Fishtail or peak effect due to proximity in superconductor with normal inclusions

Abstract

The possible rise of the peak (or fishtail) effect due to the proximity-based mechanism is discussed for a superconductor with normal inclusions. The proximity induces only a slight variation of the order parameter near the normal inclusion-superconductor (NS) interface at low magnetic field and this results in a small pinning force. The superconductivity induced in normal inclusions decays at higher magnetic fields and the pinning force at the NS interface increases. As a result, the peak (or fishtail) may be observed in the magnetic field dependence of the critical current. It is shown that both the characteristic size of a normal inclusion and the coherence length in it should be larger than (or at least comparable to) the coherence length in the superconductor to provide the clearly pronounced peak effect. This condition assures that the characteristic magnetic field of the superconductivity decay in normal inclusions is smaller than the upper critical field H c2 in the superconductor. Therefore the pinning force at low magnetic fields is small as compared to that at high fields. The approximate expression for the elementary pinning force is found in the framework of the Ginzburg-Landau theory and the critical current is calculated for the two-dimensional model system formed by a periodic array of superconducting and normal layers. The obtained results may give some insight into the nature of the peak effect in both low- and high-temperature superconductors.