Field theoretical model of multilayered Josephson junction and dynamics of Josephson vortices

Abstract

Multilayered Josephson junctions are modeled in the context of a field theory, and dynamics of Josephson vortices trapped inside insulators are studied. Starting from a theory consisting of complex and real scalar fields coupled to a U(1) gauge field which admit parallel N − 1 domain-wall solutions, Josephson couplings are introduced weakly between the complex scalar fields. The N − 1 domain walls behave as insulators separating N superconductors, where one of the complex scalar fields has a gap. We construct the effective Lagrangian on the domain walls, which reduces to a coupled sine-Gordon model for well-separated walls and contains more interactions for walls at short distance. We then construct sine-Gordon solitons emerging in an effective theory in which we identify Josephson vortices carrying singly quantized magnetic fluxes. When two neighboring superconductors tend to have the same phase, the ground state does not change with the positions of domain walls (the width of superconductors). On the other hand, when two neighboring superconductors tend to have π -phase differences, the ground state has a phase transition depending on the positions of domain walls; when the two walls are close to each other (one superconductor is thin), frustration occurs because of the coupling between the two superconductors besides the thin superconductor. Focusing on the case of three superconductors separated by two insulators, we find for the former case that the interaction between two Josephson vortices on different insulators changes its nature, i.e., attractive or repulsive, depending on the positions of the domain walls. In the latter case, there emerges fractional Josephson vortices when two degenerate ground states appear due to spontaneous charge-symmetry breaking, and the number of the Josephson vortices varies with the position of the domain walls. Our predictions should be verified in multilayered Josephson junctions.

Exact solutions of domain wall junctions in arbitrary dimensions

“…Finally, let us mention possible applications of our model to physics. Single or parallel domain walls can be applied to Josephson junction arrays of superconductors sandwiching insulators [95,96]. This can be extended to three-dimensional junction found in this paper.…”

Relations among topological solitons

“…We can consider multi-monopoles (multi-walls in the CP N −1 model). In that case, we will obtain a U (1) N −1 coupled sine-Gordon model [106] in which the interaction of sine-Gordon solitons on different domain walls was studied. In our purpose, a single monopole is enough.…”

“…A Josephson junction can be regarded as a heavy tension limit of a domain wall in a U (1) gauge theory coupled with two complex scalar fields [100]. Josephson vortices in different domain walls can be also studied [106].…”

Fractional Skyrmion molecules in a ℂPN−1 model

“…As for potential terms for (2 + 1)-dimensional CP N −1 models, 4 a generalization of the easy-axis anisotropic potential, which appears for example in the multi-layered Josephson junction [113,114], has been studied in refs. [115][116][117][118][119][120][121].…”