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/0303605 · Physical Review Letters

Superconducting Gap for a Two-Leg t−J Ladder

Didier Poilblanc, Douglas J. Scalapino, Sylvain Capponi

Published Sep 24, 2003• 29 citations
arXivHTMLPDF

Abstract

Single-particle diagonal and off-diagonal Green's functions of a two-leg t-J ladder at 1/8 doping are investigated by exact diagonalizations techniques. A numerically tractable expression for the superconducting gap is proposed and the frequency dependence of the real and imaginary parts of the gap are determined. The role of the low-energy gapped spin modes, whose energies are computed by a (one-step) contractor renormalization procedure, is discussed.

DOI
10.1103/physrevlett.91.137203

Related papers

Calculation of Δ(k,ω) for a two-dimensional t−J cluster

Didier Poilblanc, Douglas J. Scalapino

Using numerical techniques, the diagonal and off-diagonal superconducting one-electron Green's functions are calculated for a two-dimensional $t\ensuremath{-}J$ model on a periodic 32-site cluster at low doping. From these Green's functions, the momentum and frequency dependence of both the real and the imaginary parts of the pairing gap $\ensuremath{\Delta}(\mathbf{k},\ensuremath{\omega})$ are extracted. It has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry and exhibits $\ensuremath{\omega}$-dependent structure over a scale of several J. The pairing gap at the gap edge $\ensuremath{\Delta}(\mathbf{k},\ensuremath{\omega}={\ensuremath{\Delta}}_{\mathbf{k}})$ at the antinode persists down to small $J/t$ values. The frequency- and momentum-dependent renormalized energy and renormalization factor are also calculated.

arXiv:cond-mat/0202180•Physical review. B, Condensed matter•Aug 29, 2002•23 citations

Calculation of Delta (k,omega) for a 2D t-J cluster

Didier Poilblanc, Douglas J. Scalapino

Using numerical techniques, the diagonal and off-diagonal superconducting one-electron Green's functions are calculated for a two-dimensional (2D) t-J model on a periodic 32-site cluster at low doping. From these Green's functions, the momentum and frequency dependence of the pairing gap $\Delta ({\bf k}, \omega)$ are extracted. It has $d_{x^2-y^2}$ symmetry and exhibits $\omega$-dependent structure which depend upon J/t. We find that the pairing gap persists down to small J/t values. The frequency- and momentum-dependent renormalized energy and renormalization factor are also calculated.

•Jan 1, 2002•0 citations

Evolution of the spin gap upon doping a 2-leg ladder

Didier Poilblanc, O. Chiappa, José A. Riera +2 more

The evolution of the spin gap of a 2-leg ladder upon doping depends upon the nature of the lowest triplet excitations in a ladder with two holes. Here we study this evolution using various numerical techniques for a $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}J$ ladder as the next-near-neighbor hopping ${t}^{\ensuremath{'}}$ is varied. We find that depending on the value of ${t}^{\ensuremath{'}},$ the spin gap can evolve continuously or discontinuously and the lowest triplet state can correspond to a magnon, a bound magnon-hole-pair, or two separate quasiparticles. Previous experimental results on the superconducting two-leg ladder ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ are discussed.

arXiv:cond-mat/0005403•Physical review. B, Condensed matter•Dec 1, 2000•31 citations

Superconducting fluctuations in the Luther-Emery liquid

E. Orignac, Didier Poilblanc

The single-particle superconducting Green's functions of a Luther-Emery liquid is computed by bosonization techniques. Using a formulation introduced by Poilblanc and Scalapino [Phys. Rev. B 66, 052513 (2002)], an asymptotic expression of the superconducting gap is deduced in the long wavelength and small frequency limit. Due to superconducting phase fluctuations, the gap exhibits as a function of size L a ${(1/L)}^{{1/2K}_{\ensuremath{\rho}}}$ power-law decay as well as an interesting singularity at the spectral gap energy. Similarities and differences with the two-leg $t\ensuremath{-}J$ ladder are outlined.

arXiv:cond-mat/0303053•Physical review. B, Condensed matter•Aug 14, 2003•15 citations

Doped two-leg ladder with ring exchange: Exact diagonalization and density matrix renormalization group computations

Guillaume Roux, Steven R. White, Sylvain Capponi +2 more

The effect of a ring exchange on doped two-leg ladders is investigated combining exact diagonalization (ED) and density matrix renormalization group (DMRG) computations. We focus on the nature and weights of the low-energy magnetic excitations and on superconducting pairing. The stability with respect to this cyclic term of a remarkable resonant mode originating from a hole pair-magnon bound state is examined. We also find that, near the zero-doping critical point separating rung-singlet and dimerized phases, doping reopens a spin gap.

