Current and potential distributions in highly anisotropic superconductors with inclusions

Thin whiskers of orthorhombic Bi₂Sr₂Ca₁Cu₂O_x have been grown from powders and their resistive transitions have been studied at constant current. The potential difference between the voltage electrodes on some of the whiskers showed an abrupt increase when they were cooled below ∼ 105 K. It is shown that this increase may be explained by one or more intercalated layers of superconducting Bi₂Sr₂Ca₂Cu₃O_x inside the bulk Bi₂Sr₂Ca₁Cu₂O_x material. The whisker is represented by an orthorhombic solid which extends from -∞ to ∞in the b-direction and has a thickness in the c-direction which is much less than the length in the a-direction. The ratio of the electrical conductivities σ_aa/σ_cc is taken to be of the order of 10⁴ as is the case for Bi₂Sr₂Ca₁Cu₂O_x. The two-dimensional potential distribution in the whisker satisfies Laplace's equation in a co-ordinate system in which the displacements along the c-direction are scaled by a factor of √(σ_aa/σ_cc). This equation is solved by a standard relaxation method. Two cases have been considered. In the first, the entire crystal is in its normal state and in the second there is an intercalated superconducting layer of Bi₂Sr₂Ca₂Cu₃O_x perpendicular to the c-direction and inside normally conducting Bi₂Sr₂Ca₁Cu₂O_x which constitutes the bulk material. It is this layer which gives rise to the observed anomalous resistive transitions at 105 K and to changes in potential distributions. Figures are presented to illustrate the changes.