Motivated by aspects of layered high-temperature superconductors and related quasi-one-dimensional materials, we consider polaron structure, dynamics, and coherence in certain extended Peierls–Hubbard models. We emphasize the qualitative importance of electron–lattice interactions even in the presence of dominant electron–electron correlations, the signatures of polaron structure and dynamics in energy-resolved pair-distribution structure functions, and the effect of disorder on polaron propagation and stability. Introduction The formation and dynamics of polarons (and bipolarons), despite a halfcentury of theoretical and experimental study, remain fascinating topics in many-body physics, combining as they do (often competing) aspects of coupled fields with distinct natural time scales (e.g., electron–phonon, spin–phonon, exciton–phonon), electron–electron interactions, lattice discreteness, nonadiabaticity, collective quantum tunneling, thermal fluctuations, competitions between disorder and polaronic localization, etc. Direct observation of polarons through real-space imaging of any of the coupled fields is rare even with the advent of STEM , AFM techniques, etc. Likewise, global measurements such as that of electronic band-structure are insensitive to polaron features. Thus, experiments and theoretical techniques have had to focus on indirect effects on microscopic probes such as transport coefficients, electronic absorption, vibrational spectroscopy, and so forth. Our purpose here is to briefly review three qualitative effects in polaron physics that have arisen in modeling two components of the lattice structure of the layered cuprate superconductors [1] – namely, extended multi-band Peierls–Hubbard models of (a) the active CuO 2 planes and (b) polarizable Cu–O clusters in the axial direction (polarizable interplanar medium).
Motivated by aspects of layered high-temperature superconductors and related quasi-one-dimensional materials, we consider polaron structure, dynamics, and coherence in certain extended Peierls–Hubbard models. We emphasize the qualitative importance of electron–lattice interactions even in the presence of dominant electron–electron correlations, the signatures of polaron structure and dynamics in energy-resolved pair-distribution structure functions, and the effect of disorder on polaron propagation and stability. Introduction The formation and dynamics of polarons (and bipolarons), despite a halfcentury of theoretical and experimental study, remain fascinating topics in many-body physics, combining as they do (often competing) aspects of coupled fields with distinct natural time scales (e.g., electron–phonon, spin–phonon, exciton–phonon), electron–electron interactions, lattice discreteness, nonadiabaticity, collective quantum tunneling, thermal fluctuations, competitions between disorder and polaronic localization, etc. Direct observation of polarons through real-space imaging of any of the coupled fields is rare even with the advent of STEM , AFM techniques, etc. Likewise, global measurements such as that of electronic band-structure are insensitive to polaron features. Thus, experiments and theoretical techniques have had to focus on indirect effects on microscopic probes such as transport coefficients, electronic absorption, vibrational spectroscopy, and so forth. Our purpose here is to briefly review three qualitative effects in polaron physics that have arisen in modeling two components of the lattice structure of the layered cuprate superconductors [1] – namely, extended multi-band Peierls–Hubbard models of (a) the active CuO 2 planes and (b) polarizable Cu–O clusters in the axial direction (polarizable interplanar medium).
An enormous theoretical effort has been made to treat electron-phonon coupled systems, with particular emphasis on Many Body aspects for dense electron systems, taking into account continuum as well as lattice polaron effects. Treating such aspects of polaron theory has been made possible because of powerful Many Body techniques which include: Exact Diagonalization techniques, Quantum Monte Carlo approaches, Density Matrix renormalization group and Dynamical Mean Field Theory. All these advances in polaron theory needed to be accompanied by: an equally important advance in material research which produced many new materials such as the high Tc cuprates, the manganites and nickelates and the fullerines; as well as significant advances in the refinement of experimental analysis and, in particular, the spectroscopic means such as Angel Resolved Photoemission Spectroscopy, X Ray Absorption Spectroscopy (EXAFS, XANES), Pulsed Neutron Diffraction measurements allowing to study the local dynamical lattice de-formations and optical spectroscopy including time resolved measurements. The scope and purpose of this publication is to review both these theoretical and experimental advances which occurred over the last few decades and to introduce the study of such systems, where both strong electron-electron correlations and large electron-phonon coupling strengths play important roles.
We review a series of exact, analytical and numerical results obtained on the adiabatic Holstein–Hubbard model, many of which are new and non-trivial. We study next the role of the quantum lattice fluctuations that were initially neglected. The possibility of having high- T c bipolaronic superconductors is analysed on the basis of these results. We suggest that models that involve only electron–phonon coupling are very unlikely to produce bipolaronic superconductivity, which is prevented by the spatial ordering of the bipolarons associated with a lattice instability. This is due to a very large effective mass of the bipolarons that can be related to the large Peierls–Nabarro energy barrier required to move these bipolarons through the lattice in the adiabatic limit. We conjecture that high- T c superconductivity originates specifically from the exceptionally well-balanced competition between electron–phonon coupling and electron–electron repulsion. In the restricted region in which, within the mean field approach, the energy of a bipolaron is close to those of two polarons, a new type of electron pairing occurs by formation of pairs of polarons in the spin singlet state. Such a polaron pair, called a spin resonant bipolaron (SRB), is not the standard bipolaron (both could exist in the adiabatic case). Its Peierls–Nabarro energy barrier can be sharply depressed, almost to zero. As a result of quantum lattice fluctuations, its tunnelling energy is sharply enhanced. Then, superconductivity could persist for a relatively large electron–phonon coupling, with an unusually large critical temperature as a Bose condensate of SRBs before becoming, at larger coupling and in any case, an insulating spin–Peierls polaronic phase.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.
