Influence of cluster size on the normal- and superconducting-state properties of granular Bi films

The Hall coefficient $R_H$ and the magnetic-field dependence of the superconducting transition temperature $T_c$ of granular films built from well defined Bi clusters has been measured as a function of Bi cluster size L $(3.5\mathrm{}<~L<~10\mathrm{nm})$ in magnetic fields up to 8 T and at temperatures $T>\mathrm{}1.8\mathrm{}\mathrm{K}.$ From these experimental results we can conclude that with decreasing L the original rhombohedral bulk structure of the Bi clusters becomes more and more distorted (increasing number of defects), until at ${L=L}^{*}\approx 4.0\mathrm{nm}$ the structure changes into the “amorphous” Bi structure. For ${L=L}^{*}$ the Bi conduction electrons become almost localized and ${(dB}_{c2\mathrm{}}{/dT)}_{T_c}$ has an unusually large value of -16.7 T/K. The good agreement between the L dependencies of normal and superconducting properties indicates that the electronic structure of the Bi clusters changes with L, but is rather homogeneous for a given L.