Abstract
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.
Highlights
The Josephson effect is especially appealing to physicists because it reveals macroscopically the quantum order and phase
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
The dc Josephson effect, in particular, describes the zero-bias supercurrent occurring in a Josephson junction – a device consisting of two coupled condensates with a relative phase applied
Summary
The Josephson effect is especially appealing to physicists because it reveals macroscopically the quantum order and phase. Unique effects for excitons in bilayer include the interlayer tunneling anomaly[14,15,16,17,18,19,20,21] and the current counterflow[17,22,23,24,25,26,27]. Both offer exotic twists to the already fascinating supercurrent phenomena – among all the Josephson effect. Because of the continuously varying nature, abrupt occurrence of solitons with increasing relative phase φ0 is not observed – the solitons appear progressively starting from infinitesimal φ0
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