Branched Josephson junctions: Current carrying solitons in external magnetic fields

Abstract

We consider the branched Josephson junction created by planar superconductors connected to each other through the Y-junction insulator. Assuming that the structure interacts with the external constant magnetic field, we study static sine-Gordon solitons in such system by modeling them in terms of the stationary sine-Gordon equation on metric graph. Exact analytical solutions of the problem are obtained and their stability is analyzed.

Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks

“…Again, as it was done in the case of star branched graph, by substituting the solution of DSGE on a line into the vertex quasi-boundary conditions given by Eqs. ( 21) and (22), one can obtain the following constraints: Fulfilling of this constraint implies that the problem given by Eqs. ( 6), ( 21) and ( 22) is integrable and its (kink) soliton solution can be written as…”

“…Such a task has become subject of extensive study recently (see, Refs. [6]- [22]). Especially, this concerns condensed matter systems, where particle and wave transport in linear(quantum) and nonlinear regimes, where the problem of tunable transport is of crucial importance.…”

Transparent boundary conditions for the sine-Gordon equation:Modeling the reflectionless propagation of kink solitons on a line

“…Recently, soliton dynamics in networks described in terms of sine-Gordon equation on metric graphs attracted some attention [18][19][20][21]. Utilization of such approach makes possible modeling the charged solitons in conducting polymers [22] and static solitons in branched Josephson junctions [23]. However, despite the great progress made on this topic, some issues are still remaining unresolved.…”

“…Here we will adopt this approach for the sine-Gordon equation on a real line. The motivation for the study of TBCs for the sine-Gordon equation comes from different practical important problems, such as tunable soliton transport in Josephson junctions [7,23], energy transfer in DNA [12,13], seismic waves and deformation propagation in tectonic plates [10,11] and many others. In all these systems for certain cases one needs to achieve reflectionless propagation of waves and particles to avoid different losses in charge, energy and signal transfer.…”

Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks

“…it was done in the case of star branched graph, by substituting the solution of DSGE on a line into the vertex quasi-boundary conditions given by equations (23) and(24), one can obtain the following constraints:…”