Coupling to optical phonons in the one-dimensional t-J model: Effects on superconducting fluctuations and phase separation

The one-dimensional (1D) $t$-$J$ Holstein model is studied by exact diagonalization of finite rings using a variational approximation for the phonon states. Due to renormalization effects induced by the phonons, for intermediate electron-phonon coupling, the phase separation (PS) boundary, and with it the region of dominating superconducting fluctuations is shifted substantially to smaller values of $J/t$ as compared to the pure $t$-$J$ model. Superconducting correlations are weakened through charge density wave interactions mediated by the phonons. Possible consequences for the high $T_c$ oxides are discussed.Comment: 4 pages, Latex2

Phonon Dispersion Relations in PrBa2Cu3O6+x (x ~ 0.2)

We report measurements of the phonon dispersion relations in non-superconducting, oxygen-deficient PrBa2Cu3O6+x (x ~ 0.2) by inelastic neutron scattering. The data are compared with a model of the lattice dynamics based on a common interaction potential. Good agreement is achieved for all but two phonon branches, which are significantly softer than predicted. These modes are found to arise predominantly from motion of the oxygen ions in the CuO2 planes. Analogous modes in YBa2Cu3O6 are well described by the common interaction potential model.Comment: 4 pages, 3 figures. Minor changes following referees' comment

Phenomenological BCS theory of the high-TcT_c cuprates

A BCS model characterized by a phenomenological pair potential with on-site ($V_0$), nearest ($V_1$), and next nearest ($V_2$) neighbour coupling constants, and an empirical quasiparticle dispersion taken from angle-resolved photoemission spectra is considered. The model can consistently explain the experimental data concerning the pair state of the hole doped cuprates. Three ingredients are required to make the interpretation possible: the existence of flat bands, a very small effective on-site repulsion, and a slightly dominating effective nnn attraction $V_2$ of the order of 60-80meV with a ratio $V_2/V_1 \approx 1.5$.Comment: 13 pages, uuencoded Postscrip

Anomalous behaviors of the charge and spin degrees of freedom in the CuO double chains of PrBa2_2Cu4_4O8_8

The density-matrix renormalization-group method is used to study the electronic states of a two-chain Hubbard model for CuO double chains of PrBa$_2$Cu$_4$O$_8$. We show that the model at quarter filling has the charge ordered phases with stripe-type and in-line--type patterns in the parameter space, and in-between, there appears a wide region of vanishing charge gap; the latter phase is characteristic of either Tomonaga-Luttinger liquid or a metallic state with a spin gap. We argue that the low-energy electronic state of the CuO double chains of PrBa$_2$Cu$_4$O$_8$ should be in the metallic state with a possibly small spin gap.Comment: REVTEX 4, 10 pages, 9 figures; submitted to PR

Phenomenological Models for the Gap Anisotropy of Bi-2212 as Measured by ARPES

Recently, high resolution angle-resolved photoemission spectroscopy has been used to determine the detailed momentum dependence of the superconducting gap in the high temperature superconductor Bi-2212. In this paper, we first describe tight binding fits to the normal state dispersion and superlattice modulation effects. We then discuss various theoretical models in light of the gap measurements. We find that the simplest model which fits the data is the anisotropic s-wave gap $\cos(k_x)\cos(k_y)$, which within a one-band BCS frame- work suggests the importance of next near neighbor Cu-Cu interactions. Various alternative interpretations of the observed gap are also discussed, along with the implications for microscopic theories of high temperature superconductors.Comment: 14 pages, revtex, 9 uuencoded postscript figure

Spin dynamics and antiferromagnetic order in PrBa2Cu4O8 studied by Cu nuclear respnance

Results of the nuclear resonance experiments for the planar Cu sites in PrBa2Cu4O8 are presented. The NMR spectrum at 1.5 K in zero magnetic field revealed an internal field of 6.1 T, providing evidence for an antiferromagnetic order of the planar Cu spins. This confirms that the CuO2 planes are insulating, therefore, the metallic conduction in this material is entirely due to the one-dimensional zigzag Cu2O2 chains. The results of the spin-lattice relaxation rates measured by zero field NQR above 245 K in the paramagnetic state are explained by the theory for a Heisenberg model on a square lattice.Comment: 4 pages, 2 figure

