Insulating state of granular superconductors in a strong-coupling regime

We analyze the possibility of the formation of a magnetic-field-induced insulating state in a two-dimensional granular superconductor with relatively strong intergranular coupling and show that such a state appears in a model with spatial variations of the single-grain critical magnetic field. This model describes realistic granular samples with a dispersion in grain sizes and explains the mechanism leading to a giant peak in the magnetoresistance.

Figure 1

(a) Superconductor film consisting of grains of slightly different sizes. (b) The same granular array under applied magnetic field close to the average single-grain critical field. Varying magnetic field results in a change of the relative concentration of superconducting (white) and normal (gray) grains.

Figure 2

Phase diagram of a superconducting grain at $T=0$ in coordinates of Zeeman energy $h$ vs pair-breaking parameter $\alpha$. The dashed line separates the gapless (GS) and gapful (S) superconducting states. First- and second-order phase transition lines are shown by thick and thin solid lines, respectively.

Figure 3

Diagram (a) represents the coupling of the normal grains (${\mathrm{N}}_1$ and ${\mathrm{N}}_2$) via the superconducting grain S. Diagram (b) describes the processes of Cooper pair tunneling between the superconducting grains (${\mathrm{S}}_1$ and ${\mathrm{S}}_2$) via the normal grain N. Solid (electron) lines are connected via dashed lines that represent impurities forming the zero-dimensional diffuson or Cooperon. Solid lines with two arrows represent the anomalous Green’s functions of the superconductors.