arXiv:cond-mat/0504027•Physical Review B•Jul 14, 2005•14 citations

Resonant magnetic mode in superconducting two-leg ladders

Didier Poilblanc, E. Orignac, Steven R. White +1 more

The spin dynamics of a doped two-leg spin ladder is investigated by numerical techniques. We show that a hole pair-magnon boundstate evolves at finite hole doping into a sharp magnetic excitation below the two-particle continuum. This is supported by a field theory argument based on a $\mathrm{SO}(6)$-symmetric ladder. Similarities and differences with the resonant mode of the high-${T}_{C}$ cuprates are discussed.

arXiv:cond-mat/0402011•Physical Review B•Jun 18, 2004•21 citations
Single-particle diagonal and off-diagonal Green's functions of a two-leg t-J ladder at 1/8 doping are investigated by exact diagonalizations techniques. A numerically tractable expression for the superconducting gap is proposed and the frequency dependence of the real and imaginary parts of the gap are determined. The role of the low-energy gapped spin modes, whose energies are computed by a (one-step) contractor renormalization procedure, is discussed.
Using numerical techniques, the diagonal and off-diagonal superconducting one-electron Green's functions are calculated for a two-dimensional $t\ensuremath{-}J$ model on a periodic 32-site cluster at low doping. From these Green's functions, the momentum and frequency dependence of both the real and the imaginary parts of the pairing gap $\ensuremath{\Delta}(\mathbf{k},\ensuremath{\omega})$ are extracted. It has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry and exhibits $\ensuremath{\omega}$-dependent structure over a scale of several J. The pairing gap at the gap edge $\ensuremath{\Delta}(\mathbf{k},\ensuremath{\omega}={\ensuremath{\Delta}}_{\mathbf{k}})$ at the antinode persists down to small J/tJ/tJ/t values. The frequency- and momentum-dependent renormalized energy and renormalization factor are also calculated.
Using numerical techniques, the diagonal and off-diagonal superconducting one-electron Green's functions are calculated for a two-dimensional (2D) t-J model on a periodic 32-site cluster at low doping. From these Green's functions, the momentum and frequency dependence of the pairing gap Δ(k,ω)\Delta ({\bf k}, \omega)Δ(k,ω) are extracted. It has dx2−y2d_{x^2-y^2}dx2−y2​ symmetry and exhibits ω\omegaω-dependent structure which depend upon J/t. We find that the pairing gap persists down to small J/t values. The frequency- and momentum-dependent renormalized energy and renormalization factor are also calculated.
The evolution of the spin gap of a 2-leg ladder upon doping depends upon the nature of the lowest triplet excitations in a ladder with two holes. Here we study this evolution using various numerical techniques for a $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}J$ ladder as the next-near-neighbor hopping ${t}^{\ensuremath{'}}$ is varied. We find that depending on the value of ${t}^{\ensuremath{'}},$ the spin gap can evolve continuously or discontinuously and the lowest triplet state can correspond to a magnon, a bound magnon-hole-pair, or two separate quasiparticles. Previous experimental results on the superconducting two-leg ladder ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ are discussed.
The single-particle superconducting Green's functions of a Luther-Emery liquid is computed by bosonization techniques. Using a formulation introduced by Poilblanc and Scalapino [Phys. Rev. B 66, 052513 (2002)], an asymptotic expression of the superconducting gap is deduced in the long wavelength and small frequency limit. Due to superconducting phase fluctuations, the gap exhibits as a function of size L a ${(1/L)}^{{1/2K}_{\ensuremath{\rho}}}$ power-law decay as well as an interesting singularity at the spectral gap energy. Similarities and differences with the two-leg $t\ensuremath{-}J$ ladder are outlined.
The effect of a ring exchange on doped two-leg ladders is investigated combining exact diagonalization (ED) and density matrix renormalization group (DMRG) computations. We focus on the nature and weights of the low-energy magnetic excitations and on superconducting pairing. The stability with respect to this cyclic term of a remarkable resonant mode originating from a hole pair-magnon bound state is examined. We also find that, near the zero-doping critical point separating rung-singlet and dimerized phases, doping reopens a spin gap.
The spin dynamics of a doped two-leg spin ladder is investigated by numerical techniques. We show that a hole pair-magnon boundstate evolves at finite hole doping into a sharp magnetic excitation below the two-particle continuum. This is supported by a field theory argument based on a SO(6)\mathrm{SO}(6)SO(6)-symmetric ladder. Similarities and differences with the resonant mode of the high-TC{T}_{C}TC​ cuprates are discussed.