Josephson Current of Monopolar Spinons through a Quantum Spin Ice Junction

Quantum spin liquids are novel states of magnetic materials exhibiting long range quantum entanglement and topological order. They are characterized by exotic quasiparticles called spinons carrying fractionalized spin quanta and by emergent gauge fields. In particular quantum spin ice system accommodates bosonic magnetic monopolar spinons coupled to analogous electromagnetic fields. It can host a U(1) quantum spin liquid as a monopole insulator and a Higgs ferromagnet as a monopole superconductor. Here, we demonstrate an interference phenomena of spinons producing monopole supercurrent. Two Higgs ferromagnets weakly linked by a U(1) quantum spin liquid generates "Josephson supercurrent" of monopoles across the junction. Due to the analogous Amp`ere's law, the current produces an electric polarization in the U(1) quantum spin liquid medium, which is expected to be experimentally observed.