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arXiv:cond-mat/9708145 · Physical review. B, Condensed matter

Bipolaronic charge excitations in t−J two-leg ladders

Dmitri A. Ivanov, Patrick A. Lee

Published Jan 15, 1998• 9 citations
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Abstract

We present a low-energy effective model for the charge degrees of freedom in two-leg $t\ensuremath{-}J$ ladders. Starting from $\mathrm{SU}(2)$ mean-field theory, we exclude the spin degrees of freedom that have an energy gap. At low temperatures, the mean-field solution is the staggered-flux phase. For gapless charge excitations the effective theory is the Luther-Emery liquid. Our analysis is applicable at low doping and in the ``physical'' range of parameters $t/J\ensuremath{\sim}3$ where there is only one massless mode in the charge sector and no massless modes in the spin sector. Within our model we make predictions about correlation exponents and the superconductivity order parameter, and discuss the comparison with the existing numerical results.

DOI
10.1103/physrevb.57.2118

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We propose a low-energy effective theory of lightly doped two-leg $t\ensuremath{-}J$ ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions, which are coupled to the O(3) nonlinear sigma model in terms of the gauge coupling with opposite sign of ``charges.'' In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg $t\ensuremath{-}J$ ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle-density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.

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The three-leg ladder has one odd-parity and two even-parity channels. At low doping these behave quite differently. Numerical calculations for a $t\ensuremath{-}J$ model show that the initial phase upon hole doping has two components---a conducting Luttinger liquid in the odd-parity channel, coexisting with an insulating (i.e., undoped) spin-liquid phase in the even-parity channels. This phase has a partially truncated Fermi surface and violates the Luttinger theorem. This coexistence of conducting fermionic and insulating paired bosonic degrees of freedom is similar to the recent proposal of Geshkenbein, Ioffe, and Larkin [Phys. Rev. B 55, 3173 (1997)] for the underdoped spin-gap normal phase of the cuprates. A mean-field approximation is derived which has many similarities to the numerical results. One difference however is an induced hole pairing in the odd-parity channel at arbitrary small dopings, similar to that proposed by Geshkenbein, Ioffe, and Larkin for the two-dimensional case. At higher dopings, we propose that a quantum phase transition will occur as holes enter the even-parity channels, resulting in a Luther-Emery liquid with hole pairing with essentially $d$-wave character. In the mean-field approximation a crossover occurs which we interpret as a reflection of this quantum phase transition deduced from the numerical results.

