© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:cond-mat/0301585 · Physical review. B, Condensed matter

Pairing and density correlations of stripe electrons in a two-dimensional antiferromagnet

Henrik Johannesson, G. I. Japaridze

Published Dec 15, 2003• 3 citations

Abstract

We study a one-dimensional (1D) electron liquid embedded in a 2D antiferromagnetic insulator, and coupled to it via a weak antiferromagnetic spin-exchange interaction. We argue that this model may qualitatively capture the physics of a single charge stripe in the cuprates on length and time scales shorter than those set by its fluctuation dynamics. Using a local mean-field approach we identify the low-energy effective theory that describes the electronic-spin sector of the stripe as that of a sine-Gordon model. We determine its phases via a perturbative renormalization-group analysis. For realistic values of the model parameters we obtain a phase characterized by enhanced spin density and composite charge-density-wave correlations, coexisting with subleading triplet and composite singlet-pairing correlations. This result is shown to be independent of the spatial orientation of the stripe on the square lattice. We argue that slow transverse fluctuations of the stripes tend to suppress the density correlations, thus promoting the pairing instabilities. The largest amplitudes for the composite instabilities appear when the stripe forms an antiphase domain wall in the antiferromagnet. For twisted spin alignments the amplitudes decrease and leave room for a new type of composite pairing correlation, breaking parity but preserving time-reversal symmetry.

DOI: 10.1103/physrevb.68.214507

Related papers

One-Dimensional Electron Liquid in an Antiferromagnetic Environment: Spin Gap from Magnetic Correlations

Mats Granath, Henrik Johannesson

We study a one-dimensional electron liquid coupled by a weak spin-exchange interaction to an antiferromagnetic spin- $S$ ladder with $n$ legs. A perturbative renormalization group analysis in the semiclassical limit reveals the opening of a spin gap, driven by the local magnetic correlations on the ladder. The effect, which we argue is present for any gapful ladder or gapless ladder with $\mathrm{nS}\ensuremath{\gg}1$, is enhanced by the repulsive interaction among the conduction electrons but is insensitive to the sign of the spin exchange interaction with the ladder. Possible implications for the striped phases of the cuprates are discussed.

arXiv:cond-mat/9906004•Physical Review Letters•Jul 5, 1999•16 citations

Stripe Phase: Analytical Results for Weakly Coupled Repulsive Hubbard Model

Sergei I. Mukhin, Sergey I. Matveenko

Motivated by the stripe developments in cuprates, we review analytical results for the spin-charge solitonic superstructures derived in the framework of the Hubbard model in our studies of weakly coupled (quasi) one-dimensional repulsive electron systems on a lattice. These results demonstrate that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wavevectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, besides the wavevectors, mutual phases of the charge and spin densities also become coupled due to a quantum interference phenomenon, leading to the stripe phase instability. It is shown that away from half filling, periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential leads to the vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group ("parquet") analysis away from half filling are also presented. They reveal transient-scale correlations resembling the mean-field pattern. Possible correspondence of our theory with the experimental data on stripe phase in high Tc cuprates is discussed.

arXiv:cond-mat/0311019•International Journal of Modern Physics B•Aug 20, 2003•4 citations

Antiferromagnetic Spin Ladders Effectively Coupled by One-Dimensional Electron Liquids

W. Vincent Liu, Eduardo Fradkin

We study a model of the stripe state in strongly correlated systems consisting of an array of antiferromagnetic spin ladders, each with n(leg) legs, coupled to each other through the spin-exchange interaction to charged stripes in between each pair of ladders. The charged stripes are assumed to be Luttinger liquids in a spin-gap regime. An effective interaction for a pair of neighboring ladders is calculated by integrating out the gapped spin degrees of freedom in the charged stripes. The low energy effective theory of each ladder is a nonlinear sigma model with additional cross couplings of neighboring ladders, which favor either in-phase or antiphase short-range spin orderings depending on the physical parameters of the charged stripe.

