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arXiv:cond-mat/9512143 · Physical review. B, Condensed matter

Polarons and bipolarons in strongly interacting electron-phonon systems

Gerhard Wellein, Heinrich Röder, Holger Fehske

Published Apr 15, 1996• 163 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.53.9666

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We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.

arXiv:cond-mat/9911218•Physical review. B, Condensed matter•Mar 15, 2000•96 citations
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.
Polaronic features of dopant-induced charge carriers are manifest in recent experiments on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4+y{\mathrm{CuO}}_{4+\mathit{y}}CuO4+y​ and ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Nix{\mathrm{Ni}}_{\mathit{x}}Nix​CuO4+y{\mathrm{CuO}}_{4+\mathit{y}}CuO4+y​. To study the formation of hole (bi)polarons in such systems exhibiting strong Coulomb interactions, the Holstein t-J model is examined by means of a variational diagonalization technqiue for a wide range of phonon frequencies and electron-phonon (EP) couplings on finite square lattices, up to 18 effective sites in size. Including static displacement field, polaron, and squeezing effects, our approach allows for the description of nearly free polarons in the weak-coupling limit as well as for adiabatic Holstein polarons and nonadiabatic Lang-Firsov polarons in the case of strong EP interactions. At low doping levels and low phonon frequencies we demonstrate that antiferromagnetic spin correlations and EP interactions reinforce each other to the effect of lowering the threshold for polaronic self-localization in a strongly distorted lattice. This is contrasted with the nonadiabatic regime, where we observe the formation of Lang-Firsov polarons with moderate polaronic mass enhancement in a nearly undistorted lattice. In the case of two doped holes, the hole binding energy is analyzed in detail and we find that hole binding is enhanced as a dynamical (static) effect of a rather weak (extremely strong) EP interaction for delocalized (self-trapped) polarons. At quarter-filling we notice, in the adiabatic regime, a sequence of transitions as the EP coupling increases from nearly free mobile polarons to a polaronic superlattice and finally to a charge-separated state. The ordering of polarons disappears at higher phonon frequencies.
We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion UUU and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large UUU at intermediate and large electron-phonon coupling, corresponding to two polarons bound on nearest-neighbor sites. We discuss both the properties of the different bipolaron states and the transition from one state to another. We present a phase diagram in parameter space defined by the electron-phonon coupling and UUU. Our numerical method does not use any artificial approximation and can be easily modified to other bipolaron models with longer range electron-phonon and∕or electron-electron interaction.
We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency ω 0 . Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case ω 0 < t , the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic ( i.e. , extremely localized) regime ε pol overcomes the energy of the purely electronic system ε el . In the antiadiabatic case, ω 0 > t , polaron formation is instead driven by the condition of a large ionic displacement g / ω 0 < 1 ( g being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed.
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:
missing to date is an application of the powerful ED technique to the calculation of dynamical properties of the Holstein t--J model (HtJM), including the full quantum nature of phonons. In this contribution, we employ the Lanczos algorithm in combination with a kernel polynomial moment expansion and the Maximum Entropy method [5] to investigate the quasiparticle spectrum of a single hole--polaron in the 2D HtJM on a ten--site square lattice. Moreover, we compute different hole--hole/phonon correlation functions at higher doping level in order to comment on hole--binding effects and charge-densitywave (CDW) formation. The HtJM is described by the Hamiltonian [4] H = H ph + H t\\GammaJ \\Gamma p " p ¯h! X i \\Gamma b y i + b i \\Delta ~ h i<F25.
We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.