Two-leg Ladder System Research Articles

Pseudogap and Collective Mode in the Optical Conductivity Spectra of Hole-Doped Ladders inSr14−xCaxCu24O41

Anisotropic optical conductivity spectra have been investigated for the hole-doped two-leg ladder system ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. As in the case of the underdoped high- ${T}_{\mathrm{c}}$ cuprates, upon cooling a pseudogap opens in the spectrum for the transverse ( $a$-axis) polarization, and concurrently a peak develops in the far infrared region of the longitudinal ( $c$-axis) spectrum. A possible interpretation for these results is that the pseudogap signals a formation of hole pairs on the ladders and the peak might correspond to a pinned collective mode of a regular array of hole pairs.

Comparison of quasiparticle energy dispersions and shadow peaks of doped two-leg ladder systems between various models including anSO(5)symmetry model

Considering various models including an $\mathrm{SO}(5)$ symmetry model, mean-field and exact diagonalization studies on the quasiparticle excitation of two-leg ladder systems are reported. It is shown that the energy gap in the quasiparticle excitation is caused by the formation of rung singlet states. We find that shadow peaks can occur above the Fermi surface with antiferromagnetic electron correlations involving only rungs in the spin ladder.

Spin Gap in the Hole-Doped Spin Ladder System(Sr2.5Ca11.5)Cu24O41: Neutron Inelastic Scattering Study

The spin liquid state in the hole-doped two-leg ladder system $({\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}){\mathrm{Cu}}_{24}\mathrm{O}{}_{41}$, which exhibits unique superconductivity under high pressure, has been studied by neutron inelastic scattering at ambient pressure. The spin gap energy for the ladder is found to be $32.1\ifmmode\pm\else\textpm\fi{}0.3\mathrm{meV}$, which is still almost the same as that of the parent material ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. From the observed dispersion relation, the exchange coupling is roughly estimated at ${J}_{\ensuremath{\parallel}}\ensuremath{\sim}90\ifmmode\pm\else\textpm\fi{}15\mathrm{meV}$ (along the ladders) and ${J}_{\ensuremath{\perp}}\ensuremath{\sim}65\ifmmode\pm\else\textpm\fi{}10\mathrm{meV}$ (along the rungs). The coupling constant ${J}_{\ensuremath{\parallel}}$ is slightly decreased from that obtained for the parent compound.

Mean field and exact diagonalization studies on an SO(5) symmetric ladder

Mean field and exact diagonalization studies on the quasiparticle excitation of an SO(5) symmetric two-leg ladder system are reported. It is shown that the two results are in good agreement with each other in the weak coupling limit. It is found that shadow peaks appear above the Fermi surface as a result of quasiparticle excitation which represents a mixture of electron and hole states.

Superconductivity and Magnetism in Quasi-One-Dimensional Two-Band Systems.

We study crossovers from one to quasi-one dimensions in doped two-leg ladder systems, using a renormalization group method. When quasi-one dimensionality is regarded as controlled by incomplete interference between the Cooper and Peierls channels, we obtain spin-density wave, d-wave superconductor, and metallic phases with decreasing dominance of the Peierls channel. When transverse single-particle hopping is treated perturbationally, we obtain a one-particle crossover from incoherent to coherent transverse motion for weak interaction and a two-particle crossover from short- to long-range ordering of a d-wave superconductor for strong interaction. We also study a magnetic property in a doped Heisenberg-Kondo chain, using the exact diagonalization method. A fully saturated ferromagnetism in the ferromagnetic Kondo chain is destroyed by rather weak antiferromagnetic Heisenberg coupling between localized S=1/2 spins.

Gauge theory description of spin ladders

A s=1/2 antiferromagnetic spin chain is equivalent to the two-flavor massless Schwinger model in an uniform background charge density in the strong coupling. The gapless mode of the spin chain is represented by a massless boson of the Schwinger model. In a two-leg spin ladder system the massless boson aquires a finite mass due to inter-chain interactions. The gap energy is found to be about .25 k |J'| when the inter-chain Heisenberg coupling J' is small compared with the intra-chain Heisenberg coupling. k is a constant of O(1). It is also shown that a cyclically symmetric N-leg ladder system is gapless or gapful for an odd or even N, respectively.

Spin Gap ofS=1/2Heisenberg Ladder: Field Theoretical Study of Magnetic Susceptibility and NMR Relaxation Rate

The temperature dependence of the static spin susceptibility, χ, and NMR relaxation rate, T 1 -1 , of S =1/2 Heisenberg two-leg ladder systems have been studied based on the Majorana fermion representation of the S =1/2 Heisenberg spin Hamiltonian introduced by Shelton, Nersesyan and Tsvelik (Phys. Rev. B 53 (1996) 8521). It is shown that in the case of SrCu 2 O 3 , we can fit the experimental data of χ and T 1 -1 in terms of the massive Majorana fermion excitation with mass m =440 K to resolve the apparent discrepancy of the spin gap activation energies between χ and T 1 -1 .

Nonmagnetic Impurities in Spin Gap Systems

The effect of nonmagnetic impurities in the two-leg Heisenberg ladder system and other spin liquids with excitation gap is discussed. It is shown that the random depletion of spins introduces a random Berry phase term into the nonlinear σ model. The classical nature of the antiferromagnetic correlation is enhanced by the topological decoherence, and the staggered susceptibility shows more singular behavior at low temperatures than the uniform antiferromagnetic Heisenberg chain.

Impurity Induced Antiferromagnetism in Spin-1/2 Heisenberg Two-Leg Ladder Systems

Based on the phase Hamiltonian representation of a spin-1/2 Heisenberg two-leg ladder system coupled antiferromagnetically, which has a spin gap if clean, it is shown that a non-magnetic impurity replacing a spin induces a staggered spin modulation. This results in the long range order of antiferromagnetism in the presence of three-dimensional coupling between the ladders. This will be in accordance with a recent experimental observation by Azuma et al. on Sr(Cu 1- x Zn x ) 2 O 3 .

Spin Gap Behavior in Ladder-Type of Quasi-One-Dimensional Spin (S=1/2) System SrCu2O3

Low-energy spin excitation in a spin S =1/2 two-leg ladder system SrCu 2 O 3 has been investigated by Cu NMR. From an activated decrease of the nuclear-spin lattice relaxation rate, 1/ T 1 , in a T -range of 100–300 K, a spin gap, Δ, is demonstrated to open with a value of 680 K, which is in quantitative agreement with the theoretical value of Δ∼0.5 J =650 K , if the same value of 1300 K as in the square lattice system is used as the antiferromagnetic exchange coupling constant, J . It is furthermore deduced from the measurement of the spin-echo decay rate, 1/ T 2G , that a magnetic coherence length, ξ/ a ( a : lattice spacing between Cu atoms along the chain), remains finite with (ξ/ a )∼13, comparable to a value in La 2 CuO 4 near T N . This class of cuprate is thus a frustrated quntum antiferromagnet (AF) with a spin gap.