The Josephson effect is especially appealing to physicists because it reveals macroscopically the quantum order and phase. In excitonic bilayers the effect is even subtler due to the counterflow of supercurrent as well as the tunneling between layers (interlayer tunneling). Here we study, in a quantum Hall bilayer, the excitonic Josephson junction: a conjunct of two exciton condensates with a relative phase ϕ0 applied. The system is mapped into a pseudospin ferromagnet then described numerically by the Landau-Lifshitz-Gilbert equation. In the presence of interlayer tunneling, we identify a family of fractional sine-Gordon solitons which resemble the static fractional Josephson vortices in the extended superconducting Josephson junctions. Each fractional soliton carries a topological charge Q that is not necessarily a half/full integer but can vary continuously. The calculated current-phase relation (CPR) shows that solitons with Q = ϕ0/2π is the lowest energy state starting from zero ϕ0 – until ϕ0 > π – then the alternative group of solitons with Q = ϕ0/2π − 1 takes place and switches the polarity of CPR.
We study theoretically the exciton-condensate/normal-barrier/exciton-condensate (EC/N/EC) structures in bilayers with a tunable relative phase f 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=f 0 /π (for the same relative phase f 0 ), as opposed to a full portion fraction soliton of charge Q=f 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.
Scientific Reports 5: Article number: 15796; published online: 29 October 2015; updated: 07 June 2017 In this Article, an affiliation has been omitted for Ya-Fen Hsu. The correct affiliations are listed below: Department of Electrophysics, National Chiao Tung University, Hsinchu 300, Taiwan. PhysicsDivision, National Center for Theoretical Science, Hsinchu, 30013, Taiwan.
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