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Impact of Coulomb repulsion on charge excitations in the t-J model

A. Greco, Hiroyuki Yamase, Matías Bejas

Published Aug 29, 2016• 0 citations
OpenAlex

Abstract

We study the density-density correlation function in a large-N scheme of the t-t'-J-V model. When the nearest-neighbor Coulomb interaction V is zero, our model exhibits phase separation in a wide doping region and we obtain large spectral weight near momentum q=(0,0) at low energy, which originates from the proximity to phase separation. These features are much stronger for electron doping than for hole doping. However, once phase separation is suppressed by including a finite V, the low-energy spectral weight around q=(0,0) is substantially suppressed. Instead a sharp zero-sound mode is stabilized above the particle-hole continuum. We discuss that the presence of a moderate value of V, which is frequently neglected in the t-J model, is important to understand low-energy charge excitations especially close to q=(0,0) for electron doping. This insight should be taken into account in a future study of x-ray scattering measurements.

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Large- N expansion based on the Hubbard operator path integral representation and its application to the t − J model. II. The case for finite J

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Charge susceptibility in the t−J model

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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 ($J$ 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.

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We study the density-density correlation function in a large-N scheme of the t-t'-J-V model. When the nearest-neighbor Coulomb interaction V is zero, our model exhibits phase separation in a wide doping region and we obtain large spectral weight near momentum q=(0,0) at low energy, which originates from the proximity to phase separation. These features are much stronger for electron doping than for hole doping. However, once phase separation is suppressed by including a finite V, the low-energy spectral weight around q=(0,0) is substantially suppressed. Instead a sharp zero-sound mode is stabilized above the particle-hole continuum. We discuss that the presence of a moderate value of V, which is frequently neglected in the t-J model, is important to understand low-energy charge excitations especially close to q=(0,0) for electron doping. This insight should be taken into account in a future study of x-ray scattering measurements.
We study the density-density correlation function in a large-N scheme of the t-tA-J-V model.When the nearestneighbor Coulomb interaction V is zero, our model exhibits phase separation in a wide doping region and we obtain large spectral weight near momentum q ¼ ð0; 0Þ at low energy, which originates from the proximity to phase separation.These features are much stronger for electron doping than for hole doping.However, once phase separation is suppressed by including a finite V, the low-energy spectral weight around q ¼ ð0; 0Þ is substantially suppressed.Instead a sharp zero-sound mode is stabilized above the particle-hole continuum.We discuss that the presence of a moderate value of V, which is frequently neglected in the t-J model, is important to understand low-energy charge excitations especially close to q ¼ ð0; 0Þ for electron doping.This insight should be taken into account in a future study of x-ray scattering measurements.
We have introduced a new perturbative approach for $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model where Hubbard operators are treated as fundamental objects. Using our vertices and propagators we have developed a controllable large-NNN expansion to calculate different correlation functions. We have investigated charge density-density response and the phase diagram of the model. The charge correlations functions are not very sensitive to the value of JJJ and they show collective peaks (or zero sound) which are more pronounced when they are well separated (in energy) from the particle-hole continuum. For a given JJJ a Fermi liquid state is found to be stable for doping $\ensuremath{\delta}$ larger than a critical doping ${\ensuremath{\delta}}_{c}$. ${\ensuremath{\delta}}_{c}$ decreases with decreasing JJJ. For the physical region of the parameters and, for $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}$, the system enters in an incommensurate flux or DDW phase. The inclusion of the nearest-neighbor Coulomb repulsion VVV leads to a charge density wave phase when VVV is larger than a critical value Vc{V}_{c}Vc​. The dependence of Vc{V}_{c}Vc​ with $\ensuremath{\delta}$ and JJJ is shown. We have compared the results with other ones in the literature.
