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:cond-mat/0406239 · Physical Review B

Spin dynamics in a doped-Mott-insulator superconductor

Wei-Qiang Chen, Zheng-Yu Weng

Published Apr 25, 2005• 17 citations
arXivHTMLPDF

Abstract

We present a systematic study of spin dynamics in a superconducting ground state, which itself is a doped Mott insulator and can correctly reduce to an antiferromagnetic (AF) state at half-filling with an AF long-range order (AFLRO). Such a doped Mott insulator is described by a mean-field theory based on the phase string formulation of the $t\text{\ensuremath{-}}J$ model. We show that the well-known spin wave excitation in the AFLRO state at half-filling evolves into a resonancelike peak at a finite energy in the superconducting state, which is located around the AF wave vectors. The width of such a resonancelike peak in momentum space decides a spin correlation length scale which is inversely proportional to the square root of doping concentration, while the energy of the resonancelike peak scales linearly with the doping concentration at low doping. These properties are consistent with experimental observations in the high-${T}_{c}$ cuprates. An important prediction of the theory is that, while the total spin sum rule is satisfied at different doping concentrations, the weight of the resonancelike peak does not vanish, but is continuously saturated to the weight of the AFLRO at zero-doping limit. Besides the low-energy resonancelike peak, we also show that the high-energy excitations still track the spin wave dispersion in momentum space, contributing to a significant portion of the total spin sum rule. The fluctuational effect beyond the mean-field theory is also examined, which is related to the broadening of the resonancelike peak in energy space. In particular, we discuss the incommensurability of the spin dynamics by pointing out that its visibility is strongly tied to the low-energy fluctuations below the resonancelike peak. We finally investigate the interlayer coupling effect on the spin dynamics as a function of doping, by considering a bilayer system.

DOI
10.1103/physrevb.71.134516

Related papers

Hourglasslike spin excitation in a doped Mott insulator

Jiaxin Zhang, Chuan Chen, Jian-Hao Zhang +1 more

We examine the dynamical magnetic response in a two-component resonating-valence-bond (RVB) description of the doped Mott insulator. The half-filled antiferromagnetic phase described by the Schwinger-boson mean-field theory will evolve into a bosonic-RVB state in the superconducting phase upon doping, where the doped holes introduce another fermionic itinerant spinon which forms a BCS-like RVB order. The spin excitations are thus composed of a resonance-like mode from the former and a weak dispersive mode from the itinerant component at the mean-field level. These two-component spinons are shown to give rise to an hourglasslike spin excitation at the random-phase approximation level via an antiferromagnetic coupling between the two modes, which provides an unconventional explanation of the experimental observations in the cuprate. In particular, we also discuss an instability towards an incommensurate magnetic order in this theoretical framework. Published by the American Physical Society 2024

arXiv:2307.05671•Physical Review Research•Jan 29, 2024•3 citations

Doped carrier formulation and mean-field theory of the tt′t″J model

Tiago C. Ribeiro, Xiao-Gang Wen

In the generalized-$tJ$ model the effect of a large local Coulomb repulsion is accounted for by restricting the Hilbert space to states with at most one electron per site. In this case the electronic system can be viewed in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator. To explicitly capture the interplay between the hole dynamics and local spin correlations we derive a formulation of the generalized-$tJ$ model where doped carrier operators are used instead of the original electron operators. This ``doped carrier'' formulation provides a starting point to address doped spin systems, and we use it to develop a fully fermionic, mean-field description of doped Mott insulators. This mean-field approach reveals a mechanism for superconductivity---namely, spinon-dopon mixing---and we apply it to the $t{t}^{\ensuremath{'}}{t}^{\ensuremath{''}}J$ model as of interest to high-temperature superconductors. In particular, we use model parameters borrowed from band calculations and from fitting angle-resolved photoemission spectroscopy data to obtain a mean-field phase diagram that reproduces semiquantitatively that of hole- and electron-doped cuprates. The mean-field approach hereby presented accounts for the local antiferromagnetic and $d$-wave superconducting correlations which, we show, provide a rational for the role of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ in strengthening superconductivity as expected by experiments and other theoretical approaches. As we discuss how $t$, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$ affect the phase diagram, we also comment on possible scenarios to understand the differences between as-grown and oxygen-reduced electron-doped samples.

arXiv:cond-mat/0601174•Physical Review B•Oct 17, 2006•42 citations

Mean-field description of the phase string effect in the t−J model

Zheng-Yu Weng, D. N. Sheng, C. S. Ting

A mean-field treatment of the phase string effect in the $t\ensuremath{-}J$ model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and the metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long-range ordering (AFLRO) at half-filling and superconducting condensation in the metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.

arXiv:cond-mat/9809362•Physical review. B, Condensed matter•Apr 1, 1999•43 citations

Doping-driven evolution of the superconducting state from a doped Mott insulator: Cluster dynamical mean-field theory

