Effective 2D thickness for the Berezinskii-Kosterlitz-Thouless-like transition in a highly underdoped La$_{2-x}$Sr$_x$CuO$_4$

TL;DR

This study investigates the BKT-like transition in highly underdoped La$_{2-x}$Sr$_x$CuO$_4$ films, revealing a layered superfluid stiffness scale and a large vortex-core energy through transport measurements.

Contribution

It demonstrates that the BKT transition in underdoped cuprate films is governed by a superfluid stiffness characteristic of a few layers, highlighting the layered nature of the transition.

Findings

BKT signatures observed in paraconductivity and I-V characteristics.

Large vortex-core energy indicated by superfluid stiffness analysis.

Transition controlled by a superfluid stiffness of a few layers.

Abstract

The nature of the superconducting transition in highly underdoped thick films of La$_{2-x}$Sr$_x$CuO$_4$ ($x=0.07$ and 0.08) has been investigated using the in-plane transport measurements. The contribution of superconducting fluctuations to the conductivity in zero magnetic field, or paraconductivity, was determined from the magnetoresistance measured in fields applied perpendicular to the CuO$_2$ planes. Both the temperature dependence of the paraconductivity above the transition and the nonlinear current-voltage ($I-V$) characteristics measured across it, exhibit the main signatures of the Berezinskii-Kosterlitz-Thouless (BKT) transition. The quantitative comparison of the superfluid stiffness, extracted from the $I-V$ data, with the renormalization-group results for the BKT theory, reveals a large value of the vortex-core energy. This finding is confirmed by the analysis of the paraconductivity obtained using different methods. The results strongly suggest that the characteristic energy scale controlling the BKT behavior in this layered system corresponds to the superfluid stiffness of a few layers.