Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2104.12812 · Physical review. B./Physical review. B

Unified theory of spin and charge excitations in high- Tc cuprate superconductors: A quantitative comparison with experiment and interpretation

Maciej Fidrysiak, Józef Spałek

Published Jul 26, 2021• 22 citations
arXivHTMLPDF

Abstract

We provide a unified interpretation of both paramagnon and plasmon modes in high-${T}_{c}$ copper-oxides, and verify it quantitatively against available resonant inelastic $x$-ray scattering (RIXS) data across the hole-doped phase diagram. The three-dimensional extended Hubbard model, with included long-range Coulomb interactions and doping-independent microscopic parameters for both classes of quantum fluctuations, is used. Collective modes are studied using $\mathrm{VWF}+1/{\mathcal{N}}_{f}$ approach which extends variational wave function (VWF) scheme by means of an expansion in inverse number of fermionic flavors $(1/{\mathcal{N}}_{f})$. We show that intense paramagnons persist along the antinodal line from the underdoped to the overdoped regime and undergo rapid overdamping in the nodal direction. Plasmons exhibit a three-dimensional character, with minimal energy corresponding to antiphase oscillations on neighboring ${\mathrm{CuO}}_{2}$ planes. The theoretical spin- and charge excitation energies reproduce semiquantitatively RIXS data for ${(\mathrm{Bi},\mathrm{Pb})}_{2}{(\mathrm{Sr},\mathrm{La})}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$. The present $\mathrm{VWF}+1/{\mathcal{N}}_{f}$ analysis of dynamics and former VWF results for static quantities combine into a consistent description of the principal properties of hole-doped high-${T}_{c}$ cuprates as strongly correlated systems.

DOI
10.1103/physrevb.104.l020510

Related papers

Collective spin and charge excitations in the t-J-U model of high- Tc cuprates

Maciej Fidrysiak, Danuta Goc-Jagło, Józef Spałek

The t-J-U model of high-Tc copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the t-J-U model. We employ VWF+1/Nf approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors (1/Nf). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and t-J-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, t-J, and t-J-U models. The results are discussed in the context of recent resonant inelastic x-ray scattering experiments for the high-Tc cuprates.

arXiv:2107.02152•Journal of Magnetism and Magnetic Materials•Aug 16, 2021•3 citations

Electron-Hole Asymmetry of Quantum Collective Excitations in High-Tc Copper Oxides

Maciej Fidrysiak

We carry out a systematic study of collective spin and charge excitations for the canonical single-band Hubbard, t–J–U, and t–J models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. A~recently developed variational wave function approach, combined with the expansion in the inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron–hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic X-ray scattering data for the cuprates. The t–J model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on the electron-doped side of the phase diagram.

arXiv:2210.16109•Acta Physica Polonica A•Feb 1, 2023•0 citations

Universal collective modes from strong electronic correlations: Modified 1/Nf theory with application to high- Tc cuprates

Maciej Fidrysiak, Józef Spałek

A nonzero-temperature technique for strongly correlated electron lattice systems, combining elements of both variational wave function (VWF) approach and expansion in the inverse number of fermionic flavors ($1/{\mathcal{N}}_{f}$), is developed. The departure point, VWF method, goes beyond the renormalized mean-field theory and provides semiquantitative description of principal equilibrium properties of high-${T}_{c}$ superconducting cuprates. The developed here scheme of $\text{VWF}+1/{\mathcal{N}}_{f}$, in the leading order provides dynamical spin and charge responses around the VWF solution, generalizing the weak-coupling spin-fluctuation theory to the regime of strong correlations. Thermodynamic corrections to the correlated saddle-point state arise systematically at consecutive orders. Explicitly, $\text{VWF}+1/{\mathcal{N}}_{f}$ is applied to evaluate dynamical response functions for the hole-doped Hubbard model and compared with available determinant quantum Monte Carlo data, yielding a good overall agreement in the regime of coherent collective-mode dynamics. The emergence of well-defined spin and charge excitations from the incoherent continua is explicitly demonstrated and a nonmonotonic dependence of the charge-excitation energy on the interaction magnitude is found. The charge mode energy saturates slowly when approaching the strong-coupling limit, which calls for a reevaluation of the $t\text{\ensuremath{-}}J$-model approach to the charge dynamics in favor of more general $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ and $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U\text{\ensuremath{-}}V$ models. The results are also related to recent inelastic resonant x-ray and neutron-scattering experiments for the high-${T}_{c}$ cuprates.

arXiv:2012.06630•Physical review. B./Physical review. B•Apr 9, 2021•6 citations

Robust spin and charge excitations throughout the high- Tc cuprate phase diagram from incipient Mottness

