Vison crystal in quantum spin ice on the breathing pyrochlore lattice

Recent excitement in the quantum spin ice (QSI) community has come from the experimental discovery of pseudospin-12 breathing pyrochlores, including Ba3Yb2Zn5O11, in which inversion symmetry is broken by the "up" and "down" tetrahedra taking different physical sizes. We show here that the often-neglected Jz +/- coupling between Kramers ions, in combination with the breathing nature of the lattice, can produce an imaginary ring flip term. This can lead to an unconventional "U (1)pi /2 phase", corresponding to a maximally dense packing of visons on the lattice. The coherent, emergent QED dynamics of conventional QSI persist in this phase, in a manner reminiscent of fragmentation in spinon crystals. We characterize the excitations of the system within the enlarged QSI phase diagram, showing that the imaginary ring flip acts both as a chemical potential for visons and as an effective three-photon vertex akin to strong light-matter coupling. The coupling causes a structured high-energy continuum to emerge above the photon dispersion, which is naturally interpreted as three photon up-conversion in a nonlinear optical crystal.