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arXiv:2503.06018 · Physical review. B./Physical review. B

Evolution of the pseudogap band structure in a system of electron-correlated lattice polarons

Elena I. Shneyder, M. V. Zotova, A. V. Dudarev, Sergey V. Nikolaev, Sergei G. Ovchinnikov

Published Aug 20, 2025• 2 citations
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Abstract

The evolution of the role of lattice vibrations in the formation of the pseudogap state in strongly correlated electron systems has been investigated concerning changes in the electron-phonon coupling parameters and the concentration of doped charge carriers. We apply the polaronic version of the generalized tight-binding method to analyze the band structure of a realistic multiband two-dimensional model that incorporates the electron-lattice contributions of both Holstein and Peierls types. It has been demonstrated that the emergence of polaronic effects begins with the modulation of spectral function intensity. However, within a specific region of the phase diagram, a significant transformation of the electron band structure and pseudogap state occurs. It results from coherent polaron excitations that create a partially flat band near the Fermi level. This process leads to a change in the topology of the Fermi surface and the emergence of corresponding features in the density of states.

DOI
10.1103/xzzp-w7bd

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The evolution of the role of lattice vibrations in the formation of the pseudogap state in strongly correlated electron systems has been investigated concerning changes in the electron-phonon coupling parameters and the concentration of doped charge carriers. We apply the polaronic version of the generalized tight-binding method to analyze the band structure of a realistic multiband two-dimensional model that incorporates the electron-lattice contributions of both Holstein and Peierls types. It has been demonstrated that the emergence of polaronic effects begins with the modulation of spectral function intensity. However, within a specific region of the phase diagram, a significant transformation of the electron band structure and pseudogap state occurs. It results from coherent polaron excitations that create a partially flat band near the Fermi level. This process leads to a change in the topology of the Fermi surface and the emergence of corresponding features in the density of states.
In this work we investigate doping and temperature dependences of electronic structure of system with strong electronic correlations and strong electron-phonon interaction modeling cuprates in the frameworks of the three-band p-d-Holstein model by a polaronic version of the generalized tight binding (GTB) method. Within this approach the electronic structure is formed by polaronic quasiparticles constructed as excitations between initial and final polaronic multielectron states. Doping and temperature effects are taken into account by occupation numbers of local excited polaronic states and variations in the magnitude of spin-spin correlation functions. Both effects are manifested in the reconstruction of band structure, Fermi contours, density of states and redistribution of the spectral weight over the Hubbard polaron subbands. Doping leads to transformation of Fermi contour from small hole pockets around k=(pi/2,pi/2) with inhomogeneous spectral weight distribution at small hole concentration to large contour around k=(pi,pi) in the overdoped compound as a result of two quantum phase transitions. In the system with phonon subsystem and EPI doping results in the top of the valence band splitting off and new polaron subbands appearance. Temperature increasing in the system with doped holes and moderate EPI leads to formation of the flatband around k=(pi,pi) and transfer of the spectral weight to the splitted off top of the valence band.
In this work we investigate temperature dependence of electronic structure of system with strong electronic correlations and strong electron-phonon interaction modeling cuprates in the frameworks of the three-band p-d-Holstein model by a polaronic version of the generalized tight binding (GTB) method. Within this approach the electronic structure is formed by polaronic quasiparticles constructed as excitations between initial and final polaronic multielectron states. Temperature effect is taken into account by occupation numbers of local excited polaronic states and variations in the magnitude of spin-spin correlation functions and it is manifested in the redistribution of the spectral weight over the Hubbard polaron subbands, and the temperature dependent band structure. Temperature increasing leads to broadening of the spectral function peak at the top of the valence band, shift of the peak, the decreasing of the peak intensity, the growth of bandwidth and reduction of the insulator energy gap. These effects are in a qualitative agreement to the temperature dependence of the ARPES spectra observed in the undoped HTSC cuprates.
The effects of electron-lattice coupling in a multiband Hubbard model are investigated by exact diagonalization. For a system with one doped hole, and with parameters relevant to cuprate superconductors, we find a continuous transition from a delocalized to a small polaron state at a critical value of the electron-phonon interaction. We characterize this state as a Zhang-Rice singlet with distortions in the CuO4 cluster. We find, in addition, a polaronic shift of the band near the Fermi level in the spectral function of the system. An enhancement of the transfer of the low-energy spectral weight is also observed. These results are in qualitative agreement with different spectroscopic measurements for high-T(c) superconductors.
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.
Many-polaron systems with finite charge-carrier density are often encountered experimentally. However, until recently, no satisfactory theoretical description of these systems was available even in the framework of simple models such as the one-dimensional spinless Holstein model considered here. In this work, previous results obtained using numerical as well as analytical approaches are reviewed from a unified perspective, focussing on spectral properties which reveal the nature of the quasiparticles in the system. In the adiabatic regime and for intermediate electron-phonon coupling, a carrier-density driven crossover from a polaronic to a rather metallic system takes place. Further insight into the effects due to changes in density is gained by calculating the phonon spectral function, and the fermion-fermion and fermion-lattice correlation functions. Finally, we provide strong evidence against the possibility of phase separation.