Planar 17O NMR study of Pr_yY_{1-y}Ba_2Cu_3O_{6+x}

We report the planar ^{17}O NMR shift in Pr substituted YBa_{2}Cu_{3}O_{6+x}, which at x=1 exhibits a characteristic pseudogap temperature dependence, confirming that Pr reduces the concentration of mobile holes in the CuO_{2} planes. Our estimate of the rate of this counterdoping effect, obtained by comparison with the shift in pure samples with reduced oxygen content, is found insufficient to explain the observed reduction of T_c. From the temperature dependent magnetic broadening of the ^{17}O NMR we conclude that the Pr moment and the local magnetic defect induced in the CuO_2 planes produce a long range spin polarization in the planes, which is likely associated with the extra reduction of T_c. We find a qualitatively different behaviour in the oxygen depleted Pr_yY_{1-y}Ba_2Cu_3O_{6.6}, i.e. the suppression of T$_c$ is nearly the same, but the magnetic broadening of the ^{17}O NMR appears weaker. This difference may signal a weaker coupling of the Pr to the planes in the underdoped compound, which might be linked with the larger Pr to CuO_2 plane distance, and correspondingly weaker hybridization.Comment: 8 pages, 9 figures, accepted in Phys Rev

Transport and Magnetic Studies on the Spin State Transition of Pr1-xCaxCoO3 up to High Pressure

Transport and magnetic measurements and structural and NMR studies have been carried out on (Pr1-yR'y)1-xAxCoO3 {R'=(rare earth elements and Y); A=(Ca, Ba and Sr)} at ambient pressure or under high pressure. The system exhibits a phase transition from a nearly metallic to an insulating state with decreasing temperature T, where the low spin (LS) state of Co3+ is suddenly stabilized. For y=0, we have constructed a T-x phase diagram at various values of the external pressure p. It shows that the (T, x) region of the low temperature phase, which is confined to a very narrow region around x=0.5 at ambient pressure, expands as p increases, suggesting that the transition is not due to an order-disorder type one. For the occurrence of the transition, both the Pr and Ca atoms seem to be necessary. The intimate relationship between the local structure around the Co ions and the electronic (or spin) state of Co3+ ions is discussed: For the smaller unit cell volume or the smaller volume of the CoO6 octahedra and for the larger tilting angle of the octahedra, the temperature of the transition becomes higher. The role of the carriers introduced by the doping of the A atoms, is also discussed. By analyzing the data of 59Co-NMR spectra and magnetic susceptibilities of Pr1-xCaxCoO3 the energy separations among the different spin states of Co3+ and Co4+ are roughly estimated.Comment: 15 pages, 15 figures, 2 tables, submitted to J. Phys. Soc. Jp

Problems With the Vortex-Boson Mapping in 1+1 Dimensions

Using the well known boson mapping, we relate the transverse magnetic susceptibility of a system of flux vortices in 1+1 dimensions to an appropriately defined conductivity of a one-dimensional boson system. The tilt response for a system free of disorder is calculated directly, and it is found that a subtle order of limits is required to avoid deceptive results.Comment: 4 Pages (REVTeX 3.0). Postscript file for this paper is available on the World Wide Web at http://cmtw.harvard.edu/~simon/

Critical temperature and superfluid density suppression in disordered high-TcT_c cuprate superconductors

We argue that the standard Abrikosov-Gorkov (AG) type theory of $T_c$ in disordered $d$-wave superconductors breaks down in short coherence length high-$T_c$ cuprates. Numerical calculations within the Bogoliubov-de Gennes formalism demonstrate that the correct description of such systems must allow for the spatial variation of the order parameter, which is strongly suppressed in the vicinity of impurities but mostly unaffected elsewhere. Suppression of $T_c$ as measured with respect to the attendant decrease in the superfluid density is found to be significantly weaker than that predicted by the AG theory, in good agreement with experiment.Comment: REVTeX, 4 pages, 3 ps figures included [The version to appear in PRB Sept. 1. Conclusions of the paper unchanged; several changes in text and figures for added clarity, discussion of phase fluctuations added.