Fine frequency shift of single vortex entrance and exit in superconducting loops

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.