arXiv:cond-mat/0008394•Physical Review Letters•Feb 26, 2001•9 citations

Dynamical Mean-Field Theory of Stripe Ordering

Alexander I. Lichtenstein, Marcus Fleck, Andrzej M. Oleś +1 more

Applying the dynamical mean-field theory to the two-dimensional Hubbard model, we calculate self-consistent solutions of doped antiferromagnets with spatially varying spin density ‹ n iσ › using realistic tight-binding parameters. The local self-energy of the supercell includes transverse and longitudinal spin fluctuations with an effective local potential due to short-range electron-electron correlations. It is found that metallic stripes are stabilized by a pseudogap. The stripes along (1,0) direction filled by one hole per two-domain wall unit cells change with increasing Coulomb interaction U to the more extended stripes along (1,1) direction consisting of four atoms filled by 1/4 doped hole each. These findings agree qualitatively with the experimental observations in the superconducting cuprates, and predict a qualitative difference between various compounds due to differences in the extended hopping parameters. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Kluwer Academic Publishers eBooks•Mar 29, 2006•0 citations

Electron correlations in stripe phases for doped antiferromagnets

Dariusz Gora, Krzysztof Rościszewski, Andrzej M. Oleś

We present the charge and magnetization density distribution in various stripe phases obtained for two-dimensional models of correlated electrons solved within the Hartree-Fock approximation and a variational local ansatz. Apart from the Hubbard model with local Coulomb interaction U, we investigate its two extensions by adding either static Peierls electron-lattice coupling, or the correlated hopping term in the so-called Hirsch model. It has been found that the stripe ordering is robust and occurs in underdoped $(\ensuremath{\delta}=1/8)$ and overdoped $(\ensuremath{\delta}=1/4)$ systems. At intermediate values of U in underdoped systems $(\ensuremath{\delta}=1/8)$ local correlations stabilize the vertical (01) antiferromagnetic domains, separated by nonmagnetic domain walls filled by one doped hole per two wall atoms. A stripe phase with the same size of magnetic domains and an increased filling of one hole per one wall atom is stable for overdoped $(\ensuremath{\delta}=1/4)$ systems. At larger values of U, both structures are replaced by more extended magnetic domain walls oriented along the (11) direction. These findings agree qualitatively with the experimental results.

Physical review. B, Condensed matter•Sep 1, 1999•26 citations

Effective interactions in the stripe state of the two-dimensional Hubbard model

S. Varlamov, G. Seibold

We investigate the structure of the pairing potential in the stripe phase of the two-dimensional Hubbard model. Based on the random-phase approximation we discuss in detail the interactions in the charge and spin channel and compare our calculations with related considerations in commensurate antiferromagnets. Our main finding is that due to the incommensurate charge-density wave formation the exchange of collective modes in the charge channel is significantly enhanced with respect to the spin-bag approach whereas due to the inhomogeneous charge distribution the coupling to transverse spin fluctuations tends to be suppressed.

arXiv:cond-mat/0102374•Physical review. B, Condensed matter•Jan 28, 2002•8 citations

We study a one-dimensional (1D) electron liquid embedded in a 2D antiferromagnetic insulator, and coupled to it via a weak antiferromagnetic spin-exchange interaction. We argue that this model may qualitatively capture the physics of a single charge stripe in the cuprates on length and time scales shorter than those set by its fluctuation dynamics. Using a local mean-field approach we identify the low-energy effective theory that describes the electronic-spin sector of the stripe as that of a sine-Gordon model. We determine its phases via a perturbative renormalization-group analysis. For realistic values of the model parameters we obtain a phase characterized by enhanced spin density and composite charge-density-wave correlations, coexisting with subleading triplet and composite singlet-pairing correlations. This result is shown to be independent of the spatial orientation of the stripe on the square lattice. We argue that slow transverse fluctuations of the stripes tend to suppress the density correlations, thus promoting the pairing instabilities. The largest amplitudes for the composite instabilities appear when the stripe forms an antiphase domain wall in the antiferromagnet. For twisted spin alignments the amplitudes decrease and leave room for a new type of composite pairing correlation, breaking parity but preserving time-reversal symmetry.

