  Higher-rank generalisations of electrodynamics have recently attracted
considerable attention because of their ability to host "fracton" excitations,
with connections to both quantum stabilizer codes and holography. However, the
search for higher-rank gauge theories in experiment has been greatly hindered
by the lack of materially-relevant microscopic models. Here we show how a spin
liquid described by rank-2 $U(1)$ gauge theory can arise in a magnet on the
breathing pyrochlore lattice. We identify Yb-based breathing pyrochlores as
candidate systems, and make explicit predictions for how the rank-2 $U(1)$ spin
liquid would manifest itself in experiment.

Strongly Correlated Electrons