Superconductivity in mesoscopic high-$T_c$ superconducting particles

Abstract

Based on the Hubbard model in the framework of non-phonon kinematical mechanism and taking into account the discreetness of an electronic energy spectrum, the superconducting critical temperature of a mesoscopic high-$T_c$ sphere is analyzed as a function of doping and as a function of a particle's radius. The critical temperature $T_c$ is found to be an oscillating function of the radius of a particle. The size-dependent doping regime is revealed in high-$T_c$ nanoparticles. Our analysis shows that each oscillation in $T_c$ corresponds to the increase of a number of the energy levels in the sphere by one. The amplitude of oscillations of $T_c$ increases with decreasing $R$ and can reach a value of 6 K for nanopartilces with sizes about 25 nm, in a good agreement with experimental studies of YBa${}_2$Cu${}_3$O${}_{7-\delta }$ nanoparticles.

8 pages, 3 figures, to be published in Solid State Commun., E-mail addresses: [email protected], [email protected]