Parabolic Scaling in Overdoped Cuprate Films

TL;DR

This paper derives a theoretical explanation for the observed parabolic scaling between transition temperature and superfluid stiffness in overdoped cuprate films, linking it to quantum criticality and providing a formula for the scaling coefficient.

Contribution

It introduces a quantum critical model that exactly derives the parabolic scaling law and predicts the scaling coefficient based on fundamental material parameters.

Findings

Derived the parabolic scaling law from quantum critical theory.

Calculated the scaling coefficient $\

Matched theoretical $\

Abstract

It was recently reported that, in the highly overdoped side of single-crystal $La_{2-x}Sr_xCuO_4$ films, the transition temperature $T_c$ and zero-temperature superfluid phase stiffness $\rho_s(0)$ will obey a parabolic scaling $T_c=\gamma \cdot \sqrt{\rho_s(0)}$. Parabolic scaling indicates a quantum phase transition from a superconductor to a normal metal, for which there has been scant understanding [Nature 536, 309-311 (2016)]. The current study shows that, using the quantum critical model for zero-temperature Cooper pairs [EPL 118, 57007 (2017)], parabolic scaling can be exactly derived, where $\gamma=\gamma(\varepsilon_F,a)$ is uniquely determined by the Fermi energy $\varepsilon_F$ and the minimal lattice constant $a$ of superconducting materials. For single-crystal $La_{2-x}Sr_xCuO_4$ films, we calculate the theoretical value of $\gamma$, which yields $4.29 K^{1/2}$ and is in accordance with an experimental measure value $(4.2 \pm 0.5) K^{1/2} $ with high accuracy. Our formula for $\gamma$ can be further tested by investigating other BCS-like materials.