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arXiv:1608.08018 · Journal of the Physical Society of Japan

Charge-Density-Excitation Spectrum in the t–t′–J–V Model

Andrés Greco, Hiroyuki Yamase, Matías Bejas

Published Feb 15, 2017• 10 citations
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Abstract

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.

DOI
10.7566/jpsj.86.034706

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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 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 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.
Using a recently developed perturbative approach, which considers Hubbard operators as fundamental excitations, we have performed electronic self-energy and spectral function calculations for the $t\text{\ensuremath{-}}J$ model on the square lattice. We have found that the spectral functions along the Fermi surface are isotropic, even close to the critical doping where the ddd density wave phase occurs. Fermi liquid behavior with scattering rate $\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ and a finite quasiparticle weight ZZZ was obtained. ZZZ decreases with decreasing doping taking low values for low doping. Results are compared with others obtained by analytical and numerical methods like the slave-boson and Lanczos diagonalization approaches, finding agreement. We discuss our results in the light of recent angle-resolved photoemission spectroscopy experiments in cuprates.
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.