Attojoule Calorimetry of Mesoscopic Superconducting Loops

We report the first experimental evidence of nontrivial thermal behavior of the simplest mesoscopic system—a superconducting loop. By measuring the specific heat $C$ of an array of 450 000 noninteracting aluminum loops with very high accuracy of $\sim 20\mathrm{f}\mathrm{J}/\mathrm{K}$, we show that the loops go through a periodic sequence of phase transitions (with a period of an integer number of magnetic flux quanta) as the magnetic flux threading each loop is increased. The transitions are well described by the Ginzburg-Landau theory and are accompanied by discontinuities of $C$ of only several thousands of Boltzmann constants $k_B$.