Momentum and doping dependence of the static charge susceptibility $\ensuremath{\chi}(\mathbf{q})$ in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model is investigated. Correlations lead to a strongly momentum-dependent renormalization of $\ensuremath{\chi}(\mathbf{q})$. The charge susceptibility near the $(\ensuremath{\pi},\ensuremath{\pi})$ region of the Brillouin zone is strongly suppressed as the hole density $\ensuremath{\delta}$ is decreased. However, contrary to naive expectations, $\ensuremath{\chi}(\mathbf{q})$ around $\mathbf{q}=(\ensuremath{\pi},0)$ and $(0,\ensuremath{\pi})$ remains large and practically unchanged at $\ensuremath{\delta}\ensuremath{\sim}0.1--0.5$. This effect is consistent with a tendency towards low-energy charge fluctuations with the wave vectors along the $\ensuremath{\Gamma}\text{\ensuremath{-}}X$ direction, reported in earlier studies. Our main finding is that the above trends are amplified by JJJ-driven pairing effects, indicating that the pseudogap formation may promote the charge inhomogeneity. The next-nearest hopping ${t}^{\ensuremath{'}}$ leads to weakening of the above momentum-selective renormalizations of $\ensuremath{\chi}(\mathbf{q})$. We analyze the effects of long-range Coulomb interaction, taking into account a layered structure of cuprates. As an application, the results are discussed in the context of bond-stretching phonon softening in hole-doped cuprates. In particular, a peculiar doping and momentum dependence of the electron-phonon coupling constant is found.
The study of the charge excitations in cuprates is presently an interesting topic because of the development of new and precise x-ray experiments. Based on a large-NNN formulation of the two-dimensional $t\text{\ensuremath{-}}J$ model, which allows us to consider all possible charge excitations on an equal footing, we investigate the charge spectrum for both electron- and hole-doped cases. In both cases, the instability toward phase separation, which has momentum modulation q=(0,0)\mathbf{q}=(0,0)q=(0,0), is found to be robust in a large region of the doping-temperature phase diagram. If a short-range Coulomb repulsion is included the phase separation region shrinks, but the instability remains at q=(0,0)\mathbf{q}=(0,0)q=(0,0). If on the other hand a two-dimensional long-range Coulomb interaction is included the instability sets in at q\mathbf{q}q momenta forming a ring around q=(0,0)\mathbf{q}=(0,0)q=(0,0). The computed charge spectrum in the translation-invariant phase shows well-formed rings. We discuss our results in the light of recent x-ray experiments in electron- and hole-doped cuprates, where ring-like shaped charge modulations have been reported.
The renormalization of the electron-phonon interaction by strong electronic correlations is studied using a one-band Hubbard model with infinite repulsion and nearest (t model) and nearest and second-nearest (tt\ensuremath{'} model) neighbor hopping terms and an on-site electron-phonon coupling. Using Hubbard's X operators and an extension from 2 to N degrees of freedom for the electrons the leading contributions for the electron self-energy and the vertex function in 1/N and the electron-phonon coupling constant are given and numerically evaluated for a square lattice. We find that the momentum dependence of the vertex function depends strongly on doping: For large dopings it is rather weak, with decreasing doping it becomes more and more pronounced leading to a strong reduction of the vertex at larger momentum transfers until, for very small dopings, the vertex essentially consists of a forward scattering peak with a width proportional to the doping. This behavior occurs both in the t and the tt\ensuremath{'} models and also in one dimension where analytic expressions are derived. Correlation effects also change ${\mathrm{\ensuremath{\alpha}}}^{2}$F in general: The full-symmetric component ${\mathrm{\ensuremath{\alpha}}}^{2}$F1{\mathit{F}}_{1}F1​ is in the t model somewhat, in the tt\ensuremath{'} model rather strongly suppressed, especially near half-filling; the other symmetry components ${\mathrm{\ensuremath{\alpha}}}^{2}$Fi{\mathit{F}}_{\mathit{i}}Fi​ with i=2,...,5 increase strongly with decreasing doping and are of similar magnitude as ${\mathrm{\ensuremath{\alpha}}}^{2}$F1{\mathit{F}}_{1}F1​ near half-filling.Including also direct Coulomb repulsion nontrivial symmetries such as d wave become more stable than the s-wave order parameter below a critical value for the doping even for the considered phonon-mediated superconductivity. Most dramatic, however, is the quenching of the resistivity due to electron-phonon scattering both in the t and the tt\ensuremath{'} models at intermediate and small dopings. This result may explain the absence of phonon features in the experimental transport coefficients of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ compounds. \textcopyright{} 1996 The American Physical Society.
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.