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

The effects of lattice anisotropies on the physics of copper oxide planes

J. M. Tipper

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The class of high T c superconductors share one common structural aspect, the existence of planes of copper and oxygen ions.These planes are thought to be the source of the superconducting behaviour.They can be represented as a two-dimensional lattice of ions, which facilitates their study using numerical models.One such model is the t -J model.In most studies utilising numerical models, the planes have been considered isotropic.However, recent analysis of cuprate structure has illustrated that this may not be representative of the copper oxide planes.A number of cuprate structures exhibit different phases in which the planes are not isotropic, such as the low temperature orthorhombic and low temperature tetragonal phases.This work will examine the effects of introducing anisotropy into the t -J model in order to understand how these phases affect the results gained from numerical studies.

Related papers

Investigation of the adequacy of the two-dimensional t−J model for high-temperature superconductivity

Gang Su

It is widely thought that the two-dimensional (2D) $t\text{\ensuremath{-}}J$ model captures essential features of the cuprate oxides. However, some recent results on the pairing correlations in this model, which were obtained by various numerical or analytical methods, are controversial. Therefore, whether the 2D $t\text{\ensuremath{-}}J$ model is really suitable for the cuprate oxides is still under debate. We argue that the 2D $t\text{\ensuremath{-}}J$ model may be inadequate for overall describing high temperature superconductivity.

Physical Review B•Sep 21, 2005•4 citations

Quantum Monte Carlo Simulations of Models Related to High-Tc Superconductivity on a Transputer Network

Joseph D. Reger

Much of the insight into the low temperature behaviour of two-dimensional quantum antiferromagnets has been recently obtained by extensive Monte Carlo. These models are relevant in the study of the magnetic behaviour of high Tc compounds containing copper-oxide layers. While of little technical importance, the physical properties of these models are certainly important for the understanding of the new type of behaviour that leads to superconductivity under certain conditions.

International Journal of Modern Physics C•Mar 1, 1991•0 citations

Exploring phases in copper oxides: numerical data fitting in superconductivity investigation

Júlia Henriques Lamarca dos Santos

In this dissertation we investigate superconductivity in strongly correlated systems, with a specific focus on copper oxides, known as cuprates. These materials exhibit a variety of emerging phases as we vary parameters such as temperature, doping, and pressure. In addition to the superconducting phase, other phases, such as the pseudogap, remain poorly understood. The pseudogap phase is characterized by a suppression of spectral weight in certain directions in momentum space. Understanding this phase is fundamental to understanding superconductivity, as it is believed that there are signatures of the superconducting phase in the pseudogap phase. The Hubbard model is used to describe strongly correlated systems, as it well describes the competition between the kinetic energy and the Coulomb interaction of electrons. It is believed that much can be learned about cuprates considering the Hubbard model in two spatial dimensions, corresponding to the planes of copper and oxygen, in the presence of doping, arising from the other atoms. However, the model does not have an exact solution in two dimensions, requiring the use of a numerical method for its resolution. In previous work by the group, the model was solved numerically without considering superconductivity via extensions of Dynamical Mean Field Theory (DMFT). This technique maps the Hubbard model onto the Anderson impurity problem, simplifying the resolution. The results obtained revealed two distinct metallic phases, conventional and pseudogap, as the system doping varied. The objective of this dissertation is to verify whether the different metallic phases mentioned above give rise to different superconducting phases. For this, an electron pair formation term was added to the Hamiltonian and new numerical DMFT results were obtained. These results are difficult to understand; to analyze them, we use a phenomenological model that describes electron dynamics at low energies. We built a code that simultaneously adjusts the DMFT curves for the real and imaginary parts of the normal and anomalous self-energies to the phenomenological model for each doping value, allowing the analysis of the model parameters starting from the different metallic regions. Our preliminary results show fluctuations in these parameters when we vary the doping, suggesting that it would be desirable to obtain more accurate DMFT results, which is in progress, so that new adjustments to the phenomenological model can be made.

