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/0310371 · Journal of the Physical Society of Japan

Nontrivial Behavior of the Fermi Arc in the Staggered-Flux Ordered Phase

Koichi Hamada, D. Yoshioka

Published Jul 15, 2004• 0 citations
arXivHTMLPDF

Abstract

The doping and temperature dependences of the Fermi arc in the staggered-flux, or the d-density wave, ordered phase of the t-J model are analyzed by the U(1) slave boson theory. Nontrivial behavior is revealed by the self-consistent calculation. At low doped and finite-temperature region, both the length of the Fermi arc and the width of the Fermi pocket are proportional to $δ$ and the area of the Fermi pocket is proportional to $δ^2$. This behavior is completely different from that at the zero temperature, where the area of the Fermi pocket becomes $π^2 δ$. This behavior should be observed by detailed experiments of angle-resolved photoemission spectroscopy in the pseudogap phase of high-T_c cuprates if the pseudogap phase is the staggered-flux ordered phase.

DOI
10.1143/jpsj.73.1631

Related papers

Staggered flux state of electrons in a two-dimensional t−J model

Koichi Hamada, D. Yoshioka

The competition between the staggered flux state, or the d-density wave state, and the d-wave pairing state is analyzed in a two-dimensional $t\ensuremath{-}J$ model based on the U(1) slave boson mean-field theory. Not only staggered flux of spinons but also staggered flux of holons are considered. In this formalism, the hopping order parameter of physical electron is described by the product of hopping order parameters of spinons and holons. The staggered flux amplitude of electrons is the difference of staggered flux amplitude of spinons and that of holons. In the $\ensuremath{\pi}$-flux phase of spinons, staggered fluxes of spinons and holons cancel completely and the staggered flux order of electrons does not exist. However, in the staggered flux phase of spinons whose staggered flux amplitude is not $\ensuremath{\pi},$ fluxes does not cancel completely and the staggered flux amplitude of electron remains. Thus the phase transition between these two phases, the $\ensuremath{\pi}$-flux phase and the staggered flux phase of spinons, becomes a second-order transition in the physical electron picture. The order parameter which characterizes this transition is the staggered flux order parameter of electrons. A mean-field phase diagram is shown. It is proved analytically that there is no coexistence of staggered flux and d-wave pairing. The temperature dependence of Fermi surface and excitation gap at $(0,\ensuremath{\pi})$ are shown. These behaviors are consistent with angle-resolved photoemission spectroscopy experiments.

arXiv:cond-mat/0211406•Physical review. B, Condensed matter•May 6, 2003•16 citations

Theory of Underdoped Cuprates

Xiao-Gang Wen, Patrick A. Lee

We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping which respects an $\mathrm{SU}(2)$ symmetry---a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain $d$-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.

arXiv:cond-mat/9506065•Physical Review Letters•Jan 15, 1996•537 citations

SU(2) formulation of the t−J model: Application to underdoped cuprates

Patrick A. Lee, Naoto Nagaosa, Tai Kai Ng +1 more

We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain $d$-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.

arXiv:cond-mat/9701168•Physical review. B, Condensed matter•Mar 1, 1998•213 citations

Microscopic approach to high-temperature superconductors: Pseudogap phase

Steffen Sykora, K. W. Becker

Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gap-like behavior on parts of the Fermi surface, leaving a non-gapped segment known as Fermi arc around the diagonal of the Brillouin zone. Starting from the $t$-$J$ model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase in the framework of a novel renormalization scheme called PRM. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at a renormalized 'free' Hamiltonian for correlated electrons. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: We find well-defined excitation peaks around $ω=0$ near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small $ω$-range around the Fermi energy. In a subsequent paper, also the supercunducting phase at moderate hole doping will be discussed within the PRM approach.

arXiv:0903.0921•Mar 5, 2009•0 citations

Microscopic approach to high-temperature superconductors within the t-J model

Steffen Sykora, K. W. Becker

Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors leading to an unprecedented high transition temperature ${T}_{c}$ is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gaplike behavior on parts of the Fermi surface, leaving a nongapped segment known as Fermi arc around the diagonal of the Brillouin zone. Two main interpretations of the origin of the pseudogap have been proposed: either the pseudogap is a precursor to superconductivity, or it arises from another order competing with superconductivity. Starting from the t-J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase as well as the superconducting phase in the framework of a renormalization scheme called projector-based renormalization method. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at renormalized ``free'' Hamiltonians for correlated electrons for both phases. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: For the pseudogap phase we find well-defined excitation peaks around $\ensuremath{\omega}=0$ near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small $\ensuremath{\omega}$ range around the Fermi energy. In the superconducting phase, the order parameter turns out to have $d$-wave symmetry with a coherence length of a few lattice constants. In good agreement with experiments, we find no superconducting solutions for very small hole doping.

Physical Review B•Jul 14, 2009•6 citations

Thermal SU(2) lattice gauge theory for intertwined orders and hole pockets in the cuprates

Harshit Pandey, Maine Christos, Pietro M. Bonetti +3 more

The cuprate pseudogap phase displays Fermi arc spectral weight in photoemission and scanning tunneling microscopy, while recent magnetotransport observations yield evidence for the existence of hole pockets of fractional area p /8, where p is the doping density. We present a Monte Carlo study of a thermal SU(2) lattice gauge theory which can reconcile these observations. Our simulation includes the SU(2) gauge field U of a π -flux spin liquid, and a SU(2) fundamental charge e Higgs boson B . There is a Yukawa coupling between B , the fermionic spinons of the spin liquid, and the hole pockets of a fractionalized Fermi liquid. At the higher temperatures of the pseudogap, the finite-doping sign problem is evaded by including only thermal fluctuations of B and U , while the fermions are diagonalized exactly for each boson background. Our study also yields a fractionalized description of intertwined orders at lower temperatures, including the onset of d -wave superconductivity by the expulsion of vortices with flux h / ( 2 e ) , each with charge-order halos. We discuss conditions under which quantum oscillations in the density of states from hole pockets of area p / 8 could be observable in clean under-hole-doped cuprates.