Maciej Fidrysiak, Józef Spałek

The generic phase diagram of lightly hole doped high-${T}_{c}$ cuprates hosts an antiferromagnetic insulating phase with well-defined spin-wave excitations. Contrary to the weak-coupling prediction, these modes persist up to the overdoped metallic regime as intense and dispersive paramagnons. Here we report on our study of the low-energy magnetic and charge excitations within the extended Hubbard model at strong coupling, using a modified $1/N$ expansion method with a variational state serving as the saddle point solution. Despite clear separation of magnetic and Hubbard-$U$ energy scales, we find that incipient Mottness affects qualitatively dispersions and widths of magnetic modes throughout the entire phase diagram. The obtained magnetic and charge dynamical structure factors agree semiquantitatively with recent resonant x-ray and neutron scattering data for ${\mathrm{La}}_{2\ensuremath{-}\mathit{x}}{\mathrm{Sr}}_{\mathit{x}}{\mathrm{CuO}}_{4}$ and ${(\mathrm{Bi},\mathrm{Pb})}_{2}{(\mathrm{Sr},\mathrm{La})}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ at all available doping levels. The weak-coupling random-phase approximation fails already for underdoped samples, pointing to the nontrivial intertwining of distinct energy scales in cuprate superconductors. The existence of a discrete charge mode which splits off the electron-hole continuum is also predicted.

arXiv:1912.06232•Physical review. B./Physical review. B•Jul 13, 2020•12 citations

Plasmon excitations in layered high- T c cuprates

A. Greco, Hiroyuki Yamase, Matías Bejas

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 $t$ when the out-of-plane momentum ${q}_{z}$ is zero. However, when ${q}_{z}$ 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 ${t}_{z}$. We discuss the mode recently observed by RIXS near ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ in terms of the plasmon mode with a finite ${q}_{z}$.

arXiv:1601.08249•Physical review. B./Physical review. B•Aug 17, 2016•45 citations

Universal collective modes from strong correlations: Modified $1/\mathcal{N}_f$ theory with application to high-$T_c$ cuprates

Maciej Fidrysiak, Józef Spałek

A nonzero-temperature technique for strongly correlated electron lattice systems, combining elements of both variational wave function (VWF) approach and expansion in the inverse number of fermionic flavors ($1/\mathcal{N}_f$), is developed. To the leading order, the combined VWF+$1/\mathcal{N}_f$ scheme provides dynamical spin and charge response around the strongly-correlated VWF solution, whereas thermodynamic corrections to the saddle-point state arise systematically at consecutive orders. VWF+$1/\mathcal{N}_f$ is used to evaluate dynamical response functions for the hole-doped Hubbard model and compared with available determinant quantum Monte-Carlo data, yielding a good overall agreement in the regime of coherent collective-mode dynamics. Emergence of well-defined spin and charge excitations from the incoherent continua is explicitly demonstrated, and a non-monotonic dependence of the charge-excitation energy on the interaction magnitude is found. The charge-mode energy saturates slowly when approaching the strong-coupling limit, which calls for a reevaluation of the $t$-$J$-model approach to charge dynamics. The results are also related to recent inelastic resonant $X$-ray scattering experiments for the high-$T_c$ cuprates.

