The heat capacity Cp of an array of independent aluminum rings has been measured under an external magnetic field H using highly sensitive ac-calorimetry based on a silicon membrane sensor. Each superconducting vortex entrance induces a phase transition and a heat capacity jump and hence Cp oscillates with H. This oscillatory and non-stationary behaviour measured versus the magnetic field has been studied using the Wigner-Ville distribution (a time-frequency representation). It is found that the periodicity of the heat capacity oscillations varies significantly with the magnetic field; the evolution of the period also depends on the sweeping direction of the field. This can be attributed to a different behavior between expulsion and penetration of vortices into the rings. A variation of more than 15% of the periodicity of the heat capacity jumps is observed as the magnetic field is varied. A description of this phenomenon is given using an analytical solution of the Ginzburg-Landau equations of superconductivity.
@article{arxiv.0708.3023,
title = {Fine frequency shift of sigle vortex entrance and exit in superconducting loops},
author = {F. R. Ong and Olivier Bourgeois and S. E. Skipetrov and J. Chaussy and Simona Popa and Jérôme Mars and Jean-Louis Lacoume},
journal= {arXiv preprint arXiv:0708.3023},
year = {2009}
}