arXiv:2507.05336•Proceedings of the National Academy of Sciences•Apr 29, 2026•3 citations
The doping and temperature dependences of the Fermi arc in the staggered-flux, or the d-density wave, ordered phase of the t-J model are analyzed by the U(1) slave boson theory. Nontrivial behavior is revealed by the self-consistent calculation. At low doped and finite-temperature region, both the length of the Fermi arc and the width of the Fermi pocket are proportional to δδδ and the area of the Fermi pocket is proportional to δ2δ^2δ2. This behavior is completely different from that at the zero temperature, where the area of the Fermi pocket becomes π2δπ^2 δπ2δ. This behavior should be observed by detailed experiments of angle-resolved photoemission spectroscopy in the pseudogap phase of high-T_c cuprates if the pseudogap phase is the staggered-flux ordered phase.
The competition between the staggered flux state, or the d-density wave state, and the d-wave pairing state is analyzed in a two-dimensional $t\ensuremath{-}J$ model based on the U(1) slave boson mean-field theory. Not only staggered flux of spinons but also staggered flux of holons are considered. In this formalism, the hopping order parameter of physical electron is described by the product of hopping order parameters of spinons and holons. The staggered flux amplitude of electrons is the difference of staggered flux amplitude of spinons and that of holons. In the $\ensuremath{\pi}$-flux phase of spinons, staggered fluxes of spinons and holons cancel completely and the staggered flux order of electrons does not exist. However, in the staggered flux phase of spinons whose staggered flux amplitude is not $\ensuremath{\pi},$ fluxes does not cancel completely and the staggered flux amplitude of electron remains. Thus the phase transition between these two phases, the $\ensuremath{\pi}$-flux phase and the staggered flux phase of spinons, becomes a second-order transition in the physical electron picture. The order parameter which characterizes this transition is the staggered flux order parameter of electrons. A mean-field phase diagram is shown. It is proved analytically that there is no coexistence of staggered flux and d-wave pairing. The temperature dependence of Fermi surface and excitation gap at $(0,\ensuremath{\pi})$ are shown. These behaviors are consistent with angle-resolved photoemission spectroscopy experiments.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping which respects an SU(2)\mathrm{SU}(2)SU(2) symmetry---a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The electron spectral function shows small Fermi pockets at low doping which continuously evolve into the large Fermi surface at high doping concentrations.
We develop a slave-boson theory for the $t\ensuremath{-}J$ model at finite doping that respects an SU(2) symmetry: a symmetry previously known to be important at half filling. The mean-field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contain ddd-wave superconductor, spin-gap, strange metal, and Fermi-liquid phases. The spin-gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping that continuously evolve into the large Fermi surface at high-doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low-energy effective theory for the low-lying fluctuations is derived and additional lying modes [which were overlooked in the U(1) theory] are identified.
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gap-like behavior on parts of the Fermi surface, leaving a non-gapped segment known as Fermi arc around the diagonal of the Brillouin zone. Starting from the ttt-JJJ model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase in the framework of a novel renormalization scheme called PRM. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at a renormalized 'free' Hamiltonian for correlated electrons. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: We find well-defined excitation peaks around ω=0ω=0ω=0 near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small ωωω-range around the Fermi energy. In a subsequent paper, also the supercunducting phase at moderate hole doping will be discussed within the PRM approach.
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors leading to an unprecedented high transition temperature Tc{T}_{c}Tc​ is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gaplike behavior on parts of the Fermi surface, leaving a nongapped segment known as Fermi arc around the diagonal of the Brillouin zone. Two main interpretations of the origin of the pseudogap have been proposed: either the pseudogap is a precursor to superconductivity, or it arises from another order competing with superconductivity. Starting from the t-J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase as well as the superconducting phase in the framework of a renormalization scheme called projector-based renormalization method. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at renormalized ``free'' Hamiltonians for correlated electrons for both phases. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: For the pseudogap phase we find well-defined excitation peaks around $\ensuremath{\omega}=0$ near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small $\ensuremath{\omega}$ range around the Fermi energy. In the superconducting phase, the order parameter turns out to have ddd-wave symmetry with a coherence length of a few lattice constants. In good agreement with experiments, we find no superconducting solutions for very small hole doping.
The cuprate pseudogap phase displays Fermi arc spectral weight in photoemission and scanning tunneling microscopy, while recent magnetotransport observations yield evidence for the existence of hole pockets of fractional area p /8, where p is the doping density. We present a Monte Carlo study of a thermal SU(2) lattice gauge theory which can reconcile these observations. Our simulation includes the SU(2) gauge field U of a π -flux spin liquid, and a SU(2) fundamental charge e Higgs boson B . There is a Yukawa coupling between B , the fermionic spinons of the spin liquid, and the hole pockets of a fractionalized Fermi liquid. At the higher temperatures of the pseudogap, the finite-doping sign problem is evaded by including only thermal fluctuations of B and U , while the fermions are diagonalized exactly for each boson background. Our study also yields a fractionalized description of intertwined orders at lower temperatures, including the onset of d -wave superconductivity by the expulsion of vortices with flux h / ( 2 e ) , each with charge-order halos. We discuss conditions under which quantum oscillations in the density of states from hole pockets of area p / 8 could be observable in clean under-hole-doped cuprates.