We study a one-dimensional electron liquid coupled by a weak spin-exchange interaction to an antiferromagnetic spin-

S

ladder with

n

legs. A perturbative renormalization group analysis in the semiclassical limit reveals the opening of a spin gap, driven by the local magnetic correlations on the ladder. The effect, which we argue is present for any gapful ladder or gapless ladder with $\mathrm{nS}\ensuremath{\gg}1$, is enhanced by the repulsive interaction among the conduction electrons but is insensitive to the sign of the spin exchange interaction with the ladder. Possible implications for the striped phases of the cuprates are discussed.

Motivated by the stripe developments in cuprates, we review analytical results for the spin-charge solitonic superstructures derived in the framework of the Hubbard model in our studies of weakly coupled (quasi) one-dimensional repulsive electron systems on a lattice. These results demonstrate that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wavevectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, besides the wavevectors, mutual phases of the charge and spin densities also become coupled due to a quantum interference phenomenon, leading to the stripe phase instability. It is shown that away from half filling, periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential leads to the vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group ("parquet") analysis away from half filling are also presented. They reveal transient-scale correlations resembling the mean-field pattern. Possible correspondence of our theory with the experimental data on stripe phase in high Tc cuprates is discussed.

We study a model of the stripe state in strongly correlated systems consisting of an array of antiferromagnetic spin ladders, each with n(leg) legs, coupled to each other through the spin-exchange interaction to charged stripes in between each pair of ladders. The charged stripes are assumed to be Luttinger liquids in a spin-gap regime. An effective interaction for a pair of neighboring ladders is calculated by integrating out the gapped spin degrees of freedom in the charged stripes. The low energy effective theory of each ladder is a nonlinear sigma model with additional cross couplings of neighboring ladders, which favor either in-phase or antiphase short-range spin orderings depending on the physical parameters of the charged stripe.

Applying the dynamical mean-field theory to the two-dimensional Hubbard model, we calculate self-consistent solutions of doped antiferromagnets with spatially varying spin density ‹ n iσ › using realistic tight-binding parameters. The local self-energy of the supercell includes transverse and longitudinal spin fluctuations with an effective local potential due to short-range electron-electron correlations. It is found that metallic stripes are stabilized by a pseudogap. The stripes along (1,0) direction filled by one hole per two-domain wall unit cells change with increasing Coulomb interaction U to the more extended stripes along (1,1) direction consisting of four atoms filled by 1/4 doped hole each. These findings agree qualitatively with the experimental observations in the superconducting cuprates, and predict a qualitative difference between various compounds due to differences in the extended hopping parameters. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We present the charge and magnetization density distribution in various stripe phases obtained for two-dimensional models of correlated electrons solved within the Hartree-Fock approximation and a variational local ansatz. Apart from the Hubbard model with local Coulomb interaction U, we investigate its two extensions by adding either static Peierls electron-lattice coupling, or the correlated hopping term in the so-called Hirsch model. It has been found that the stripe ordering is robust and occurs in underdoped $(\ensuremath{\delta}=1/8)$ and overdoped $(\ensuremath{\delta}=1/4)$ systems. At intermediate values of U in underdoped systems $(\ensuremath{\delta}=1/8)$ local correlations stabilize the vertical (01) antiferromagnetic domains, separated by nonmagnetic domain walls filled by one doped hole per two wall atoms. A stripe phase with the same size of magnetic domains and an increased filling of one hole per one wall atom is stable for overdoped $(\ensuremath{\delta}=1/4)$ systems. At larger values of U, both structures are replaced by more extended magnetic domain walls oriented along the (11) direction. These findings agree qualitatively with the experimental results.

We investigate the structure of the pairing potential in the stripe phase of the two-dimensional Hubbard model. Based on the random-phase approximation we discuss in detail the interactions in the charge and spin channel and compare our calculations with related considerations in commensurate antiferromagnets. Our main finding is that due to the incommensurate charge-density wave formation the exchange of collective modes in the charge channel is significantly enhanced with respect to the spin-bag approach whereas due to the inhomogeneous charge distribution the coupling to transverse spin fluctuations tends to be suppressed.