Paramagnetic and Diamagnetic States in Two-Dimensional Josephson-Junction Arrays

Abstract

Many experiments on high-temperature superconductors have shown paramagnetic behavior when the sample is field cooled. The paramagnetism was attributed to a d-wave order parameter creating pi-junctions in the samples. However, the same effect was later discovered in traditional low-temperature superconductors and conventional Josephson-junction arrays which are s wave. By simulating both conventional and mixed pi/conventional Josephson-junction arrays we determine that differences exist which may be sufficient to clearly identify the presence of pi junctions. In particular, the pi junctions cause a symmetry breaking providing a measurable signature of their presence.

Magnetization of multiply connected superconductors with and without -junctions loops

“…With f different from zero, the paramagnetic solution n = 0 is now the lowest energy solution until f = 1/2 which corresponds to the zero current solutions. For f > 1/2 the solution n = 0, which is diamagnetic, is the lowest energy solution [13]. In figure 2(b) we report the analogous states for the 3, 6, 12 and 24 junction loops.…”

“…To compare exact results with the above simple theory, we simulate a square array of √ N × √ N square loops each carrying four Josephson junctions. The equations describing the array in vector notation read [11,12]:…”

“…Here quantum numbers are also used to introduce noise in the system choosing them randomly distributed [11]. Details of the integration procedure to simulate field cooling can be found in [12] where the expression of mutual inductance matrix is also given. To compare our results with that in the literature, here we choose β C = 65 [10,12].…”

“…These results, however, show that the magnetization of the array is strictly connected to the properties of the single loop made of p Josephson junctions [11][12][13]. In this paper, we will show how we can obtain magnetization properties of a JJA making some simple assumptions on the energy behaviour of single loop states in the mean field generated by other loops.…”

“…In [11,12], we have shown by means of numerical simulations that there is no need of π-junctions for obtaining a paramagnetic response from a JJA, but the MCS nature of array that generates the paramagnetic response. On the other hand, we have simulated an array with π-junctions showing that there are at best only subtle differences between a conventional array and an array containing a mixture of conventional and π-junctions (see figure 1) [13].…”