A. S. Alexandrov

Carrier Density Collapse and Colossal Magnetoresistance in Doped Manganites

A novel ferromagnetic transition, accompanied by carrier density collapse, is found in doped charge-transfer insulators with strong electron-phonon coupling. The transition is driven by an exchange interaction of polaronic carriers with localized spins; the strength of the interaction determines whether the transition is first or second order. A giant drop in the number of current carriers during the transition, which is a consequence of bound pairs formation in the paramagnetic phase close to the transition, is extremely sensitive to an external magnetic field. This carrier density collapse describes the resistivity peak and the colossal magnetoresistance of doped manganites.

Fröhlich polaron and bipolaron: recent developments

It is remarkable how the Frohlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since ~1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalization (ED) and quantum Monte Carlo (QMC) techniques. This paper reviews recent developments in the field of continuum and discrete (lattice) Frohlich (bi)polarons starting with the basics and covering a number of active directions of research.

Advances in polaron physics

Continuum Polaron.- Lattice Polaron.- Bipolaron.- Multipolaron Problem.- Polarons and Bipolarons in Advanced Materials.- Current Status of Polarons and Open Problems.

Electron-Phonon Coupling in High-Temperature Cuprate Superconductors Determined from Electron Relaxation Rates

We determined electronic relaxation times via pump-probe optical spectroscopy using sub-15 fs pulses for the normal state of two different cuprate superconductors. We show that the primary relaxation process is the electron-phonon interaction and extract a measure of its strength, the second moment of the Eliashberg function λ[ω2] = 800 ± 200 meV2 for La(1.85)Sr(0.15)CuO4 and λ[ω2] = 400 ± 100 meV2 for YBa(2)Cu(3)O(6.5). These values suggest a possible fundamental role of the electron-phonon interaction in the superconducting pairing mechanism.

The Fröhlich-Coulomb model of high-temperature superconductivity and charge segregation in the cuprates

We introduce a generic Frohlich-Coulomb model of the oxides, which also includes infinite on-site (Hubbard) repulsion, and describe a simple analytical method of solving the multi-polaron problem in complex lattice structures. Two particular lattices, a zigzag ladder and a perovskite layer, are studied. We find that, depending on the relative strength of the Frohlich and Coulomb interactions, these systems are either polaronic Fermi (or Luttinger) liquids, bipolaronic superconductors, or charge-segregated insulators. In the superconducting phase the carriers are superlight mobile bipolarons. The model describes key features of the cuprates such as their Tc-values, the isotope effects, the normal-state diamagnetism, the pseudogap, and spectral functions measured in tunnelling and photoemission. We argue that a low Fermi energy and strong coupling of carriers with high-frequency phonons is the cause of high critical temperatures in novel superconductors.

Current-controlled negative differential resistance due to Joule heating in TiO2

We show that Joule heating causes current-controlled negative differential resistance (CC-NDR) in TiO2 by constructing an analytical model of the voltage-current V(I) characteristic based on polaronic transport for Ohm’s Law and Newton’s Law of Cooling and fitting this model to experimental data. This threshold switching is the “soft breakdown” observed during electroforming of TiO2 and other transition-metal-oxide based memristors, as well as a precursor to “ON” or “SET” switching of unipolar memristors from their high to their low resistance states. The shape of the V(I) curve is a sensitive indicator of the nature of the polaronic conduction.

Phase Coexistence and Resistivity near the Ferromagnetic Transition of Manganites

Pairing of oxygen holes into heavy bipolarons in the paramagnetic phase and their magnetic pair breaking in the ferromagnetic phase (the so-called current-carrier density collapse) has accounted for the first-order ferromagnetic-phase transition, colossal magnetoresistance, isotope effect, and pseudogap in doped manganites. Here we propose an explanation of the phase coexistence and describe the magnetization and resistivity of manganites near the ferromagnetic transition in the framework of the current-carrier density collapse. The present quantitative description of resistivity is obtained without any fitting parameters, by using the experimental resistivities far away from the transition and the experimental magnetization, and is essentially model-independent.

High-Tc cuprates: a new electronic state of matter?

Abstract The observation of high-temperature superconductivity in complex, layered cuprates by Bednorz and Muller must now rate as one of the greatest experimental discoveries of the last century. Identifying and understanding the microscopic origin of high-temperature superconductivity now stands as one of the greatest theoretical challenges as we enter this century. Although we are undeniably some way from a complete understanding of this remarkable natural phenomenon, we believe that evidence is accumulating for a new state of electronic matter, that of a charged Bose liquid of tightly bound pairs of small polarons, i.e., bipolarons. Thus, high-temperature superconductivity in the layered cuprates derives from the Bose–Einstein condensation (BEC) of bipolarons.

Electron relaxation in metals: Theory and exact analytical solutions

The nonequilibrium dynamics of electrons is of a great experimental and theoretical value, providing important microscopic parameters of the Coulomb and electron-phonon interactions in metals and other cold plasmas. Because of the mathematical complexity of collision integrals, theories of electron relaxation often rely on the assumption that electrons are in a “quasiequilibrium” QE with a time-dependent temperature, or on the numerical integration of the time-dependent Boltzmann equation. We transform the integral Boltzmann equation to a partial differential Schrodinger-type equation with imaginary time in a one-dimensional “coordinate” space reciprocal to energy which allows for exact analytical solutions in both cases of electron-electron and electron-phonon relaxations. The exact relaxation rates are compared with the QE relaxation rates at high and low temperatures.

Theory of colossal magnetoresistance in doped manganites

The exchange interaction of polaronic carriers with localized spins leads to a ferromagnetic/paramagnetic transition in doped charge-transfer insulators with strong electron-phonon coupling. The relative strength of the exchange and electron-phonon interactions determines whether the transition is first or second order. A giant drop in the number of current carriers during the transition, which is a consequence of local bound-pair (bipolaron) formation in the paramagnetic phase, is extremely sensitive to an external magnetic field. Below the critical temperature of the transition, , the binding of the polarons into immobile pairs competes with the ferromagnetic exchange between polarons and the localized spins on Mn ions, which tends to align the polaron moments and, therefore, breaks up those pairs. The number of carriers abruptly increases below leading to a sudden drop in resistivity. We show that the carrier-density collapse explains the colossal magnetoresistance of doped manganites close to the transition. Below , transport occurs by polaronic tunnelling, whereas at high temperatures the transport is by hopping processes. The transition is accompanied by a spike in the specific heat, as experimentally observed. The gap feature in tunnelling spectroscopy is related to the bipolaron binding energy, which depends on the ion mass. This dependence explains the giant isotope effect of the magnetization and resistivity upon substitution of for . It is shown also that the localization of polaronic carriers by disorder cannot explain the observed huge sensitivity of the transport properties to the magnetic field in doped manganites.