Marcello Civelli

In this paper we investigate the zero-temperature doping-driven evolution of a superconductor toward the Mott insulator in a two-dimensional electron model, relevant for high-temperature superconductivity. To this purpose we use a cluster extension of dynamical mean-field theory. Our results show that a standard $d$-wave superconductor, realized at high doping, is driven into the Mott insulator via an intermediate superconducting state displaying unconventional physical properties. By restoring the translational invariance of the lattice, we give an interpretation of these findings in momentum space. In particular, we show that at a finite doping a strong momentum-space differentiation takes place: non-Fermi liquid and insulatinglike (pseudogap) characters rise in some regions (antinodes), while Fermi liquid quasiparticles survive in other regions (nodes) of momentum space. We describe the consequence of these happenings on the spectral properties, stressing in particular the behavior of the superconducting gap, which reveals two distinct nodal and antinodal energy scales as a function of doping, detected in photoemission and Raman spectroscopy experiments. We study and compare with experimental results the doping-dependent behavior of other physical quantities, such as for instance, the nodal quasiparticle velocity (extracted in angle-resolved photoemission) and the low-energy slopes of the local density of states and of the Raman scattering response. We then propose a description of the evolution of the electronic structure while approaching the Mott transition. We show that, within our formalism, a strong asymmetry naturally arises in the local density of states, measured in scanning tunneling spectroscopy. We investigate in detail the doping evolution of the electronic bands, focusing on the kinklike quasiparticle dispersion observed with angle-resolved photoemission in specific cuts of the momentum-energy space. We finally show the consequences of the properties presented above in the doping dependence of the Hall resistivity, measured in magnetotransport experiments.

arXiv:0808.3948•Physical Review B•May 15, 2009•54 citations

The analytical description of a doped Mott insulator

Yu-Liang Liu

With the hierarchical Green’s function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green’s function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green’s function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: One is contributed by the spin fluctuation of the electrons, which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors and the numerical calculations in normal state above the pseudogap regime.

arXiv:1908.04453•International Journal of Modern Physics B•Nov 20, 2019•3 citations

Charge dynamics in the phase string model for high- Tc superconductors

Zheng‐Cheng Gu, Zheng-Yu Weng

An understanding of the anomalous charge dynamics in the high-${T}_{c}$ cuprates is obtained based on a model study of doped Mott insulators. The high-temperature optical conductivity is found to generally have a two-component structure: a Drude-like part followed by a mid-infrared band. The scattering rate associated with the Drude part exhibits a linear-temperature dependence over a wide range of high temperature, while the Drude term gets progressively suppressed below a characteristic energy of magnetic origin as the system enters the pseudogap phase. The high-energy optical conductivity shows a resonancelike feature in an underdoped case and continuously evolves into a $1∕\ensuremath{\omega}$ tail at higher doping, indicating that they share the same physical origin. In particular, such a high-energy component is closely correlated with the $\ensuremath{\omega}$-peak structure of the density-density correlation function at different momenta, in systematic consistency with exact diagonalization results based on the $t\text{\ensuremath{-}}J$ model. The underlying physics is attributed to the high-energy spin-charge separation in the model, in which the ``mode coupling'' responsible for the anomalous charge properties is not between the electrons and some collective mode but rather between charge carriers, holons, and a topological gauge field controlled by spin dynamics, as the consequence of the strong short-range electron-electron Coulomb repulsion in the doped Mott insulator.

