Isotope effect on superconductivity in Josephson coupled stripes in underdoped cuprates

Inelastic neutron scattering data for YBaCuO as well as for LaSrCuO indicate incommensurate neutron scattering peaks with incommensuration $\delta(x)$ away from the $(\pi,\pi)$ point. $T_c(x)$ can be replotted as a linear function of the incommensuration for these materials. This linear relation implies that the constant that relates these two quantities, one being the incommensuration (momentum) and another being $T_c(x)$ (energy), has the dimension of velocity we denote $v^*$: $k_B T_c(x) = \hbar v^* \delta(x)$. We argue that this experimentally derived relation can be obtained in a simple model of Josephson coupled stripes. Within this framework we address the role of the $O^{16} \to O^{18}$ isotope effect on the $T_c(x)$. We assume that the incommensuration is set by the {\em doping} of the sample and is not sensitive to the oxygen isotope given the fixed doping. We find therefore that the only parameter that can change with O isotope substitution in the relation $T_c(x) \sim \delta(x)$ is the velocity $v^*$. We predict an oxygen isotope effect on $v^*$ and expect it to be $\simeq 5$.Comment: 4 pages latex file, 2 eps fig

Large isotope effect on TcT_c in cuprates despite of a small electron-phonon coupling

We calculate the isotope coefficients $\alpha$ and $\alpha^\ast$ for the superconducting critical temperature $T_c$ and the pseudogap temperature $T^\ast$ in a mean-field treatment of the t-J model including phonons. The pseudogap phase is identified with the $d$-charge-density wave ($d$-CDW) phase in this model. Using the small electron-phonon coupling constant $\lambda_d \sim 0.02$ obtained previously in LDA calculations in YBa$_2$Cu$_3$O$_7$, $\alpha^{\ast}$ is negative but negligible small whereas $\alpha$ increases from about 0.03 at optimal doping to values around 1 at small dopings in agreement with the general trend observed in many cuprates. Using a simple phase fluctuation model where the $d$-CDW has only short-range correlations it is shown that the large increase of $\alpha$ at low dopings is rather universal and does not depend on the existence of sharp peaks in the density of states in the pseudogap state or on specific values of the phonon cutoff. It rather is caused by the large depletion of spectral weight at low frequencies by the $d$-CDW and thus should also occur in other realizations of the pseudogap.Comment: 8 pages, 5 figures, to be publ. in PR

Superconducting instability in the Holstein-Hubbard model: A numerical renormalization group study

We have studied the d-wave pairing-instability in the two-dimensional Holstein-Hubbard model at the level of a full fluctuation exchange approximation which treats both Coulomb and electron-phonon (EP) interaction diagrammatically on an equal footing. A generalized numerical renormalization group technique has been developed to solve the resulting self-consistent field equations. The $d$-wave superconducting phase diagram shows an optimal T_c at electron concentration ~ 0.9 for the purely electronic Hubbard system. The EP interaction suppresses the d-wave T_c which drops to zero when the phonon-mediated on-site attraction $U_p$ becomes comparable to the on-site Coulomb repulsion $U$. The isotope exponent $\alpha$ is negative in this model and small compared to the classical BCS value $\alpha_{BCS} = 1/2$ or compared to typical observed values in non-optimally doped cuprate superconductors.Comment: 4 pages RevTeX + 3 PS figures include

Intrinsic and structural isotope effects in Fe-based superconductors

The currently available results of the isotope effect on the superconducting transition temperature T_c in Fe-based high-temperature superconductors (HTS) are highly controversial. The values of the Fe isotope effect (Fe-IE) exponent \alpha_Fe for various families of Fe-based HTS were found to be as well positive, as negative, or even be exceedingly larger than the BCS value \alpha_BCS=0.5. Here we demonstrate that the Fe isotope substitution causes small structural modifications which, in turn, affect T_c. Upon correcting the isotope effect exponent for these structural effects, an almost unique value of \alpha~0.35-0.4 is observed for at least three different families of Fe-based HTS.Comment: 4 pages, 2 figure

The Isotope Effect in d-Wave Superconductors

Based on recently proposed anti-ferromagnetic spin fluctuation exchange models for $d_{x^2-y^2}$-superconductors, we show that coupling to harmonic phonons {\it{cannot}} account for the observed isotope effect in the cuprate high-$T_c$ materials, whereas coupling to strongly anharmonic multiple-well lattice tunneling modes {\it{can}}. Our results thus point towards a strongly enhanced {\it{effective}} electron-phonon coupling and a possible break-down of Migdal-Eliashberg theory in the cuprates.Comment: 12 pages + 2 figures, Postscript files, all uuencoded Phys. Rev. Lett. (1995, to be published

Implications of the isotope effects on the magnetization, magnetic torque and susceptibility

We analyze the magnetization, magnetic torque and susceptibility data of La2-xSrxCu(16,18)O4 and YBa2(63,65)CuO7-x near Tc in terms of the universal 3D-XY scaling relations. It is shown that the isotope effect on Tc mirrors that on the anisotropy. Invoking the generic behavior of the anisotropy the doping dependence of the isotope effects on the critical properties, including Tc, correlation lengths and magnetic penetration depths are traced back to a change of the mobile carrier concentration.Comment: 5 pages, 3 figure

The cosine law at the atomic scale: Toward realistic simulations of Knudsen diffusion

We propose to revisit the diffusion of atoms in the Knudsen regime in terms of a complex dynamical reflection process. By means of molecular dynamics simulation we emphasize the asymptotic nature of the cosine law of reflection at the atomic scale, and carefully analyze the resulting strong correlations in the reflection events. A dynamical interpretation of the accomodation coefficient associated to the slip at the wall interface is also proposed. Finally, we show that the first two moments of the stochastic process of reflection non uniformly depend on the incident angle

Two dimensional Leidenfrost Droplets in a Hele Shaw Cell

We experimentally and theoretically investigate the behavior of Leidenfrost droplets inserted in a Hele-Shaw cell. As a result of the confinement from the two surfaces, the droplet has the shape of a flattened disc and is thermally isolated from the surface by the two evaporating vapor layers. An analysis of the evaporation rate using simple scaling arguments is in agreement with the experimental results. Using the lubrication approximation we numerically determine the shape of the droplets as a function of its radius. We furthermore find that the droplet width tends to zero at its center when the radius reaches a critical value. This prediction is corroborated experimentally by the direct observation of the sudden transition from a flattened disc into an expending torus. Below this critical size, the droplets are also displaying capillary azimuthal oscillating modes reminiscent of a hydrodynamic instability

Oxygen-isotope effect on the superconducting gap in the cuprate superconductor Y_{1-x}Pr_xBa_2Cu_3O_{7-\delta}

The oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the zero-temperature superconducting energy gap \Delta_0 was studied for a series of Y_{1-x}Pr_xBa_2Cu_3O_{7-\delta} samples (0.0\leq x\leq0.45). The OIE on \Delta_0 was found to scale with the one on the superconducting transition temperature. These experimental results are in quantitative agreement with predictions from a polaronic model for cuprate high-temperature superconductors and rule out approaches based on purely electronic mechanisms.Comment: 5 pages, 3 figure