Abstract We investigate the electronic properties and electron correlations of the bipolaron formed with the participation of electron-hole excitations in the presence of Yukawa-type coupling (between nonrelativistic fermions) in three spatial dimension. The electron-hole excitation, which is necessary to the formation of bipolaron, leads to imaginary particle-hole channel order parameter, and provide finite boson field mass to the single-polaron dispersion in a broken-symmetry phase. We found that the bipolaron exhibits fermi-liquid features as long as the long-range strong interaction is suppressed, and it behave differently compared to the single-polaron. The bosonic momentum determines the mass of boson field propagator and the gap function, and it also related to the self-energies and the single-particle Green’s functions. The Thouless criterion is also used during the calculation of gap equation at critical temperature (which becomes lower in weak-coupling regime), which corresponds to the pole (instability) of the pair propagator in zero center-of-mass freamwork. The mean field term and the bosonic fluctuation-induced contribution to free energy in Aslamazov-Larkin-type bipolaron diagram are also studied.
Abstract We investigate the electronic properties and electron correlations of the bipolaron formed with the participation of electron-hole excitations in the presence of Yukawa-type coupling (between nonrelativistic fermions) in three spatial dimension. The electron-hole excitation, which is necessary to the formation of bipolaron, leads to imaginary particle-hole channel order parameter, and provide finite boson field mass to the single-polaron dispersion in a broken-symmetry phase. We found that the bipolaron exhibits fermi-liquid features as long as the long-range strong interaction is suppressed, and it behave differently compared to the single-polaron. The bosonic momentum determines the mass of boson field propagator and the gap function, and it also related to the self-energies and the single-particle Green’s functions. The Thouless criterion is also used during the calculation of gap equation at critical temperature (which becomes lower in weak-coupling regime), which corresponds to the pole (instability) of the pair propagator in zero center-of-mass freamwork. The mean field term and the bosonic fluctuation-induced contribution to free energy in Aslamazov-Larkin-type bipolaron diagram are also studied.
The Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.
The energies of bipolaron states in three- and two-dimensional systems are calculated variationally, treating the electron-phonon interaction in the Fr\"ohlich approximation, and separating the relative motion from the center-of-mass motion. The bipolaron is bound if the electron-phonon coupling constant \ensuremath{\alpha} is larger than 6 in three dimensions and 2 in two dimensions, provided the ratio \ensuremath{\eta}=${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$/${\mathrm{\ensuremath{\epsilon}}}_{0}$ is smaller than a critical value which depends on \ensuremath{\alpha}. The theory yields the free-polaron energies as given in the Lee, Low, and Pines approximation for arbitrary values of the electron-phonon coupling constant \ensuremath{\alpha}. For \ensuremath{\alpha} larger than \ensuremath{\sim}10 and \ensuremath{\sim}4 in the three- and two-dimensional cases, respectively, the lowest free-polaron self-energies are obtained in the strong-coupling approach; it is shown that a trial harmonic envelope wave function, localized both in the center-of-mass and relative coordinates, with a coherent phonon state gives a bound localized bipolaron state of lower energy. It is interesting for application to high-Tc superconductivity that the bipolaron bounds more easily in two dimensions than in three, and that the mean value of the pair radius is a few angstroms. Furthermore, bipolaron states obtained when the linear total momentum is conserved have intrinsically high mobility, which is also an important condition to make the bipolaron mechanism consistent with high-temperature superconductivity.
In this paper we have studied the properties of a two-fermion system interacting with the phonon field in the framework of the Holstein Hubbard model in one, two and three dimensions. We have chosen the modified Lang-Firsov variational wave function with on-site and nearest-neighbour lattice distortion for the phonon subsystem to obtain an effective electronic Hamiltonian. This effective electronic Hamiltonian is then solved exactly to obtain the binding energy and effective mass of the bipolaron. We investigated the stability of the bipolaronic phase by comparing the ground-state energy of a bipolaron and two free polarons. We observed a critical repulsive on-site Hubbard interaction U c below which the bipolaronic phases are stable for a fixed electron-phonon coupling g . In the absence of on-site repulsion, bipolaronic phases are stable over the entire range of electron-phonon coupling for one dimension, whereas there is a critical electron-phonon coupling g c for formation of a stable bipolaron in two and three dimensions.
The energy of a large bipolaron is calculated for various spacings between the centers of the polarization potential wells of the two polarons with allowance made for electron correlations (i.e., the explicit dependence of the wave function of the system on the distance between the electrons) and for permutation symmetry of the two-electron wave function. The lowest singlet and triplet 23 S states of the bipolaron are considered. The singlet polaron is shown to be stable over the range of ionic-bond parameter values η≤ηm≈0.143 (η=ɛ∞/ɛ0, where ɛ∞ and ɛ 0 are the high-frequency and static dielectric constants, respectively). There is a single energy minimum, corresponding to the single-center bipolaron configuration (similar to a helium atom). The binding energy of the bipolaron for η → 0 is J bp=−0.136512e 4 m */ℏ2ɛ ∞ 2 (e and m* are the charge and effective mass of a band electron), or 25.8% of the double polaron energy. The triplet bipolaron state (similar to an orthohelium atom) is energetically unfavorable in the system at hand. The single-center configuration of the triplet bipolaron corresponds to a sharp maximum in the distance dependence of the total energy J bp(R); therefore, a transition of the bipolaron to the orthostate (e.g., due to exchange scattering) will lead to decay of the bound two-particle state. The exchange interaction between polarons is antiferromagnetic (AFM) in character. If the conditions for the Wigner crystallization of a polaron gas are met, the AFM exchange interaction between polarons can lead to AFM ordering in the system of polarons.
Abstract. The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction υ ≥ 0, which tends to break them, generates many different ground-states. There are four domains in the g,υ phase diagram delimited by first order transition lines. Except for the domain at weak electronphonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small υ, large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large υ, large g); or 3) be a ”quadrisinglet state ” which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron. PACS. 71.10.Fd Lattice fermion models (Hubbard model, etc.) – 71.38.+i Polarons and electron phonon interactions – 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) – 74.25.Jb Electronic structure
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.