Electric Field Response In Breathing Pyrochlores

We study the effects of a uniform electric field on the the ground state and excitations of the three-dimensional U(1) spin liquid phase of a breathing pyrochlore lattice, arising due to the coupling between the conventional (Maxwell) electric field and the emergent electrodynamics of the quantum spin ice material. This is an extension of the studies for isotropic pyrochlores in Phys. Rev. B 96, 125145 (2017) to the anisotropic case, as the lattice inversion symmetry is broken in breathing pyrochlores. The emergent photons are found to exhibit birefringence, analogous to the isotropic case. However, the system possesses a nonzero polarization even in the absence of an external electric field, unlike the isotropic pyrochlore. We also find that a sufficiently strong electric field triggers a quantum phase transition into new U(1) quantum spin liquid phases which trap $\pi$-fluxes of the emergent electric field. Such transitions are seen to occur even when the applied electric field is along a direction that does not show a phase transition in the isotropic limit.