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:0803.3983 · Physical Review Letters

Orbital Currents in Extended Hubbard Models of High- Tc Cuprate Superconductors

Cédric Weber, Andreas Martin Läuchli, Frédéric Mila, Thierry Giamarchi

Published Jan 8, 2009• 118 citations
arXivHTMLPDF

Abstract

Motivated by the recent report of broken time-reversal symmetry and zero momentum magnetic scattering in underdoped cuprates, we investigate under which circumstances orbital currents circulating inside a unit cell might be stabilized in extended Hubbard models that explicitly include oxygen orbitals. Using Gutzwiller projected variational wave functions that treat on an equal footing all instabilities, we show that orbital currents indeed develop on finite clusters and that they are stabilized in the thermodynamic limit if additional interactions, e.g., strong hybridization with apical oxygens, are included in the model.

DOI
10.1103/physrevlett.102.017005

Related papers

Numerical exploration of spontaneous broken symmetries in multiorbital Hubbard models

Y. F. Kung, Cheng-Chien Chen, Brian Moritz +3 more

We study three proposals for broken symmetry in the cuprate pseudogap---oxygen antiferromagnetism, ${\ensuremath{\Theta}}_{II}$ orbital loop currents, and circulating currents involving apex oxygens---through numerical exploration of multiorbital Hubbard models. Our numerically exact results show no evidence for the existence of oxygen antiferromagnetic order or the ${\ensuremath{\Theta}}_{II}$ phase in the three-orbital Hubbard model. The model also fails to sustain an ordered current pattern even with the presence of additional apex oxygen orbitals. We thereby conclude that it is difficult to stabilize the aforementioned phases in the multiorbital Hubbard models for parameters relevant to cuprate superconductors. However, the ${\ensuremath{\Theta}}_{II}$ phase might be stabilized through explicit flux terms. We find an enhanced propensity for circulating currents with such terms in calculations simulating applied stress or strain, which skew the copper-oxygen plane to resemble a kagome lattice. We propose an experimental viewpoint to shed additional light on this problem.

arXiv:1408.6231•Physical Review B•Dec 5, 2014•20 citations

Orbital structure of the effective pairing interaction in the high-temperature superconducting cuprates

Peizhi Mai, Giovanni Balduzzi, Steven Johnston +1 more

Abstract The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO2 planes. Here, we use a dynamical cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.

arXiv:2009.14235•npj Quantum Materials•Mar 17, 2021•29 citations

Phase Diagram of a Three-Orbital Model for High- Tc Cuprate Superconductors

Cédric Weber, Thierry Giamarchi, Chandra Mohan Varma

We study the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.

arXiv:1305.7275•Physical Review Letters•Mar 18, 2014•60 citations

Circulating-current states and ring-exchange interactions in cuprates

Bruce Normand, Andrzej M. Oleś

We consider the consequences for circulating-current states of a cyclic, four-spin, ``ring-exchange'' interaction of the type shown recently to be significant in cuprate systems. The real-space Hartree-Fock approach is used to establish the existence of charge-current and spin-current phases in a generalized Hubbard model for the ${\mathrm{CuO}}_{2}$ planes in cuprates. We augment the Hartree-Fock approximation to consider correlated states renormalized by Gutzwiller projection factors, which allow us to gauge the qualitative effects of projection to no double occupancy in the limit of strong on-site Coulomb repulsion. We find that charge flux states may be competitive in the underdoped and optimally doped regime in cuprate systems, whereas spin flux states are suppressed in the strongly correlated regime. We then include the ring-exchange interaction and demonstrate its effect on current-carrying states both at and away from half-filling.

arXiv:cond-mat/0403481•Physical Review B•Oct 15, 2004•11 citations

Variational study of strongly correlated electronic models

Cédric Weber

The discovery of high-Tc superconductivity in the cuprates, and the observation that strong correlations are important in connection with these compounds has led to a tremendous interest in understanding the physics of strongly correlated electronic models. In particular the two simplest models for strongly correlated electrons, namely the Hubbard and t–J models, have been the subject of intensive studies. In a milestone paper of 1987, P.W. Anderson proposed that a resonating valence bond (RVB) wave-function, which consists of a superposition of valence-bond states, contains the ingredients to account for a consistent theory of the Hubbard and t–J models. Motivated by the success of variational Monte- Carlo to describe some of the peculiar properties of the cuprates, we propose in this dissertation, on one hand, to extend the method to further strongly correlated models to describe other compounds such as graphene, carbon nanotube or the cobaltite compounds, and on the other hand we propose to focus on the pseudo-gap phase of the cuprates, which is still prompting for a consistent theory. In particular, the issue of checkerboard spatial modulations in the density of states in the low temperature regime of the cuprates is addressed. Finally, we have studied the possibility for spontaneous orbital currents in the cuprates, that might play a key role in the theory of high Tc superconductors.

