Margaris I, Paltoglou V, Flytzanis N
Department of Electrical and Computer Engineering, University of Thessaly, 37 Glavani 28th October Str, 38221 Volos, Magnesia, Greece.
J Phys Condens Matter. 2018 May 16;30(19):195303. doi: 10.1088/1361-648X/aaba04. Epub 2018 Apr 17.
In this work we present a method of representing terms in the current-phase-relation of a ballistic Josephson junction by combinations of diagrams, used in previous work to represent an equivalent of the matching condition determinant of the junction. This is accomplished by the expansion of the logarithm of this determinant in Taylor series and keeping track of surviving terms, i.e. terms that do not annihilate each other. The types of the surviving terms are represented by connected graphs, whose points represent diagrammatic terms of the determinant expansion. Then the theory is applied to obtain approximations of the current-phase relation of relatively thick ballistic ferromagnetic Josephson junctions with non-collinear magnetizations. This demonstrates the versatility of the method in developing approximations schemes and providing physical insight into the nature of contributions to the supercurrent from the available particle excitations in the junction. We also discuss the strong second harmonic contribution to the supercurrent in junctions with three mutually orthogonal magnetization vectors and a weak intermediate ferromagnet.
在这项工作中，我们提出了一种通过图表组合来表示弹道约瑟夫森结电流-相位关系中各项的方法，该方法在之前的工作中用于表示结的匹配条件行列式的等效项。这是通过将该行列式的对数展开为泰勒级数并跟踪留存项（即不相互抵消的项）来实现的。留存项的类型由连通图表示，其节点代表行列式展开的图表项。然后将该理论应用于获得具有非共线磁化的相对较厚的弹道铁磁约瑟夫森结的电流-相位关系的近似值。这展示了该方法在开发近似方案以及深入了解结中可用粒子激发对超电流贡献的本质方面的通用性。我们还讨论了具有三个相互正交磁化矢量和一个弱中间铁磁体的结中对超电流的强二次谐波贡献。
