band dispersion and the density of states of a two dimensional lattice polaron in the region of parameters where any approximation might fail. We find an isotope effect on the band structure, which is different for different wave-vectors of the Brillouin zone and depends on the radius and strength of the electron-phonon interaction. An isotope effect on the electron spectral function is also discussed.Comment: 4 pages, 3 figure

High temperature superconductivity and charge segregation in a model with strong long-range electron-phonon and Coulomb interactions

An analytical method of studying strong long-range electron-phonon and Coulomb interactions in complex lattices is presented. The method is applied to a perovskite layer with anisotropic coupling of holes to the vibrations of apical atoms. Depending on the relative strength of the polaronic shift, Ep, and the inter-site Coulomb repulsion, Vc, the system is either a polaronic Fermi liquid, Vc > 1.23 Ep, a bipolaronic superconductor, 1.16 Ep < Vc < 1.23 Ep, or a charge segregated insulator, Vc < 1.16 Ep. In the superconducting window, the carriers are mobile bipolarons with a remarkably low effective mass. The model describes the key features of the underdoped superconducting cuprates.Comment: 5 pages, 2 figures (1 color

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

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

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

Superlight small bipolarons

Recent angle-resolved photoemission spectroscopy (ARPES) has identified that a finite-range Fr\"ohlich electron-phonon interaction (EPI) with c-axis polarized optical phonons is important in cuprate superconductors, in agreement with an earlier proposal by Alexandrov and Kornilovitch. The estimated unscreened EPI is so strong that it could easily transform doped holes into mobile lattice bipolarons in narrow-band Mott insulators such as cuprates. Applying a continuous-time quantum Monte-Carlo algorithm (CTQMC) we compute the total energy, effective mass, pair radius, number of phonons and isotope exponent of lattice bipolarons in the region of parameters where any approximation might fail taking into account the Coulomb repulsion and the finite-range EPI. The effects of modifying the interaction range and different lattice geometries are discussed with regards to analytical strong-coupling/non-adiabatic results. We demonstrate that bipolarons can be simultaneously small and light, provided suitable conditions on the electron-phonon and electron-electron interaction are satisfied. Such light small bipolarons are a necessary precursor to high-temperature Bose-Einstein condensation in solids. The light bipolaron mass is shown to be universal in systems made of triangular plaquettes, due to a novel crab-like motion. Another surprising result is that the triplet-singlet exchange energy is of the first order in the hopping integral and triplet bipolarons are heavier than singlets in certain lattice structures at variance with intuitive expectations. Finally, we identify a range of lattices where superlight small bipolarons may be formed, and give estimates for their masses in the anti-adiabatic approximation.Comment: 31 pages. To appear in J. Phys.: Condens. Matter, Special Issue 'Mott's Physics

Reply to "Comment on 'Origin of combination frequencies in quantum magnetic oscillations of two-dimensional multiband metals' " by A.S. Alexandrov and A.M. Bratkovsky [cond-mat/0207173]

In their comment on the paper (Phys. Rev. B 65, 153403 (2002); cond-mat/0110154), Alexandrov and Bratkovsky (cond-mat/0207173) argue that they correctly took into account the chemical potential oscillations in their analytical theory of combination frequencies in multiband low-dimensional metals by expanding the free energy in powers of the chemical potential oscillations. In this reply, we show that this claim contradicts their original paper (Phys. Rev. B 63, 033105 (2001)). We demonstrate that the condition given for the expansion is mathematically incorrect. The correct condition allows to understand the limits of validity of the analytical theory.Comment: 4 page

Hall effect and resistivity in underdoped cuprates

The behaviour of the Hall ratio $R_{H}(T)$ as a function of temperature is one of the most intriguing normal state properties of cuprate superconductors. One feature of all the data is a maximum of $R_{H}(T)$ in the normal state that broadens and shifts to temperatures well above $T_c$ with decreasing doping. We show that a model of preformed pairs-bipolarons provides a selfconsistent quantitative description of $R_{H}(T)$ together with in-plane resistivity and uniform magnetic susceptibility for a wide range of doping.Comment: 4 pages, 2 figures, the model and fits were refine