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