  The Coulombic quantum spin liquid in quantum spin ice is an exotic quantum
phase of matter that emerges on the pyrochlore lattice and is currently
actively searched for. Motivated by recent experiments on the Yb-based
breathing pyrochlore material Ba$_3$Yb$_2$Zn$_5$O$_{11}$, we theoretically
study the phase diagram and magnetic properties of the relevant spin model. The
latter takes the form of a quantum spin ice Hamiltonian on a breathing
pyrochlore lattice, and we analyze the stability of the quantum spin liquid
phase in the absence of the inversion symmetry which the lattice breaks
explicitly at lattice sites. Using a gauge mean-field approach, we show that
the quantum spin liquid occupies a finite region in parameter space. Moreover,
there exists a direct quantum phase transition between the quantum spin liquid
phase and featureless paramagnets, even though none of theses phases break any
symmetry. At nonzero temperature, we show that breathing pyrochlores provide a
much broader finite temperature spin liquid regime than their regular
counterparts. We discuss the implications of the results for current
experiments and make predictions for future experiments on breathing
pyrochlores.
