Linear dependence of peak width in \chi(\bq, \omega) vs T_c for YBCO superconductors

It is shown that the momentum space width of the peak in the spin susceptibility, Im$\chi(q,\omega)$, is linearly proportional to the superconducting $T_c$: $T_c = \hbar v^*\Delta q$ with $\hbar v^* \simeq 35 meV$\AA. This relation is similar to the linear relation between incommensurate peak splitting and $T_c$ in LaSrCuO superconductors, as first proposed by Yamada et al. (Phys. Rev. B 57, 6165, (1998)). The velocity $\hbar v^*$ is smaller than Fermi velocity or the spin-wave velocity of the parent compound and remains the same for a wide doping range. This result points towards strong similarities in magnetic state of YBCO and LaSrCuO.Comment: 5 pages, 3 figures, latex fil

High-Energy Spin Dynamics in La1.69_{1.69}Sr0.31_{0.31}NiO4_4

We have mapped out the spin dynamics in a stripe-ordered nickelate, La$_{2-x}$Sr$_{x}$NiO$_{4}$ with $x \simeq 0.31$, using inelastic neutron scattering. We observe spin-wave excitations up to 80 meV emerging from the incommensurate magnetic peaks with an almost isotropic spin-velocity: $\hbar c_s\sim 0.32$ eV \AA, very similar to the velocity in the undoped, insulating parent compound, La$_{2}$NiO$_{4}$. We also discuss the similarities and differences of the inferred spin-excitation spectrum with those reported in superconducting high-$T_c$ cuprates.Comment: 4 figure

Absence of an isotope effect in the magnetic resonance in high-TcT_c superconductors

An inelastic neutron scattering experiment has been performed in the high-temperature superconductor $\rm YBa_2Cu_3O_{6.89}$ to search for an oxygen-isotope shift of the well-known magnetic resonance mode at 41 meV. Contrary to a recent prediction (I. Eremin, {\it et al.}, Phys. Rev. B {\bf 69}, 094517 (2004)), a negligible shift (at best $\leq$ +0.2 meV) of the resonance energy is observed upon oxygen isotope substitution ($^{16}$O$\to^{18}$O). This suggests a negligible spin-phonon interaction in the high-$T_c$ cuprates at optimal doping.Comment: 3 figure

Spin-roton excitations in the cuprate superconductors

We identify a new kind of elementary excitations, spin-rotons, in the doped Mott insulator. They play a central role in deciding the superconducting transition temperature Tc, resulting in a simple Tc formula,Tc=Eg/6, with Eg as the characteristic energy scale of the spin rotons. We show that the degenerate S=1 and S=0 rotons can be probed by neutron scattering and Raman scattering measurements, respectively, in good agreement with the magnetic resonancelike mode and the Raman A1g mode observed in the high-Tc cuprates.Comment: 10 pages, 9 figure

Fourier-Transformed Local Density of States and Tunneling into a DD-Wave Superconductor with Bosonic Modes

We analyze the effects of the electronic coupling to bosonic modes in a d-wave superconductor. The role of the scattering due to boson on the momentum transfer between electronic states in the Brilloine zone is addressed. We consider specific examples of $B_{1g}$ phonon, breathing mode phonon and spin resonance at $(\pi,\pi)$. The Fourier spectrum of the energy derivative local density of states (LDOS) is calculated. To properly calibrate the effects of different modes we fix the quasipartilce renormalization at specific momentum points. It is found that the $B_{1g}$ mode with highly anisotropic momentum-dependent coupling matrix element gives rise to well definded features in the Fourier spectrum, at the energy of mode plus gap, with a momentum transfer along the Cu-O bond direction of cuprates. This result is in a striking contrast to the cases of the coupling to other modes and also to the case of no mode coupling. The origin of this difference is explored in detail. A comparison with the recent STM experiments is briefly discussed.Comment: 9 pages, 4 eps figures include

Double dispersion of the magnetic resonant mode in cuprates

The magnetic excitation spectra in the vicinity of the resonant peak, as observed by inelastic neutron scattering in cuprates, are studied within the memory-function approach. It is shown that at intermediate doping the superconducting gap induces a double dispersion of the peak, with an anisotropy rotated between the downward and upward branch. Similar behavior, but with a spin-wave dispersion at higher energies, is obtained for the low-doping case assuming a large pairing pseudogap.Comment: 4 LaTeX pages, 4 figure

