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.
Categories: cond-mat.supr-con cond-mat.str-el