Doping dependence of the vortex-core energy in bilayer films of cuprates

TL;DR

This paper investigates how the vortex-core energy in bilayer cuprate films depends on doping levels and influences the Berezinskii-Kosterlitz-Thouless transition, using theoretical analysis and recent experimental data.

Contribution

It provides a theoretical analysis of vortex-core energy dependence on doping in bilayer cuprates and compares it with experimental measurements to extract key parameters.

Findings

Vortex-core energy scales linearly with $T_c$ at low doping.

Theoretical model aligns with recent penetration depth measurements.

Insights into vortex fluctuations in underdoped cuprates.

Abstract

The energy needed to create a vortex core is the basic ingredient to address the physics of thermal vortex fluctuations in underdoped cuprates. Here we theoretically investigate its role on the occurrence of the Beresinskii-Kosterlitz-Thouless transition in a bilayer film with inhomogeneity. From the comparison with recent measurements of the penetration depth in two-unit cell thin films of Y$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-\d}$ (YBCO) by Hetel et al. [Nat. Phys. 3, 700 (2007)] we can extract the value of the vortex-core energy $\mu$, and show that $\mu$ scales linearly with $T_c$ at low doping.