arXiv:cond-mat/9706147•Physical review. B, Condensed matter•Dec 1, 1997•34 citations
We present a low-energy effective model for the charge degrees of freedom in two-leg t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J ladders. Starting from SU(2)\mathrm{SU}(2)SU(2) mean-field theory, we exclude the spin degrees of freedom that have an energy gap. At low temperatures, the mean-field solution is the staggered-flux phase. For gapless charge excitations the effective theory is the Luther-Emery liquid. Our analysis is applicable at low doping and in the ``physical'' range of parameters t/J\ensuremath∼3t/J\ensuremath{\sim}3t/J\ensuremath∼3 where there is only one massless mode in the charge sector and no massless modes in the spin sector. Within our model we make predictions about correlation exponents and the superconductivity order parameter, and discuss the comparison with the existing numerical results.
We propose a low-energy effective theory of lightly doped two-leg $t\ensuremath{-}J$ ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions, which are coupled to the O(3) nonlinear sigma model in terms of the gauge coupling with opposite sign of ``charges.'' In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg $t\ensuremath{-}J$ ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle-density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.
We study the $t\ensuremath{-}J$ model on a ladder using the slave-fermion-CP1{\mathrm{CP}}^{1}CP1 formalism that has been used successfully in studying lightly-doped high-Tc{T}_{c}Tc​ cuprates. We obtain a low-energy effective model assuming a short-range antiferromagnetic order (SRAFO), which includes gauge-field degrees of freedom because of the use of the slave-particle picture. We give a systematic study on the dynamics of composite gauge bosons to show that the confinement phase is realized in a two-leg system whereas the deconfinement phase is realized in a chain system. This explains why quasiexcitations are so different in the chain and ladder systems. The effective model also reveals attractive forces between holes, which generate ddd-wave-type superconductive correlations in SRAFO. The low-energy excitations on a ladder are consistently described by the universality class of the Luther-Emery liquid.
Spin-charge separation is a hallmark of one-dimensional fermionic systems, yet its realization in higher dimensions remains an open question. To address this issue, we investigate a two-leg t-J ladder using the density matrix renormalization group (DMRG) method and its time-dependent extension. By analyzing ground-state correlations and single-particle removal spectra, we systematically examine the effects of plaquette diagonal hopping, spin exchange, and hole doping. Within appropriate parameter regimes, these factors drive the system from the well-known Luther Emery phase, with gapped spin and gapless charge modes, into a Luttinger liquid phase characterized by gapless spin and charge excitations, where signatures of spin-charge separation emerge. In combination with previous studies using exact diagonalization, our results provide evidence that spin-charge separation may persist in wider ladder systems.
Two-leg $t\ensuremath{-}J$ ladders are investigated in the framework of a combination of the phase string formulation and bond-operator representation. We develop a mean-field theory in the strong rung interaction regime, i.e., ${J}_{\ensuremath{\perp}}\ensuremath{\gg}J,t,$ which provides a unified description of the undoped insulating phase and the low-doping phase---the so-called C1S0C1S0C1S0 phase. Both of them are characterized by the resonating-valence-bond (RVB) order parameter, with gap opened up in all spin excitations. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry, which is driven by the RVB correlations. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of J/tJ/tJ/t for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are analyzed in comparison with other approaches.
A lightly doped single-band Hubbard model on a two-leg ladder exhibits a Luther-Emery phase, whereas the three-band Hubbard ladder behaves as a Luttinger liquid upon hole doping. To understand this discrepancy, we present a systematic density-matrix renormalization group study of the three-band Hubbard model on two-leg cylinders with further-neighbor particle hoppings. The inclusion of the longer-range hopping is motivated by the studies of the single-band Hubbard model in which the further-neighbor hopping terms are suggested to be crucial for the unconventional superconductivity. When the longer-range hopping parameters are small, the ground state is a Luttinger liquid having mutually commensurate superconducting, charge, and spin density wave correlations. Increasing the longer-range hopping drives a transition into a Luther-Emery phase with quasi-long-ranged superconducting and charge orders but short-ranged spin-spin correlations. By down-folding the three-band Hubbard model into an effective $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J\text{\ensuremath{-}}{J}^{\ensuremath{'}}$ model, we find that in the Luther-Emery phase, both the nearest- and second-neighbor kinetic energies are enhanced due to an effective increase of copper-oxygen hybridization. Amplifying intercell oxygen orbital hopping mirrors the benefits of reducing the charge transfer energy, causing doped holes to favor oxygen orbitals and strengthening superconducting pairing.
The three-leg ladder has one odd-parity and two even-parity channels. At low doping these behave quite differently. Numerical calculations for a $t\ensuremath{-}J$ model show that the initial phase upon hole doping has two components---a conducting Luttinger liquid in the odd-parity channel, coexisting with an insulating (i.e., undoped) spin-liquid phase in the even-parity channels. This phase has a partially truncated Fermi surface and violates the Luttinger theorem. This coexistence of conducting fermionic and insulating paired bosonic degrees of freedom is similar to the recent proposal of Geshkenbein, Ioffe, and Larkin [Phys. Rev. B 55, 3173 (1997)] for the underdoped spin-gap normal phase of the cuprates. A mean-field approximation is derived which has many similarities to the numerical results. One difference however is an induced hole pairing in the odd-parity channel at arbitrary small dopings, similar to that proposed by Geshkenbein, Ioffe, and Larkin for the two-dimensional case. At higher dopings, we propose that a quantum phase transition will occur as holes enter the even-parity channels, resulting in a Luther-Emery liquid with hole pairing with essentially ddd-wave character. In the mean-field approximation a crossover occurs which we interpret as a reflection of this quantum phase transition deduced from the numerical results.