•Jan 1, 2007•2 citations

Orbital currents in insulating and doped antiferromagnets

Mathias S. Scheurer, Subir Sachdev A

We describe square lattice spin liquids, which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have nonzero scalar spin chirality, which implies the appearance of spontaneous orbital charge currents in the bulk (even in the insulator); but in some cases, orbital currents are nonzero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with ${\mathbb{Z}}_{2}$ and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases, which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the N\'eel state.

arXiv:1808.04826•Physical review. B./Physical review. B•Dec 11, 2018•29 citations
Motivated by the recent report of broken time-reversal symmetry and zero momentum magnetic scattering in underdoped cuprates, we investigate under which circumstances orbital currents circulating inside a unit cell might be stabilized in extended Hubbard models that explicitly include oxygen orbitals. Using Gutzwiller projected variational wave functions that treat on an equal footing all instabilities, we show that orbital currents indeed develop on finite clusters and that they are stabilized in the thermodynamic limit if additional interactions, e.g., strong hybridization with apical oxygens, are included in the model.
We study three proposals for broken symmetry in the cuprate pseudogap---oxygen antiferromagnetism, ${\ensuremath{\Theta}}_{II}$ orbital loop currents, and circulating currents involving apex oxygens---through numerical exploration of multiorbital Hubbard models. Our numerically exact results show no evidence for the existence of oxygen antiferromagnetic order or the ${\ensuremath{\Theta}}_{II}$ phase in the three-orbital Hubbard model. The model also fails to sustain an ordered current pattern even with the presence of additional apex oxygen orbitals. We thereby conclude that it is difficult to stabilize the aforementioned phases in the multiorbital Hubbard models for parameters relevant to cuprate superconductors. However, the ${\ensuremath{\Theta}}_{II}$ phase might be stabilized through explicit flux terms. We find an enhanced propensity for circulating currents with such terms in calculations simulating applied stress or strain, which skew the copper-oxygen plane to resemble a kagome lattice. We propose an experimental viewpoint to shed additional light on this problem.
Abstract The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO2 planes. Here, we use a dynamical cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.
We study the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.
We consider the consequences for circulating-current states of a cyclic, four-spin, ``ring-exchange'' interaction of the type shown recently to be significant in cuprate systems. The real-space Hartree-Fock approach is used to establish the existence of charge-current and spin-current phases in a generalized Hubbard model for the CuO2{\mathrm{CuO}}_{2}CuO2​ planes in cuprates. We augment the Hartree-Fock approximation to consider correlated states renormalized by Gutzwiller projection factors, which allow us to gauge the qualitative effects of projection to no double occupancy in the limit of strong on-site Coulomb repulsion. We find that charge flux states may be competitive in the underdoped and optimally doped regime in cuprate systems, whereas spin flux states are suppressed in the strongly correlated regime. We then include the ring-exchange interaction and demonstrate its effect on current-carrying states both at and away from half-filling.
The discovery of high-Tc superconductivity in the cuprates, and the observation that strong correlations are important in connection with these compounds has led to a tremendous interest in understanding the physics of strongly correlated electronic models. In particular the two simplest models for strongly correlated electrons, namely the Hubbard and t–J models, have been the subject of intensive studies. In a milestone paper of 1987, P.W. Anderson proposed that a resonating valence bond (RVB) wave-function, which consists of a superposition of valence-bond states, contains the ingredients to account for a consistent theory of the Hubbard and t–J models. Motivated by the success of variational Monte- Carlo to describe some of the peculiar properties of the cuprates, we propose in this dissertation, on one hand, to extend the method to further strongly correlated models to describe other compounds such as graphene, carbon nanotube or the cobaltite compounds, and on the other hand we propose to focus on the pseudo-gap phase of the cuprates, which is still prompting for a consistent theory. In particular, the issue of checkerboard spatial modulations in the density of states in the low temperature regime of the cuprates is addressed. Finally, we have studied the possibility for spontaneous orbital currents in the cuprates, that might play a key role in the theory of high Tc superconductors.
We describe square lattice spin liquids, which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have nonzero scalar spin chirality, which implies the appearance of spontaneous orbital charge currents in the bulk (even in the insulator); but in some cases, orbital currents are nonzero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with Z2{\mathbb{Z}}_{2}Z2​ and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases, which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the N\'eel state.