Theoretical Study of Half-Quantized Spontaneous Vortices in d-dot using 3-D Finite Element Method Model*

A d-dot is a nano-sized composite structure that consists of a d-wave superconductor (SC) embedded in an s-wave matrix. Since the phase of the superconducting order parameter in the d-wave SC depends on direction, phase difference appears at the corner junctions between d- and s-wave SCs in d-dots. Due to quantization of fluxoids including this phase difference, spontaneous half-quantized vortex (SHQV) appears at each corner in d-dots. [1]. Basic mechanism of SHQVs is studied theoretically [1] and some experiments observed appearance of SHQVs [2]. Since previous calculation model of d-dot [1] is 2-dimensional, it cannot take account of effects of 3-dimensional structure and defects. So, we extend previous model into 3-D model using volume coordinates with the finite element method (FEM). In this study, by using 3-D d-dot FEM model, we investigate the conditions of appearance of SHQV from viewpoints of c-axis anisotropy. [1] M. Kato, T. Ishida, T. Koyama, M. Machida, Superconductors – Materials, Properties and Applications. (InTech 2012) Chap. 13. [2] H. Hilgenkamp, et al. Nature 422, 50 (2003).