Determination of IVC breakpoint for josephson junction stack. Non-periodic boundary conditions with γ = 1

Abstract

We prove that, in the case of non-periodic (with γ = 1) boundary conditions, the calculation of the current-voltage characteristic (IVC) for a stack of n intrinsic Josephson junctions reduces to solving a system of [(n + 1)/2] non-linear differential equations instead of the n original ones. The current voltage characteristic V(I) has the shape of a hysteresis loop. On the back branch of the loop V(I) decreases to zero rapidly near the breakpoint Ib. We succeeded to derive an algorithm determining the approximate breakpoint location and to improve simultaneously the mixed numerical-analytical algorithm of IVC calculation for a stack of Josephson junctions developed by us before. The efficiency of the improved algorithm is shown by the calculations of IVC for stacks consisting of various numbers of intrinsic Josephson junctions.