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arXiv:cond-mat/0106586 · Physical review. B, Condensed matter

Polaron and bipolaron formation in the Hubbard-Holstein model: Role of next-nearest-neighbor electron hopping

G. De Filippis, V. Cataudella, Giuseppe Iadonisi, Vincenzo Marigliano Ramaglia, C. A. Perroni, F. Ventriglia

Published Sep 19, 2001• 12 citations
arXivHTMLPDF

Abstract

The influence of next-nearest-neighbor electron hopping ${t}^{\ensuremath{'}}$ on the polaron and bipolaron formation in a square Hubbard-Holstein model is investigated within a variational approach. The results for electron-phonon and electron-electron correlation functions show that a negative value of ${t}^{\ensuremath{'}}$ induces a strong anisotropy in the lattice distortions favoring the formation of nearest-neighbor intersite bipolaron. The role of ${t}^{\ensuremath{'}},$ electron-phonon and electron-electron interactions is briefly discussed in view of the formation of charged striped domains.

DOI
10.1103/physrevb.64.155105

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The influence of next-nearest-neighbor electron hopping t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ on the polaron and bipolaron formation in a square Hubbard-Holstein model is investigated within a variational approach. The results for electron-phonon and electron-electron correlation functions show that a negative value of t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ induces a strong anisotropy in the lattice distortions favoring the formation of nearest-neighbor intersite bipolaron. The role of t\ensuremath′,{t}^{\ensuremath{'}},t\ensuremath′, electron-phonon and electron-electron interactions is briefly discussed in view of the formation of charged striped domains.
Employing a largely unbiased variational exact diagonalization technique, we analyze the consequences of longer-ranged electron hopping and electron-phonon interaction on polaron formation in one dimension. Having at our disposal the accurate ground-state energy and wave function, we calculate and discuss various physical quantities, such as the renormalized band structure, effective mass, wave-function renormalization factor, phonon dressing, and Drude weight, characterizing the properties of the polaronic quasiparticle. We demonstrate that the electron-phonon coupling affects the relative strength of the nearest neighbor (NN) and next nearest neighbor (NNN) hopping processes in a dynamic way. Most notably we observe that the minimum of the polaron band, occurring at a finite momentum for large negative ratio between NN and NNN transfer, jumps to zero momentum as the electron-phonon coupling exceeds a critical one, thereby causing a rather sharp polaron transition in the one-dimensional extended Holstein model. The signatures of this transition are seen in the effective mass and polaron mobility, and therefore should be easily detectable by transport measurements.
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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 study the ground state of 1D Holstein single polaron with next nearest neighbour electron hopping (NNN), employing a variational approximation based on exact diagonalization. Our investigation reveals that, depending upon the sign and magnitude of the NNN hopping integral with respect to nearest neighbour hopping, the polaron band minima may occur at non-zero kGS. We compare the present scenario with the SSH polarons, where a similar feature is also observed, albeit, due to very different mechanism. Our initial investigation of triplet bipolarons, in presence of an attractive extended Hubbard interactions, further substantiates the differences between the present model and the SSH model.
We present the effect of next-nearest-neighbor hopping on Holstein polarons. The energy and wavefunction of the ground state and first excited state are obtained by using a conjugate-gradient technique on the variational Hilbert space of the electron-phonon (e-ph) system. We increase the size of the variational space systematically to obtain high accuracy. With the converged wavefunction at our disposal we obtain various physical quantities and correlation functions to get a holistic insight into the physics of e-ph interaction. Our study reveals that the effect of next-nearest-neighbor hopping is most prominent at the physically interesting crossover regime of the e-ph coupling and in the adiabatic regime. We have also performed analytical strong coupling second order perturbation with a Lang-Firsov (LF) phonon basis to account for some features in the strong coupling regime.
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