Dispersion of the odd magnetic resonant mode in near-optimally doped Bi2Sr2CaCu2O8+d

We report a neutron scattering study of the spin excitation spectrum in the superconducting state of slightly overdoped Bi2Sr2CaCu2O8+d system (Tc=87 K). We focus on the dispersion of the resonance peak in the superconducting state that is due to a S=1 collective mode. The measured spin excitation spectrum bears a strong similarity to the spectrum of the YBa2Cu3O6+x system for a similar doping level i.e. x= 0.95-1), which consists of intersecting upward- and downward-dispersing branches. A close comparison of the threshold of the electron-hole spin flip continuum, deduced from angle resolved photo-emission measurements in the same system, indicates that the magnetic response in the superconducting state is confined, in both energy and momentum, below the gapped Stoner continuum. In contrast to YBa2Cu3O6+x, the spin excitation spectrum is broader than the experimental resolution. In the framework of an itinerant-electron model, we quantitatively relate this intrinsic energy width to the superconducting gap distribution observed in scanning tunnelling microscopy experiments. Our study further suggests a significant in-plane anisotropy of the magnetic response.Comment: 10 figure

Tunneling spectra of strongly coupled superconductors: Role of dimensionality

We investigate numerically the signatures of collective modes in the tunneling spectra of superconductors. The larger strength of the signatures observed in the high-Tc superconductors, as compared to classical low-Tc materials, is explained by the low dimensionality of these layered compounds. We also show that the strong-coupling structures are dips (zeros in the d2I/dV2 spectrum) in d-wave superconductors, rather than the steps (peaks in d2I/dV2) observed in classical s-wave superconductors. Finally we question the usefulness of effective density of states models for the analysis of tunneling data in d-wave superconductors.Comment: 8 pages, 6 figure

Évaluation des transferts entre barrage et aquifères par la méthode de bilan d'une retenue en zone semi-aride. Cas d'El Haouareb en Tunisie centrale

