[WB4] Advanced Processing

11:30 AM - 11:45 AM JST(2:30 AM - 2:45 AM UTC)

[WB4-05] Analysis of critical current in network-patterned YBa₂Cu₃O_7-y films using maximum flow problem

*Ryoga Nagae¹, Tomoya Horide¹, Takuya Ohwa², Yutaka Yoshida¹ (1. Nagoya University (Japan), 2. Kyushu Institute of Technology (Japan))

Keywords:

Critical current,Ic Distribution,Inhomogeneity,Mathematical modeling

The critical current (I_c) of superconducting wires is crucial for applications such as fusion and nuclear magnetic resonance. However, practical superconducting wires often exhibit inhomogeneous I_c distributions. Due to local defects and inhomogeneities, superconducting wires exhibit non-uniform I_c distributions. While local I_c distributions have been evaluated using magnetization measurements, the I_c values obtained from magnetization reflect local properties and do not necessarily coincide with the overall I_c determined from current-voltage (I–V) measurement. To better understand the superconducting properties of wires for future applications, it is important to develop a method that estimates the overall I_c from local I_c distributions, especially under inhomogeneous conditions. In this study, we focused on the maximum flow problem, a mathematical method for analyzing flows within graph structures, to address this issue. YBa2Cu3O7-y thin films were fabricated on a SrTiO3(100) substrate using pulsed laser deposition. Grid-like network patterns with 4 × 4 or 8 × 8 bridges were then formed on the film by laser etching. First, the I_c of the initial, uncut network pattern was measured. Then, some of the bridges were cut, and I_c was measured again. Various patterns were fabricated for 4 × 4 and 8 × 8 bridge network patterns. I_c measurement was performed at 77 K, 80 K, and 83 K. The behavior of the I_c was analyzed using the maximum flow problem. The maximum flow problem is a mathematical problem that determines the maximum amount of flow that can pass through a graph. The algorithm for calculating the maximum flow searches for a path from the source to the sink. This path is subtracted from the flow network to obtain a residual network. This process is repeated until no more paths can be found from the source to the sink, at which point the maximum flow is obtained. We discussed the influence of the bridge cut pattern on the overall I_c using the maximum flow problem.The measured I_c was normalized to the critical current I_c,0 as I_c/I_c,0 and compared with I_c/I_c,0 calculated using the maximum flow problem. I_c,0 is the reference I_c estimated for the network pattern before the initial path cut. The measured I_c/I_c,0 and the calculated I_c/I_c,0 agreed well. This result indicates that the I_c of superconductors can be explained using the maximum flow problem. We also proposed a method to estimate the overall I_c from the local I_c distribution which can be measured using the magnetization measurement. We will examine the effectiveness of I_c analysis using the maximum flow problem for inhomogeneous I_c distributions. We will also discuss the concept of the minimum cut, which enables us to identify the weakest part in the local I_c distribution.