Isotope effect on superconductivity in Josephson coupled stripes in underdoped cuprates

TL;DR

This paper proposes a simple Josephson coupled stripe model to explain the linear relation between incommensurate neutron scattering peaks and superconducting transition temperature in cuprates, predicting a small isotope effect on a characteristic velocity.

Contribution

It introduces a Josephson coupled stripe model that links neutron scattering incommensuration to $T_c$, and predicts a measurable isotope effect on the velocity parameter.

Findings

Linear relation between $T_c$ and incommensuration $ o$ a velocity parameter $v^*$.

Oxygen isotope substitution affects $v^*$ by approximately 5%.

Incommensuration is primarily set by doping, not isotope mass.

Abstract

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 $\simeq 5%$.