•Sep 27, 2024•0 citations

Correlated electrons in high-temperature superconductors

Elbio R. Dagotto

Theoretical ideas and experimental results concerning high-temperature superconductors are reviewed. Special emphasis is given to calculations performed with the help of computers applied to models of strongly correlated electrons proposed to describe the two-dimensional Cu${\mathrm{O}}_{2}$ planes. The review also includes results using several analytical techniques. The one- and three-band Hubbard models and the $t\ensuremath{-}J$ model are discussed, and their behavior compared against experiments when available. The author found, among the conclusions of the review, that some experimentally observed unusual properties of the cuprates have a natural explanation through Hubbard-like models. In particular, abnormal features like the mid-infrared band of the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$, the new states observed in the gap in photoemission experiments, the behavior of the spin correlations with doping, and the presence of phase separation in the copper oxide superconductors may be explained, at least in part, by these models. Finally, the existence of superconductivity in Hubbard-like models is analyzed. Some aspects of the recently proposed ideas to describe the cuprates as having a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others. It is concluded that computational techniques provide a useful, unbiased tool for studying the difficult regime where electrons are strongly interacting, and that considerable progress can be achieved by comparing numerical results against analytical predictions for the properties of these models. Future directions of the active field of computational studies of correlated electrons are briefly discussed.

arXiv:cond-mat/9311013•Reviews of Modern Physics•Jul 1, 1994•3,118 citations

A renormalization-group study of the t-J model

E. V. L. de Mello

The t-J model has been proposed to describe the physics of copper oxide planes in high-temperature superconductors. A real-space quantum renormalization-group method is developed in order to study the t-J Hamiltonian in a square lattice. The zero-temperature phase diagram is analysed for electron concentrations near the half-filled band and ratio J/t. A critical line is found that separates two distinct regions: one of a gas of holes in an antiferromagnetic background, and the other consisting of a phase in which holes segregate into a hole-rich and a pure antiferromagnetic region, as demonstrated by chemical-potential eigenvalue calculations near the phase attractor. The results are close to the experimental observations.

Journal of Physics Condensed Matter•Jan 3, 1994•2 citations

Universality class of the structural phase transition in the normal phase of cuprate superconductors

M. N. Najafi, Ali Tavana

The tetragonal-orthorhombic structural phase transition of oxygen atoms in the basal plane of YBa_{2}Cu_{3}O_{6+δ} high-T_{C} cuprate superconductors is studied numerically. By mapping the system onto the asymmetric next-nearest-neighbor Ising model, we characterize this phase transition. Results indicate the degrees of critical behavior. We show that this phase transition occurs at the temperature T_{C}≃0.148eV in the thermodynamic limit. By analyzing the critical exponents, it is found that this universality class displays some common features, with the two-dimensional three-state Potts model universality class, although the possibility of other universality classes cannot be ruled out. Conformal invariance at T=T_{c} is investigated using the Schramm-Loewner evolution (SLE) technique, and it is found that the SLE diffusivity parameter for this system is 3.34±0.01.

