Competition between superconductivity and the pseudogap phase in the t-J model

The t-J model in the large N limit (N denotes the number of spin components) yields a pseudogap phase in the underdoped region which is related to a d-wave charge density wave (d-CDW). We present results for the doping dependence of the superconducting and d-CDW order parameters as well as for collective excitations in the presence of these two order parameters. We argue that the electronic Raman spectrum with B$_{1g}$ symmetry probes the amplitude fluctuations of the d-CDW at zero momentum.Comment: 4 pages, 4 figures, will appear in Proc. of "Physics of Magnetism'02

Theory of the hourglass dispersion of magnetic excitations in high-Tc_c cuprates

A theory for the dispersion of collective magnetic excitations in superconducting cuprates is presented with the aim to cover both high and low doping regimes. Besides of spin fluctuations describable in the random phase approximation (RPA) we allow for local spin rotations within a mode-coupling theory. At low temperatures and moderately large correlation lengths we obtain two branches of excitations which disperse up- and downwards exhibiting the hourglass behavior observed experimentally at intermediate dopings. At large and small dopings our theory essentially reduces to the RPA and spin wave theory, respectively.Comment: 4 pages, 5 Figure

Raman scattering from a superconductivity-induced bound state in MgB2MgB_2

It is shown that the sharp peak in the $E_{2g}$ Raman spectrum of superconducting $MgB_2$ is due to a bound state caused by the electron-phonon coupling. Our theory explains why this peak appears only in the spectra with $E_{2g}$ symmetry and only in the $\sigma$ but not $\pi$ bands. The properties of the bound state and the Raman spectrum are investigated, also in the presence of impurity scattering.Comment: 4 pages, 4 figures, will appear in PR

Electronic correlations, electron-phonon interaction, and isotope effect in high-Tc cuprates

Using a large-N expansion we present and solve the linearized equation for the superconducting gap for a generalized t-J model which also contains phonons within a Holstein model. The leading Tc has d-wave symmetry with phonons giving a positive contribution to Tc. The corresponding isotope coefficient is very small at optimal doping and increases towards the classical value 1/2 with increasing dopings similar as in many cuprates.Comment: 14 pages, 7 figure

C-Axis Tunneling Spectra in High-Tc_c Superconductors in the Presence of a d Charge-Density Wave

The optimally doped and underdoped region of the $t-J$ model at large N (N is the number of spin components) is governed by the competition of d-wave superconductivity (SC) and a d Charge-Density Wave (d-CDW).The partial destruction of the Fermi surface by the d-CDW and the resulting density of states are discussed. Furthermore, c-axis conductances for incoherent and coherent tunneling are calculated, considering both an isotropic and an anisotropic in-plane momentum dependence of the hopping matrix element between the planes. The influence of self-energy effects on the conductances is also considered using a model where the electrons interact with a dispersionless, low-lying branch of bosons. We show that available tunneling spectra from break-junctions are best explained by assuming that they result from incoherent tunneling with a strongly anisotropic hopping matrix element of the form suggested by band structure calculations. The conductance spectra are then characterized by one single peak which evolves continuously from the superconducting to the d-CDW state with decreasing doping. The intrinsic c-axis tunneling spectra are, on the other hand, best explained by coherent tunneling. Calculated spectra show at low temperatures two peaks due to SC and d-CDW. With increasing temperature the BCS-like peak moves to zero voltage and vanishes at T$_c$,exactly as in experiment.Our results thus can explain why break junction and intrinsic tunneling spectra are different from each other. Moreover, they support a scenario of two competing order parameters in the underdoped region of high-T$_c$ superconductors.Comment: 12 pages, 16 figure

Self-energy effects in electronic Raman spectra of doped cuprates due to magnetic fluctuations

We present results for magnetic excitations in doped copper oxides using the random phase approximation and itinerant electrons. In the [1,0] direction the observed excitations resemble dispersive quasi-particles both in the normal and superconducting state similar as in recent resonant inelastic X-ray scattering (RIXS) experiments. In the [1,1] direction the excitations form, except for the critical region near the antiferromagnetic wave vector ${\bf Q}=(\pi,\pi)$, only very broad continua. Using the obtained spin propagators we calculate electron self-energies and their effects on electronic Raman spectra. We show that the recently observed additional peak at about twice the pair breaking in B$_{1g}$ symmetry below T$_c$ in HgBa$_2$CuO$_{4+\delta}$ can be explained as a self-energy effect where a broken Cooper pair and a magnetic excitation appear as final states. The absence of this peak in B$_{2g}$ symmetry, which probes mainly electrons near the nodal direction, is explained by their small self-energies compared to those in the antinodal direction.Comment: 5 pages, 5 figure

Superconductivity, d Charge-Density Wave and Electronic Raman Scattering in High-Tc_c Superconductors

The competition of superconductivity and a d charge-density wave (CDW) is studied in the t-J model as a function of temperature at large N where N is the number of spin components. Applying the theory to electronic Raman scattering the temperature dependence of the $B_{1g}$ and the $A_{1g}$ spectra are discussed for a slightly underdoped case.Comment: 2 pages, 3 figures, Proc. M2S-HTSC-VII, to appear in Physica

Isotope effect on the superconducting critical temperature of cuprates in the presence of charge order

Using the large-$N$ limit of the $t$-$J$ model and allowing also for phonons and the electron-phonon interaction we study the isotope effect $\alpha$ for coupling constants appropriate for YBCO. We find that $\alpha$ has a minimum at optimal doping and increases strongly (slightly) towards the underdoped (overdoped) region. Using values for the electron phonon interaction from the local density approximation we get good agreement for $\alpha$ as a function of $T_c$ and doping $\delta$ with recent experimental data in YBCO. Our results strongly suggest that the large increase of $\alpha$ in the underdoped region is (a) caused by the shift of electronic spectral density from low to high energies associated with a competing phase (in our case a charge density wave) and the formation of a gap, and (b) compatible with the small electron phonon coupling constants obtained from the local density approximation. We propose a similar explanation for the anomalous behavior of $\alpha$ in Sr doped La$_2$CuO$_4$ near the doping 1/8.Comment: 14 pages, 6 figure