The effect of topological fluctuations on the heat capacity of superconductor

The effect of topological excitations in the form of small size (r << xi(T)) vortex rings on thermodynamics of a bulk superconductor is considered. These specific short wavelength fluctuations of the order parameter are analogous to small vortex-antivortex pairs in superconducting film which were recently studied in Y.N. Ovchinnikov, A.A. Varlamov, Phys. Rev. Lett. 94, 107007 (2004). The corresponding contribution to the free energy below T-c is calculated. It is shown that fluctuations of this type give the main temperature dependent contribution to the heat capacity of the superconductor in the sufficiently large interval of temperatures below the transition point. Important, that the sign of this contribution is opposite to that one appearing due to the usual long wavelength fluctuation, leading to smearing of the BCS jump of heat capacity.