Localized Superconductivity in Systems with Inhomogeneous Mass of Cooper Pairs

Abstract

Within the framework of the Ginzburg–Landau theory, we study the features of the localized nucleation of the order parameter in superconducting systems with inhomogeneous effective mass m of the Cooper pairs, which is due to the spatial modulation of the diffusion coefficient and/or fluctuations in the local anisotropy axis in the sample. In the asymptotics of the weak magnetic fields H, for which the magnetic length [Φ₀/(2πH)]^1/2, where Φ₀ is the magnetic-flux quantum, is much shorter than the inhomogeneity scale, the spatial scale of the order parameter is determined by the sample-average coherence length and the regular lattice of the Abrikosov vortices is formed in the superconductor. In sufficiently strong magnetic fields H, the order parameter is localized near the minima of the coherence length ξ ∝ m^−1/2, which results in an increase in the critical temperature and destruction of the regular lattice of the Abrikosov vortices. Therefore, competition between the two superconductivity-nucleation types is observed during a gradual increase in the magnetic field, which leads to the positive curvature of the phase-transition line. We have also studied the features of the temperature dependences of the upper critical magnetic field for some model spatial mass profiles of the Cooper pairs. The obtained results are in good agreement with direct numerical calculations.