As ones know,the polaron is a quasiparticle formed by an electron and phonons.Due to Coulomb interaction,the electron will make the lattice deformation take place,meanwhile,the deformation potential(induced) by the lattice deformation will exert on the electron,the electron-phonon interaction influence doubtless on the state of motion of an electron,for example,the energy band and effective mass of an electron could change by the interaction,the electron can also be trapped by the deformable lattice,therefore,the research on the(polaron) is very important in understanding optical and transport properties of a solid. Studying electron-phonon interaction has been a main subject in condensed matter physics;in experiments,the influences of the temperature on the forbidden-band width of semiconductors have been observed very early,with the increase of the temperature,the forbidden-band width of most semiconductors will narrow,but a few will widen,these situations are closely relevant to the electron-phonon interaction.In particular,(recently),a large amount of experimental results,ranging from infrared spectroscopy to transport properties(involving) the colossal magnetoresistance and high-T_c superconductivity,has pointed out the importance of the electron-phonon interaction,which has renewed the interest in studying the models of the electron-phonon(coupled) system,especially,the Holstein polaron,for its relative simplicity,is the most considered model for the interaction of a single tight-binding electron coupled to phonons. In the past several decades,the Holstein poloron has been studied in detail in one-dimensional lattices,various theoretical methods,such as variational approaches,the Global-Local variational method,the(coherent)-state expansion method,have been developed to study features of the Holstein polaron including ground-state energy,polaron energy band,effective mass and so on.However,so far,the work considering the influences of the temperature on features of the Holstein polaron is little still. The main aim of this paper is to investigate the influences of the temperature on the energy-band width and the effective mass of the Holstein polaron by using the canonical transformation method.It is shown that,at certain coupling strength,the energy-band width of the Holstein polaron will narrow and the effective mass will augment with the increase of the temperature,in particular,when electron-phonon coupling strength is big enough,the energy-band width will become zero rapidly in small region of temperature,in fact,the situation is rapid transition of the polaron from the energy-band state to the self-trapping local state,this is an(interesting) result obtained in the paper.It is obvious that these features of the Holstein polaron are very useful in explaining optical and transport properties of a solid.
We investigate the interplay of electron–phonon (EP) coupling and strong electronic correlations in the frame of the two–dimensional (2D) Holstein t–J model (HtJM), focusing on polaronic ordering phenomena for the quarter–filled band case. The use of direct Lanczos diagonalization on finite lattices allows us to include the effects of quantum phonon fluctuations in the calculation of spin/charge structure factors and hole–phonon correlation functions. In the adiabatic strong coupling regime we found evidence for “self-localization ” of polaronic carriers in a (π, π) charge-modulated structure, a type of superlattice solidification reminiscent of those observed in the nickel perovskites La2−xSrxNiO4+y. Electron diffraction measurements on the nickel oxide analogue of the layered high–Tc 214 copper oxide compound, La2−xNixCuO4, reveal a (π, π)–superstructure spot at quarter filling, i.e. for x = 0.5, which has been interpreted as sign of a truly 2D polaron ordered phase [1]. To study charge – and spin–ordering phenomena in such systems, exhibiting besides a substantial EP interaction strong Coulomb correlations, let us consider the planar t-J model with an additional on-site Holstein hole-phonon coupling:
In this thesis, I investigate the behavior of particles dressed by quantum field excitations and random interactions. First I consider two-carrier states in the Peierls model describing the modulation of the particle hopping due to lattice distortions. I compute the spectral response using the Momentum Average approximation. Combining accurate numerical techniques and analytical arguments, I provide a complete picture of the Peierls bipolarons. It is found that polarons bind into strongly bound yet light bipolarons in the singlet sector, even at large values of the electron-phonon coupling strength. At finite electron fillings, these bipolarons may condense into a high-Tc superconductor. On the other hand, phonons mediate a repulsive interaction in the triplet sector, or equivalently (in one dimension), between two hard-core particles, in which case the ground-state dimers bound by sufficiently attractive bare interactions exhibit two sharp transitions, one of which is the first known example of a self-trapping transition at the two-carrier level. In both situations, phonons mediate pair-hopping effective interactions between the carriers. I further study some aspects of the excited spectrum for the two hard-core particles, a situation relevant to ultracold quantum simulators. It is found that the repulsive phonon-mediated interaction binds a repulsive bipolaron embedded in the excited spectrum. I then turn to the study of quenched randomness in an ultracold molecular plasma. I argue that the quenched ultracold plasma presents an experimental platform for studying quantum many-body physics of disordered systems in the long-time and finite energy-density limits. I analyze an experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, ions and electrons that exhibits a long-lived state of arrested relaxation. The qualitative features of this state fail to conform with classical models. I develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model appears to offer a way to envision the essential quantum disordered non-equilibrium physics of this system. This thesis thus examines the quantum many-body response in interacting systems coupled to bosonic fields or in disordered environments.