•Dec 11, 2020•0 citations
We provide a unified interpretation of both paramagnon and plasmon modes in high-Tc{T}_{c}Tc​ copper-oxides, and verify it quantitatively against available resonant inelastic xxx-ray scattering (RIXS) data across the hole-doped phase diagram. The three-dimensional extended Hubbard model, with included long-range Coulomb interactions and doping-independent microscopic parameters for both classes of quantum fluctuations, is used. Collective modes are studied using VWF+1/Nf\mathrm{VWF}+1/{\mathcal{N}}_{f}VWF+1/Nf​ approach which extends variational wave function (VWF) scheme by means of an expansion in inverse number of fermionic flavors (1/Nf)(1/{\mathcal{N}}_{f})(1/Nf​). We show that intense paramagnons persist along the antinodal line from the underdoped to the overdoped regime and undergo rapid overdamping in the nodal direction. Plasmons exhibit a three-dimensional character, with minimal energy corresponding to antiphase oscillations on neighboring CuO2{\mathrm{CuO}}_{2}CuO2​ planes. The theoretical spin- and charge excitation energies reproduce semiquantitatively RIXS data for (Bi,Pb)2(Sr,La)2CuO6+\ensuremathδ{(\mathrm{Bi},\mathrm{Pb})}_{2}{(\mathrm{Sr},\mathrm{La})}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}(Bi,Pb)2​(Sr,La)2​CuO6+\ensuremathδ​. The present VWF+1/Nf\mathrm{VWF}+1/{\mathcal{N}}_{f}VWF+1/Nf​ analysis of dynamics and former VWF results for static quantities combine into a consistent description of the principal properties of hole-doped high-Tc{T}_{c}Tc​ cuprates as strongly correlated systems.
The t-J-U model of high-Tc copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the t-J-U model. We employ VWF+1/Nf approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors (1/Nf). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and t-J-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, t-J, and t-J-U models. The results are discussed in the context of recent resonant inelastic x-ray scattering experiments for the high-Tc cuprates.
We carry out a systematic study of collective spin and charge excitations for the canonical single-band Hubbard, t–J–U, and t–J models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. A~recently developed variational wave function approach, combined with the expansion in the inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron–hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic X-ray scattering data for the cuprates. The t–J model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on the electron-doped side of the phase diagram.
A nonzero-temperature technique for strongly correlated electron lattice systems, combining elements of both variational wave function (VWF) approach and expansion in the inverse number of fermionic flavors (1/Nf1/{\mathcal{N}}_{f}1/Nf​), is developed. The departure point, VWF method, goes beyond the renormalized mean-field theory and provides semiquantitative description of principal equilibrium properties of high-Tc{T}_{c}Tc​ superconducting cuprates. The developed here scheme of VWF+1/Nf\text{VWF}+1/{\mathcal{N}}_{f}VWF+1/Nf​, in the leading order provides dynamical spin and charge responses around the VWF solution, generalizing the weak-coupling spin-fluctuation theory to the regime of strong correlations. Thermodynamic corrections to the correlated saddle-point state arise systematically at consecutive orders. Explicitly, VWF+1/Nf\text{VWF}+1/{\mathcal{N}}_{f}VWF+1/Nf​ is applied to evaluate dynamical response functions for the hole-doped Hubbard model and compared with available determinant quantum Monte Carlo data, yielding a good overall agreement in the regime of coherent collective-mode dynamics. The emergence of well-defined spin and charge excitations from the incoherent continua is explicitly demonstrated and a nonmonotonic dependence of the charge-excitation energy on the interaction magnitude is found. The charge mode energy saturates slowly when approaching the strong-coupling limit, which calls for a reevaluation of the $t\text{\ensuremath{-}}J$-model approach to the charge dynamics in favor of more general $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ and $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U\text{\ensuremath{-}}V$ models. The results are also related to recent inelastic resonant x-ray and neutron-scattering experiments for the high-Tc{T}_{c}Tc​ cuprates.
The generic phase diagram of lightly hole doped high-Tc{T}_{c}Tc​ cuprates hosts an antiferromagnetic insulating phase with well-defined spin-wave excitations. Contrary to the weak-coupling prediction, these modes persist up to the overdoped metallic regime as intense and dispersive paramagnons. Here we report on our study of the low-energy magnetic and charge excitations within the extended Hubbard model at strong coupling, using a modified 1/N1/N1/N expansion method with a variational state serving as the saddle point solution. Despite clear separation of magnetic and Hubbard-UUU energy scales, we find that incipient Mottness affects qualitatively dispersions and widths of magnetic modes throughout the entire phase diagram. The obtained magnetic and charge dynamical structure factors agree semiquantitatively with recent resonant x-ray and neutron scattering data for ${\mathrm{La}}_{2\ensuremath{-}\mathit{x}}{\mathrm{Sr}}_{\mathit{x}}{\mathrm{CuO}}_{4}$ and ${(\mathrm{Bi},\mathrm{Pb})}_{2}{(\mathrm{Sr},\mathrm{La})}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ at all available doping levels. The weak-coupling random-phase approximation fails already for underdoped samples, pointing to the nontrivial intertwining of distinct energy scales in cuprate superconductors. The existence of a discrete charge mode which splits off the electron-hole continuum is also predicted.
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​.
Universal collective modes from strong correlations: Modified 1/Nf1/\mathcal{N}_f1/Nf​ theory with application to high-TcT_cTc​ cuprates
A nonzero-temperature technique for strongly correlated electron lattice systems, combining elements of both variational wave function (VWF) approach and expansion in the inverse number of fermionic flavors (1/Nf1/\mathcal{N}_f1/Nf​), is developed. To the leading order, the combined VWF+1/Nf1/\mathcal{N}_f1/Nf​ scheme provides dynamical spin and charge response around the strongly-correlated VWF solution, whereas thermodynamic corrections to the saddle-point state arise systematically at consecutive orders. VWF+1/Nf1/\mathcal{N}_f1/Nf​ is used to evaluate dynamical response functions for the hole-doped Hubbard model and compared with available determinant quantum Monte-Carlo data, yielding a good overall agreement in the regime of coherent collective-mode dynamics. Emergence of well-defined spin and charge excitations from the incoherent continua is explicitly demonstrated, and a non-monotonic dependence of the charge-excitation energy on the interaction magnitude is found. The charge-mode energy saturates slowly when approaching the strong-coupling limit, which calls for a reevaluation of the ttt-JJJ-model approach to charge dynamics. The results are also related to recent inelastic resonant XXX-ray scattering experiments for the high-TcT_cTc​ cuprates.