Physical review. E•Aug 8, 2016•5 citations
The class of high T c superconductors share one common structural aspect, the existence of planes of copper and oxygen ions.These planes are thought to be the source of the superconducting behaviour.They can be represented as a two-dimensional lattice of ions, which facilitates their study using numerical models.One such model is the t -J model.In most studies utilising numerical models, the planes have been considered isotropic.However, recent analysis of cuprate structure has illustrated that this may not be representative of the copper oxide planes.A number of cuprate structures exhibit different phases in which the planes are not isotropic, such as the low temperature orthorhombic and low temperature tetragonal phases.This work will examine the effects of introducing anisotropy into the t -J model in order to understand how these phases affect the results gained from numerical studies.
It is widely thought that the two-dimensional (2D) $t\text{\ensuremath{-}}J$ model captures essential features of the cuprate oxides. However, some recent results on the pairing correlations in this model, which were obtained by various numerical or analytical methods, are controversial. Therefore, whether the 2D $t\text{\ensuremath{-}}J$ model is really suitable for the cuprate oxides is still under debate. We argue that the 2D $t\text{\ensuremath{-}}J$ model may be inadequate for overall describing high temperature superconductivity.
In this dissertation we investigate superconductivity in strongly correlated systems, with a specific focus on copper oxides, known as cuprates. These materials exhibit a variety of emerging phases as we vary parameters such as temperature, doping, and pressure. In addition to the superconducting phase, other phases, such as the pseudogap, remain poorly understood. The pseudogap phase is characterized by a suppression of spectral weight in certain directions in momentum space. Understanding this phase is fundamental to understanding superconductivity, as it is believed that there are signatures of the superconducting phase in the pseudogap phase. The Hubbard model is used to describe strongly correlated systems, as it well describes the competition between the kinetic energy and the Coulomb interaction of electrons. It is believed that much can be learned about cuprates considering the Hubbard model in two spatial dimensions, corresponding to the planes of copper and oxygen, in the presence of doping, arising from the other atoms. However, the model does not have an exact solution in two dimensions, requiring the use of a numerical method for its resolution. In previous work by the group, the model was solved numerically without considering superconductivity via extensions of Dynamical Mean Field Theory (DMFT). This technique maps the Hubbard model onto the Anderson impurity problem, simplifying the resolution. The results obtained revealed two distinct metallic phases, conventional and pseudogap, as the system doping varied. The objective of this dissertation is to verify whether the different metallic phases mentioned above give rise to different superconducting phases. For this, an electron pair formation term was added to the Hamiltonian and new numerical DMFT results were obtained. These results are difficult to understand; to analyze them, we use a phenomenological model that describes electron dynamics at low energies. We built a code that simultaneously adjusts the DMFT curves for the real and imaginary parts of the normal and anomalous self-energies to the phenomenological model for each doping value, allowing the analysis of the model parameters starting from the different metallic regions. Our preliminary results show fluctuations in these parameters when we vary the doping, suggesting that it would be desirable to obtain more accurate DMFT results, which is in progress, so that new adjustments to the phenomenological model can be made.
Theoretical ideas and experimental results concerning high-temperature superconductors are reviewed. Special emphasis is given to calculations performed with the help of computers applied to models of strongly correlated electrons proposed to describe the two-dimensional CuO2{\mathrm{O}}_{2}O2​ planes. The review also includes results using several analytical techniques. The one- and three-band Hubbard models and the $t\ensuremath{-}J$ model are discussed, and their behavior compared against experiments when available. The author found, among the conclusions of the review, that some experimentally observed unusual properties of the cuprates have a natural explanation through Hubbard-like models. In particular, abnormal features like the mid-infrared band of the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$, the new states observed in the gap in photoemission experiments, the behavior of the spin correlations with doping, and the presence of phase separation in the copper oxide superconductors may be explained, at least in part, by these models. Finally, the existence of superconductivity in Hubbard-like models is analyzed. Some aspects of the recently proposed ideas to describe the cuprates as having a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others. It is concluded that computational techniques provide a useful, unbiased tool for studying the difficult regime where electrons are strongly interacting, and that considerable progress can be achieved by comparing numerical results against analytical predictions for the properties of these models. Future directions of the active field of computational studies of correlated electrons are briefly discussed.
The t-J model has been proposed to describe the physics of copper oxide planes in high-temperature superconductors. A real-space quantum renormalization-group method is developed in order to study the t-J Hamiltonian in a square lattice. The zero-temperature phase diagram is analysed for electron concentrations near the half-filled band and ratio J/t. A critical line is found that separates two distinct regions: one of a gas of holes in an antiferromagnetic background, and the other consisting of a phase in which holes segregate into a hole-rich and a pure antiferromagnetic region, as demonstrated by chemical-potential eigenvalue calculations near the phase attractor. The results are close to the experimental observations.
The tetragonal-orthorhombic structural phase transition of oxygen atoms in the basal plane of YBa_{2}Cu_{3}O_{6+δ} high-T_{C} cuprate superconductors is studied numerically. By mapping the system onto the asymmetric next-nearest-neighbor Ising model, we characterize this phase transition. Results indicate the degrees of critical behavior. We show that this phase transition occurs at the temperature T_{C}≃0.148eV in the thermodynamic limit. By analyzing the critical exponents, it is found that this universality class displays some common features, with the two-dimensional three-state Potts model universality class, although the possibility of other universality classes cannot be ruled out. Conformal invariance at T=T_{c} is investigated using the Schramm-Loewner evolution (SLE) technique, and it is found that the SLE diffusivity parameter for this system is 3.34±0.01.