Le barrage d'El Haouareb est situé en Tunisie centrale, dans une zone caractérisée par un climat semi-aride. Il draine le bassin versant de l'oued Merguellil d'une superficie d'environ 1 200 km2. Le but de cette recherche est d'évaluer, à partir du bilan du barrage, l'impact de la mise en place de cet ouvrage sur les ressources en eau de surface et souterraine, en vue de mieux cerner le fonctionnement de l'ensemble de ce système et faciliter ainsi sa gestion.Le bilan en eau de surface fait appel à deux termes non mesurés : l'infiltration à travers la cuvette de la retenue et les apports des oueds incomplètement contrôlés. Par une méthodologie originale, nous avons modélisé et calculé l'infiltration. Les apports journaliers au barrage, déduits du bilan ont été ensuite validés par comparaison aux débits mesurés sur une station située, plus en amont, sur le tributaire principal.Cette recherche a mis en évidence que, malgré des pertes non négligeables par évaporation (25% des apports), l'infiltration constitue, de loin, le terme le plus important du bilan de la retenue d'El Haouareb (63% des apports).Cette dernière a ainsi injecté, directement ou par nappe interposée, dans l'aquifère aval de la plaine de Kairouan plus de 9 millions de m3 par an.The El Haouareb dam and the neighbouring dams (Nebhana and Sidi Saâd) were constructed with the objective of protecting the inhabitants of the Kairouan plain from floods. This area constitutes the natural downstream region of three principal wadis of central Tunisia (Merguellil, Nebhana and Zeroud) where there have been floods in the past. The second objective of this dam is to control the recharge of the Kairouan groundwater aquifer in the absence of natural wadi flows, by diverting flows from the dam and by infiltration through the foundation and basin of the dam. In a semi-arid region characterized by very strong evaporation and plant transpiration rates (about 1700 mm per year), it is obviously of great importance to recharge the underground water systems, which are less subject to these kinds of losses and which better preserve the water resources. The last objective of this dam is to supply water to the population, especially for agricultural needs. The dam was expected to supply water to an irrigated area of about 2500 hectares in this region. During the construction of the El Haouareb dam spillway, underground flows occurred in the limestone of the El Haouareb Hill. At the beginning of the exploitation of the dam these underground flows increased. This development has affected the management plans for the dam and accordingly a monitoring program has been put in place to follow of the evolution over time of the infiltration. The purpose of this research was to evaluate, by the water balance method, the impact of the construction of this dam on surface and ground water. This research will improve the understanding of the system, and thus, facilitate management. In addition, this project will evaluate recharge rates towards the groundwater reserves of the Kairouan plain, which constitutes the natural downstream region of this system.The dam is situated at an interface of several superficial and underground hydraulic systems. For surface water, the El Haouareb dam drains the Merguellil wadi catchment whose surface area is about 1200 km2. Besides the Merguellil wadi, two of its tributaries flow directly into the El Haouareb dam (Hammam and Ben Zitoune wadis) but without any measurement of their flows. Nevertheless, two hydrometric stations were established on the Merguellil wadi, upstream of El Haouareb dam: Haffouz in 1966 and Sidi Boujdaria in 1974. The first station is still functional whereas the second one stopped working in 1989. For underground systems, the Aïn Baïdha groundwater located upstream from the dam, and the downstream groundwater of the Kairouan plain constitute the principal aquifers in relation to this dam. A third aquifer of the El Haouareb hill, composed mainly of limestone, was also identified. It receives both Aïn Baïdha groundwater and infiltrations from the El Haouareb dam, and empties towards the groundwater of the Kairouan plain. A daily database of El Haouareb dam management, collected by the agricultural ministry, was available. The data-base contained the following elements: rainfall amounts for the site; water levels in the dam; evaporation rates measured by a Colorado tub; three states of the physical characteristics of dam measured before the beginning of exploitation (1989) and during two drying times of the dam (1994 and 1997); releases from the dam for irrigation; releases from the dam to fight against siltation of the dam and to recharge the Kairouan plain aquifer. There were also rain data measured from the surrounding rain gages and hydrometric data observed at the Haffouz and Sidi Boujdaria stations. The water balance equation of this dam presents two unknowns: the infiltration from the dam and the flows that arrive in the dam by wadis. To resolve these unknowns, we proceeded by minimizing one of the two unknowns with a goal to determine the other one.As infiltration rates were inaccessible, we worked on periods without flows, chosen according to four criteria. During these periods the rain on the dam and on the surrounding rain gages must be equal to 0 mm, the flows measured at the upstream station of Haffouz must be inferior or equal to 50 L/s, and the variation of the water level in the dam must always be decreasing. Finally, the fourth criterion is that the length of these periods that must be equal or greater than 15 d. Thus we were able to calculate the infiltration flows during the periods without flows. These values were corrected by adding the low water flows, which were assumed to arrive at the dam. These flows were calculated by a linear equation established between the low water flows at the Haffouz and Sidi Boujdaria stations. The representation of this calculated infiltration according to the water level in the dam gave a cluster of points from which three simple linear adjustments were done. Thus, we obtained a model composed of three linear equations that represented the changes in infiltration as a function of time. This model showed that the infiltration flow ratecorresponding to a particular level, decreased with time as sedimentation in the dam proceeded. For the daily average level (206 meters), the infiltration rate passed from 650 L/s in 1989 to 310 L/s in 1998.Despite the scarcity of "periods without flows" between 1989 and 1991, and some uncertainties due essentially to the measurement of water levels in the dam, this model is representative of reality because it takes into account the evolution of sedimentation in the dam. The model yielded infiltration flow rates that were higher than those calculated in preceding studies. The infiltration model obtained was then applied to the entire period of study, allowing resolution of the water balance equation for the dam (which now has only one unknown): the flows of the different wadis arriving in the dam.In conclusion, this research showed that despite considerable losses by evaporation (25% of flows), infiltration (accounting for 63% of flows) constituted the more important term in the water balance of the El Haouareb dam. This dam has thus injected, directly or via the interposed limestone aquifer, more than 9 million m3 per year into the downstream groundwater of the Kairouan plain