arXiv:cond-mat/0612696•Physical Review B•Jul 2, 2007•5 citations
We present a systematic study of spin dynamics in a superconducting ground state, which itself is a doped Mott insulator and can correctly reduce to an antiferromagnetic (AF) state at half-filling with an AF long-range order (AFLRO). Such a doped Mott insulator is described by a mean-field theory based on the phase string formulation of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model. We show that the well-known spin wave excitation in the AFLRO state at half-filling evolves into a resonancelike peak at a finite energy in the superconducting state, which is located around the AF wave vectors. The width of such a resonancelike peak in momentum space decides a spin correlation length scale which is inversely proportional to the square root of doping concentration, while the energy of the resonancelike peak scales linearly with the doping concentration at low doping. These properties are consistent with experimental observations in the high-Tc{T}_{c}Tc​ cuprates. An important prediction of the theory is that, while the total spin sum rule is satisfied at different doping concentrations, the weight of the resonancelike peak does not vanish, but is continuously saturated to the weight of the AFLRO at zero-doping limit. Besides the low-energy resonancelike peak, we also show that the high-energy excitations still track the spin wave dispersion in momentum space, contributing to a significant portion of the total spin sum rule. The fluctuational effect beyond the mean-field theory is also examined, which is related to the broadening of the resonancelike peak in energy space. In particular, we discuss the incommensurability of the spin dynamics by pointing out that its visibility is strongly tied to the low-energy fluctuations below the resonancelike peak. We finally investigate the interlayer coupling effect on the spin dynamics as a function of doping, by considering a bilayer system.
We examine the dynamical magnetic response in a two-component resonating-valence-bond (RVB) description of the doped Mott insulator. The half-filled antiferromagnetic phase described by the Schwinger-boson mean-field theory will evolve into a bosonic-RVB state in the superconducting phase upon doping, where the doped holes introduce another fermionic itinerant spinon which forms a BCS-like RVB order. The spin excitations are thus composed of a resonance-like mode from the former and a weak dispersive mode from the itinerant component at the mean-field level. These two-component spinons are shown to give rise to an hourglasslike spin excitation at the random-phase approximation level via an antiferromagnetic coupling between the two modes, which provides an unconventional explanation of the experimental observations in the cuprate. In particular, we also discuss an instability towards an incommensurate magnetic order in this theoretical framework. Published by the American Physical Society 2024
In the generalized-tJtJtJ model the effect of a large local Coulomb repulsion is accounted for by restricting the Hilbert space to states with at most one electron per site. In this case the electronic system can be viewed in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator. To explicitly capture the interplay between the hole dynamics and local spin correlations we derive a formulation of the generalized-tJtJtJ model where doped carrier operators are used instead of the original electron operators. This ``doped carrier'' formulation provides a starting point to address doped spin systems, and we use it to develop a fully fermionic, mean-field description of doped Mott insulators. This mean-field approach reveals a mechanism for superconductivity---namely, spinon-dopon mixing---and we apply it to the $t{t}^{\ensuremath{'}}{t}^{\ensuremath{''}}J$ model as of interest to high-temperature superconductors. In particular, we use model parameters borrowed from band calculations and from fitting angle-resolved photoemission spectroscopy data to obtain a mean-field phase diagram that reproduces semiquantitatively that of hole- and electron-doped cuprates. The mean-field approach hereby presented accounts for the local antiferromagnetic and ddd-wave superconducting correlations which, we show, provide a rational for the role of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ in strengthening superconductivity as expected by experiments and other theoretical approaches. As we discuss how ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$ affect the phase diagram, we also comment on possible scenarios to understand the differences between as-grown and oxygen-reduced electron-doped samples.
A mean-field treatment of the phase string effect in the $t\ensuremath{-}J$ model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and the metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long-range ordering (AFLRO) at half-filling and superconducting condensation in the metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.
In this paper we investigate the zero-temperature doping-driven evolution of a superconductor toward the Mott insulator in a two-dimensional electron model, relevant for high-temperature superconductivity. To this purpose we use a cluster extension of dynamical mean-field theory. Our results show that a standard ddd-wave superconductor, realized at high doping, is driven into the Mott insulator via an intermediate superconducting state displaying unconventional physical properties. By restoring the translational invariance of the lattice, we give an interpretation of these findings in momentum space. In particular, we show that at a finite doping a strong momentum-space differentiation takes place: non-Fermi liquid and insulatinglike (pseudogap) characters rise in some regions (antinodes), while Fermi liquid quasiparticles survive in other regions (nodes) of momentum space. We describe the consequence of these happenings on the spectral properties, stressing in particular the behavior of the superconducting gap, which reveals two distinct nodal and antinodal energy scales as a function of doping, detected in photoemission and Raman spectroscopy experiments. We study and compare with experimental results the doping-dependent behavior of other physical quantities, such as for instance, the nodal quasiparticle velocity (extracted in angle-resolved photoemission) and the low-energy slopes of the local density of states and of the Raman scattering response. We then propose a description of the evolution of the electronic structure while approaching the Mott transition. We show that, within our formalism, a strong asymmetry naturally arises in the local density of states, measured in scanning tunneling spectroscopy. We investigate in detail the doping evolution of the electronic bands, focusing on the kinklike quasiparticle dispersion observed with angle-resolved photoemission in specific cuts of the momentum-energy space. We finally show the consequences of the properties presented above in the doping dependence of the Hall resistivity, measured in magnetotransport experiments.
With the hierarchical Green’s function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green’s function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green’s function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: One is contributed by the spin fluctuation of the electrons, which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors and the numerical calculations in normal state above the pseudogap regime.
An understanding of the anomalous charge dynamics in the high-Tc{T}_{c}Tc​ cuprates is obtained based on a model study of doped Mott insulators. The high-temperature optical conductivity is found to generally have a two-component structure: a Drude-like part followed by a mid-infrared band. The scattering rate associated with the Drude part exhibits a linear-temperature dependence over a wide range of high temperature, while the Drude term gets progressively suppressed below a characteristic energy of magnetic origin as the system enters the pseudogap phase. The high-energy optical conductivity shows a resonancelike feature in an underdoped case and continuously evolves into a $1∕\ensuremath{\omega}$ tail at higher doping, indicating that they share the same physical origin. In particular, such a high-energy component is closely correlated with the $\ensuremath{\omega}$-peak structure of the density-density correlation function at different momenta, in systematic consistency with exact diagonalization results based on the $t\text{\ensuremath{-}}J$ model. The underlying physics is attributed to the high-energy spin-charge separation in the model, in which the ``mode coupling'' responsible for the anomalous charge properties is not between the electrons and some collective mode but rather between charge carriers, holons, and a topological gauge field controlled by spin dynamics, as the consequence of the strong short-range electron-electron Coulomb repulsion in the doped Mott insulator.