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

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

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

Effective action for phase fluctuations in d-wave superconductors near a Mott transition

Phase fluctuations of a d-wave superconducting order parameter are theoretically studied in the context of high-T$_c$ cuprates. We consider the $t-J$ model describing layered compounds, where the Heisenberg interaction is decoupled by a d-wave order parameter in the particle-particle channel. Assuming first that the equilibirum state has long-range phase order, the effective action $\mathcal{S}_{eff}$ is derived perturbatively for small fluctuations within a path integral formalism, in the presence of the Coulomb and Hubbard interaction terms. In a second step, a more general derivation of $\mathcal{S}_{eff}$ is performed in terms of a gradient expansion which only assumes that the gradients of the order parameter are small whereas the value of the phase may be large. We show that in the phase-only approximation the resulting $\mathcal{S}_{eff}$ reduces in leading order in the field gradients to the perturbative one which thus allows to treat also the case without long-range phase order or vortices. Our result generalizes previous expressions for $\mathcal{S}_{eff}$ to the case of interacting electrons, is explicitly gauge invariant, and avoids problematic singular gauge transformations.Comment: 11 pages, 4 figures, REVTe

Competition between spin-induced charge instabilities in underdoped cuprates

We study the static charge correlation function in a one-band model on a square lattice. The Hamiltonian consists of effective hoppings of the electrons between the lattice sites and the Heisenberg Hamiltonian. Approximating the irreducible charge correlation function by a single bubble yields the ladder approximation for the charge correlation function. In this approximation, one finds, in general, three charge instabilities - two of them are due to nesting, the third one is the flux phase instability. Since these instabilities cannot explain the experiments in hole-doped cuprates, we have included in the irreducible charge correlation function also Aslamasov-Larkin (AL) diagrams where charge fluctuations interact with products of spin fluctuations. We then find at high temperatures a nematic or d-wave Pomeranchuk instability with a very small momentum. Its transition temperature decreases roughly linearly with doping in the underdoped region and vanishes near optimal doping. Decreasing the temperature further, a secondary axial charge-density wave (CDW) instability appears with mainly d-wave symmetry and a wave vector somewhat larger than the distance between nearest-neighbor hot spots. At still lower temperatures, the diagonal flux phase instability emerges. A closer look shows that the AL diagrams enhance mainly axial and not diagonal charge fluctuations in our one-band model. This is the main reason why axial and not diagonal instabilities are the leading ones in agreement with experiment. The two instabilities due to nesting vanish already at very low temperatures and do not play any major role in the phase diagram. Remarkable is that the nematic and the axial CDW instabilities show a large reentrant behavior.Fil: Zeyher, Roland. Max Planck Institute For Solid State Research; AlemaniaFil: Greco, Andres Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentin

Self-localization of composite spin-lattice polarons

Self-localization of holes in the Holstein t-J model is studied in the adiabatic limit using exact diagonalization and the retraceable path approximation. It is shown that the critical electron-phonon coupling \lambda_c decreases with increasing J and that this behavior is determined mainly by the incoherent rather than by the coherent motion of the hole. The obtained spin correlation functions in the localized region can be understood within a percolation picture where antiferromagnetic order can persist up to a substantial hole doping. These results restrict the possibility of self-localization of holes in lightly doped cuprates.Comment: 4 pages, 5 figure