Isotope effect on Tc and the superfluid density of high-temperature superconductors

TL;DR

This paper presents a model explaining the oxygen isotope effect in cuprates, showing it affects superfluid density but not pseudo-gap, with results aligning with experimental data across doping levels.

Contribution

The study introduces a theoretical framework combining spin-charge separation and polaron physics to explain isotope effects in high-temperature superconductors.

Findings

OIE affects superfluid density across all doping levels.

OIE influences Tc only in underdoped cuprates.

The model aligns with experimental observations.

Abstract

In this paper, I study the oxygen isotope effect (OIE) in cuprates. I introduce a simple model that can explain experiments both qualitatively and quantitatively. In this theory, isotope substitution only affects the superfluid density, but not the pseudo-gap. Within the spin-charge separation picture, I argue that the spinon-phonon interaction is in the adiabatic limit, and therefore within the Migdal-Eliashberg theory, there is no isotope effect in the spinon mass renormalization. On the other hand, I show that the holon-phonon interaction is in the non-adiabatic limit. Therefore, the small polaron picture is applicable and there is a large mass enhancement in an isotope-dependent way. Our theory explains why upon $^{16}$O/$^{18}$O substitution, the superconducting transition temperature changes only in underdoped cuprates, while there is no considerable OIE at the optimal doped as well as the overdoped cuprates. Additionally, in contrast to the conventional superconductors, we obtain OIE on the superfluid density for whole superconducting region in agreement with the experimental observations.