An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective-fermion model, a fictious model of hole quasiparticles derived from numerical studies of the two-dimensional $t\ensuremath{-}J$ model at low doping. We show that there is actually a reasonable range of parameter values where the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap parameter of a size ${\ensuremath{\Delta}}_{d}\ensuremath{\simeq}0.13|V|$ (where $V$ is the attractive interaction between holes) is estimated at low doping levels. The paired state gives way to the state of clustering of holes for some stronger attractions.An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective-fermion model, a fictious model of hole quasiparticles derived from numerical studies of the two-dimensional $t\ensuremath{-}J$ model at low doping. We show that there is actually a reasonable range of parameter values where the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap parameter of a size ${\ensuremath{\Delta}}_{d}\ensuremath{\simeq}0.13|V|$ (where $V$ is the attractive interaction between holes) is estimated at low doping levels. The paired state gives way to the state of clustering of holes for some stronger attractions.

arXiv:cond-mat/9707262Physical review. B, Condensed matterNov 1, 19972 citations

s - and d -wave superconductivity in a two-band model

Daniel Reyes, M. A. Contínentino, Christopher Thomas +1 more

arXiv:1505.03790Annals of PhysicsJul 22, 20169 citations

Competition between Antiferromagnetism and Superconductivity in High- T c Cuprates

David Sénéchal, Pierre-Luc Lavertu, M.-A. Marois +1 more

Using variational cluster perturbation theory we study the competition between $d$ -wave superconductivity ( $d\mathrm{SC}$ ) and antiferromagnetism (AF) in the $t\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}U$ Hubbard model. Large scale computer calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors as well as the one-particle excitation spectra for both hole and electron doping. We identify clear signatures of the Mott gap as well as of AF and of $d\mathrm{SC}$ that should be observable in photoemission experiments.Using variational cluster perturbation theory we study the competition between $d$-wave superconductivity ($d\mathrm{SC}$) and antiferromagnetism (AF) in the $t\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}U$ Hubbard model. Large scale computer calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors as well as the one-particle excitation spectra for both hole and electron doping. We identify clear signatures of the Mott gap as well as of AF and of $d\mathrm{SC}$ that should be observable in photoemission experiments.

arXiv:cond-mat/0410162Physical Review LettersApr 20, 2005231 citations

Superconductivity enhanced by d-density wave: A weak-coupling theory

Kim Ha, Su-Bok Ri, Ri Ilmyong +2 more

Physica B Condensed MatterJan 29, 20113 citations

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

Muhammad Zafur, Hiroyuki Yamase

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.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.

arXiv:2404.02219Physical review. B./Physical review. BJun 20, 20245 citations

V

is the attractive interaction between holes) is estimated at low doping levels. The paired state gives way to the state of clustering of holes for some stronger attractions.

Using variational cluster perturbation theory we study the competition between

d

-wave superconductivity (

d\mathrm{SC}

) and antiferromagnetism (AF) in the $t\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}U$ Hubbard model. Large scale computer calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors as well as the one-particle excitation spectra for both hole and electron doping. We identify clear signatures of the Mott gap as well as of AF and of

d\mathrm{SC}

that should be observable in photoemission experiments.

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.