TY - JOUR

T1 - Field theoretical model of multilayered Josephson junction and dynamics of Josephson vortices

AU - Fujimori, Toshiaki

AU - Iida, Hideaki

AU - Nitta, Muneto

N1 - Funding Information:
We would like to thank Zhao Huang for useful comments and discussions and Naoki Yamamoto for a discussion at the early stage of this work. This work is supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) Supported Program for the Strategic Research Foundation at Private Universities Topological Science (Grant No. S1511006). The work of M.N. is also supported in part by a Grant-in-Aid for Scientific Research on Innovative Areas Topological Materials Science (KAKENHI Grant No. 15H05855) and Nuclear Matter in Neutron Stars Investigated by Experiments and Astronomical Observations (KAKENHI Grant No. 15H00841) from the MEXT of Japan and by a Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI Grant No. 16H03984). H.I. was supported by the RSF grant 15-12-20008.
Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/9/8

Y1 - 2016/9/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990884966&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990884966&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.94.104504

DO - 10.1103/PhysRevB.94.104504

M3 - Article

AN - SCOPUS:84990884966

SN - 2469-9950

VL - 94

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 10

M1 - 104504

ER -