Quantum phase transition in overdoped La$_{2-x}$Sr$_x$CuO$_4$ evinced by the superfluid density

TL;DR

This study investigates the superfluid density in overdoped La$_{2-x}$Sr$_x$CuO$_4$ thin films, revealing evidence of a quantum phase transition driven by quantum fluctuations, with finite size effects influencing the transition behavior.

Contribution

The paper provides a finite size scaling analysis showing that the superfluid density data are consistent with a (3+1)D-xy quantum phase transition in overdoped cuprate films.

Findings

Superfluid density follows the expected QPT behavior as Tc approaches zero.

Finite size effects, such as film thickness and inhomogeneity, limit the transition.

Evidence of a crossover from thermal to quantum critical regimes as Tc decreases.

Abstract

The superfluid density of overdoped La$_{2-x}$Sr$_x$CuO$_4$ thin films of high quality have been measured with Tc (defined by the onset of the Meissner effect) from 5.1 to 41.6 K by Bosovic et al. Given this Tc the superfluid density shows no clear evidence of critical fluctuations and no indication of vortex unbinding as T->Tc. Nevertheless, the superfluid density displays the expected behavior for for a quantum phase transition (QPT) in the (3+1)D-xy universality class, rho(T=0)~Tc^2. However, this relation is also a hallmark of dirty superconductors, treated in the mean-field approximation. Here we attempt to clear out the nature of the suppression of ro(T) as Tc->0. Noting that for any finite system the continuous transition will be rounded we perform a finite size scaling analysis. It uncovers that the ro(T) data data are consistent with a finite length limited 3D-xy transition. In some films it is their thickness and in others their inhomogeneity that determines the limiting length. Having established the precondition for the occurrence of a QPT mapping on the (3+1) D-xy model, we explore the consistency with the hallmarks of this transition. In particular with the relations rho(T)/rho(0)=1-ycT/Tc, rho((0)^Tc^2, yc=alpha*Tc/ro(0), where alpha is the coefficient in rho(T)=rho(0)-alphaT as T->0. The emerging agreement with these characteristics points clearly to a quantum fluctuations induced suppression, revealing the crossover from the thermal to the quantum critical regime as Tc ->0. In the classical-quantum mapping it corresponds to a 3D to (3 + 1)D crossover.