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arXiv:2011.00193 · Physical review. B./Physical review. B

Electron self-energy from quantum charge fluctuations in the layered t−J model with long-range Coulomb interaction

Hiroyuki Yamase, Matías Bejas, A. Greco

Published Jul 26, 2021• 10 citations
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Abstract

Employing a large-$N$ scheme of the layered $t\ensuremath{-}J$ model with the long-range Coulomb interaction, which captures the fine details of the charge excitation spectra recently observed in cuprate superconductors, we explore the role of charge fluctuations on the electron self-energy. We fix the temperature at zero and focus on quantum charge fluctuations. We find a pronounced asymmetry of the imaginary part of the self-energy $\mathrm{Im}\mathrm{\ensuremath{\Sigma}}(\mathbf{k},\ensuremath{\omega})$ with respect to $\ensuremath{\omega}=0$, which is driven by strong electron correlation effects. The quasiparticle weight is reduced dramatically, which occurs almost isotropically along the Fermi surface. Concomitantly, an incoherent band and a sharp side band are generated and acquire sizable spectral weight. All these features are driven by the usual on-site charge fluctuations, which are realized in a rather high-energy region and yield plasmon excitations. On the other hand, the low-energy region with the scale of the superexchange interaction $J$ is dominated by bond-charge fluctuations. Surprisingly, compared with the effect of on-site charge fluctuations, their effect on the electron self-energy is much weaker, even if the system approaches close to bond-charge instabilities. Furthermore, quantum charge dynamics does not produce a clear kink nor a pseudogap in the electron dispersion.

DOI
10.1103/physrevb.104.045141

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Employing a large-NNN scheme of the layered t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model with the long-range Coulomb interaction, which captures the fine details of the charge excitation spectra recently observed in cuprate superconductors, we explore the role of charge fluctuations on the electron self-energy. We fix the temperature at zero and focus on quantum charge fluctuations. We find a pronounced asymmetry of the imaginary part of the self-energy Im\ensuremathΣ(k,\ensuremathω)\mathrm{Im}\mathrm{\ensuremath{\Sigma}}(\mathbf{k},\ensuremath{\omega})Im\ensuremathΣ(k,\ensuremathω) with respect to \ensuremathω=0\ensuremath{\omega}=0\ensuremathω=0, which is driven by strong electron correlation effects. The quasiparticle weight is reduced dramatically, which occurs almost isotropically along the Fermi surface. Concomitantly, an incoherent band and a sharp side band are generated and acquire sizable spectral weight. All these features are driven by the usual on-site charge fluctuations, which are realized in a rather high-energy region and yield plasmon excitations. On the other hand, the low-energy region with the scale of the superexchange interaction JJJ is dominated by bond-charge fluctuations. Surprisingly, compared with the effect of on-site charge fluctuations, their effect on the electron self-energy is much weaker, even if the system approaches close to bond-charge instabilities. Furthermore, quantum charge dynamics does not produce a clear kink nor a pseudogap in the electron dispersion.
Charge excitation spectra are getting clear in cuprate superconductors in momentum-energy space especially around a small momentum region, where plasmon excitations become dominant. Here, we study whether Landau quasiparticles survive in the presence of charge fluctuations observed in experiments. We employ the layered $t\text{\ensuremath{-}}J$ model with the long-range Coulomb interaction, which can reproduce the realistic charge fluctuations. We find that Landau quasiparticles are retained in a realistic temperature and doping region, although the quasiparticle spectral weight is strongly reduced to 0.08−−0.240.08--0.240.08−−0.24. Counterintuitively, the presence of this small quasiparticle weight does not work favorably to generate a pseudogap.
Motivated by the recent resonant x-ray scattering (RXS) and resonant inelastic x-ray scattering (RIXS) experiments for electron-doped cuprates, we study the charge excitation spectrum in a layered $t\text{\ensuremath{-}}J$ model with the long-range Coulomb interaction. We show that the spectrum is not dominated by a specific type of charge excitations, but by different kinds of charge fluctuations, and is characterized by a dual structure in the energy space. Low-energy charge excitations correspond to various types of bond-charge fluctuations driven by the exchange term (JJJ term), whereas high-energy charge excitations are due to usual on-site charge fluctuations and correspond to plasmon excitations above the particle-hole continuum. The interlayer coupling, which is frequently neglected in many theoretical studies, is particularly important to the high-energy charge excitations.
t−Jt-Jt−J model one-electron renormalizations: high energy features in photoemission experiments of high-TcT_cTc​ cuprates
Recent angle-resolved photoemission experiments in hole doped cuprates reported new and interesting high energy features which may be useful for understanding the electronic properties of these materials. Using a perturbative approach, which allows the calculation of dynamical properties in the t−Jt-Jt−J model, one-electron spectral properties were calculated. A strongly renormalized quasiparticle band near the Fermi surface and incoherent spectra at high energy were obtained. Among different current experimental interpretations, the obtained results are closer to the interpretation given by Pan {\it et al.}\cite{pan}. The self-energy shows large high energy contributions which are responsible for the incoherent structures showed by the spectral functions and the reduction of the quasiparticle weight and bandwidth. According to the calculation, collective charge fluctuations are the main source for the self-energy renormalizations. For testing if the obtained self-energy is compatible with transport measurement the resistivity versus temperature was estimated.
The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions [Formula: see text], temperatures [Formula: see text] and electron concentrations [Formula: see text] with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at [Formula: see text]. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from [Formula: see text] at the highest temperatures to U = 2t at [Formula: see text] for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for [Formula: see text] to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for [Formula: see text]. For [Formula: see text] and [Formula: see text] doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.
Motivated by recent experiments, we append long ranged Coulomb interactions to dominant strong local correlations and study the resulting t-J-VC model for the 2-dimensional cuprate materials. This model includes the effect of short ranged Hubbard–Gutzwiller–Kanamori type correlations and long ranged Coulomb interactions on tight binding electrons. We calculate the {q→,ω} dependent charge density fluctuations in this model using the extremely correlated Fermi liquid theory characterized by quasiparticles with very small weight Z. We develop a novel set of formulae to represent the dynamical charge susceptibility and the dielectric function, using a version of the charge-current continuity equation for a band system, valid for arbitrary q→. Combining these ingredients, we present results for the irreducible dynamical charge susceptibility χ˜ρρ(q→,ω), (longitudinal) dielectric function ɛ(q→,ω), current susceptibility χ˜JJ(q→,ω), conductivity σ(q→,ω), and the plasma frequency for any q→. We also present calculations for the first moment of the structure function and discuss a characteristic energy scale Ωp(q→) which locates a peak in Imχ˜ρρ(q→,ω).
Motivated by the recent resonant inelastic x-ray scattering (RIXS) experiment for the electron-doped cuprates ${\mathrm{Nd}}_{2\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}$ with $x\ensuremath{\approx}0.15$, we compute the density-density correlation function in the $t\ensuremath{-}J$ model on a square lattice by including interlayer hopping and the long-range Coulomb interaction. We find that collective charge excitations are realized not inside the particle-hole continuum, but above the continuum as plasmons. The plasmon mode has a rather flat dispersion near the in-plane momentum ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ with a typical excitation energy of the order of the intralayer hopping ttt when the out-of-plane momentum qz{q}_{z}qz​ is zero. However, when qz{q}_{z}qz​ becomes finite, the plasmon dispersion changes drastically near ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$, leading to a strong dispersive feature with an excitation gap scaled by the interlayer hopping tz{t}_{z}tz​. We discuss the mode recently observed by RIXS near ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ in terms of the plasmon mode with a finite qz{q}_{z}qz​.