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arXiv:2404.02219 · Physical review. B./Physical review. B

Spin and bond-charge excitation spectra in correlated electron systems near an antiferromagnetic phase

Muhammad Zafur, Hiroyuki Yamase

Published Jun 20, 2024• 5 citations
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Abstract

Magnetic and bond-charge interactions can arise from the same microscopic interaction. Motivated by this observation, we compute magnetic and bond-charge excitation spectra on an equal footing by introducing a simple effective model on a square lattice, which describes antiferromagnetic and $d$-wave superconducting phases around half-filling on the electron-doped side. The magnetic excitation spectrum $\mathrm{Im}\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega})$ has strong weight around $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ in low energy, and its intensity map exhibits a pencil-tip-like shape in $\mathbf{q}\text{\ensuremath{-}}\ensuremath{\omega}$ space. Around $\mathbf{q}=(0,0)$ magnetic excitations show a steep dispersion toward the $(\ensuremath{\pi},\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ directions, which is very similar to a spin-wave dispersion although the system is nonmagnetic. Bond-charge excitations are characterized by four different symmetries and studied for all possible couplings. Bond-charge fluctuations with three different symmetries have large spectral weight around $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ in a relatively low-energy region and extend widely more than the magnetic excitation spectrum. The $d$-wave symmetry of bond-charge excitations also has sizable spectral weight along the direction $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)\text{\ensuremath{-}}(0,0)\text{\ensuremath{-}}(\ensuremath{\pi}/2,0)$ in a low-energy region and exhibits softening around $\mathbf{q}\ensuremath{\approx}(0.5\ensuremath{\pi},0)$, whereas no such softening is present in the other symmetries. These results capture the essential features observed in electron-doped cuprates and may motivate an experimental test of bond-charge excitations around $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ on top of the strong magnetic excitations there as well as additional softening in the $d$-wave channel in the $(\ensuremath{\pi},\ensuremath{\pi})\text{\ensuremath{-}}(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ region at low temperatures near the magnetic phase. We extend the present analysis to the hole-doped side and highlight a contrast to the electron-doped side, which includes incommensurate correlations, electronic nematic correlations, and spin and bond-charge resonance modes in the superconducting state.

DOI
10.1103/physrevb.109.245127

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We study charge excitation spectra in the two-dimensional t - J model on a square lattice to explore a charge-order tendency recently found in electron-doped cuprates around the carrier density 0.15. The static susceptibility of d -wave charge density, which corresponds to the nematic susceptibility at the momentum transfer q = ( 0 , 0 ) , shows two characteristic peaks at momenta of the form q 1 = ( q ′ , q ′ ) and q 2 = ( q , 0 ) . These two peaks originate from the so-called 2 k F scattering processes enhanced by the d -wave character of the bond-charge density. The peak at q 1 is much broader, but develops to be very sharp in the vicinity of its instability, whereas the peak at q 2 becomes sharper with decreasing temperature, but does not diverge. The equal-time correlation function, which is measured by resonant x-ray scattering, exhibits a momentum dependence similar to the static susceptibility. We also present energy-resolved charge excitation spectra. The spectra show a V-shaped structure around q = ( 0 , 0 ) and bend back toward close-to-zero energy due to the charge-order tendency at q 1 and q 2 . The resulting spectra form gap-like features with a maximal gap at q ≈ q 1 / 2 and q 2 / 2 . We discuss implications for the recent experiments in electron-doped cuprates.
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Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the density matrix renormalization group technique, we calculate the dynamical spin structure factor $S(\mathbf{k},\ensuremath{\omega})$ of a generalized $t\ensuremath{-}U\ensuremath{-}J$ Hubbard model away from half filling in a two-leg ladder geometry. The addition of JJJ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\ensuremath{\pi},\ensuremath{\pi})$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave vector krung=0{k}_{\mathrm{rung}}=0krung​=0 does not change substantially with doping where pairing dominates and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one-dimensional magnetic materials can be measured and also address implications for recent resonant inelastic x-ray scattering experiments.
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Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the density matrix renormalization group technique, we calculate the dynamical spin structure factor $S(\mathbf{k},\ensuremath{\omega})$ of a generalized $t\ensuremath{-}U\ensuremath{-}J$ Hubbard model away from half filling in a two-leg ladder geometry. The addition of JJJ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\ensuremath{\pi},\ensuremath{\pi})$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave vector krung=0{k}_{\mathrm{rung}}=0krung​=0 does not change substantially with doping where pairing dominates and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one-dimensional magnetic materials can be measured and also address implications for recent resonant inelastic x-ray scattering experiments.
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.