We study theoretically the exciton-condensate/normal-barrier/exciton-condensate (EC/N/EC) structures in bilayers with a tunable relative phase φ 0 between the two exciton condensates (ECs). It is a setup inspired initially by the superconducting Josephson junction but with a special ingredient added for bilayer systems, namely, the interlayer tunneling. Our results shows that in a EC/N/EC structure of long-barrier, the single Andreev reflection at one EC/N interface dominates-as opposed to the same structure of short-barrier, in which multiple Andreev reflections can be accommodated (similar to the superconducting Josephson junctions). The single interface effect turns the other EC inert and the system can no longer be understood as a Josephson junction. The supercurrent, however, still occurs at the N/EC interface since the current conservation is still fulfilled with the assistance of the interlayer tunneling in barriers. This exotic mechanism gives rise to only a half portion from a fractional soliton of a doubled topological charge 2Q =φ 0/π (for the same relative phase φ 0), as opposed to a full portion fraction soliton of charge Q φ 0/2π in the structures of short-barriers. We predict the current phase relation for the EC/N/EC structures of long-barriers which can be tested experimentally.
- Josephson junction