Theory of the Strange Metal Sr$_3$Ru$_2$O$_7$

The bilayer perovskite Sr$_3$Ru$_2$O$_7$ has been widely studied as a canonical strange metal. It exhibits $T$-linear resistivity and a $T\log(1/T)$ electronic specific heat in a field-tuned quantum critical fan. Criticality is known to occur in `hot' Fermi pockets with a high density of states close to the Fermi energy. We show that while these hot pockets occupy a small fraction of the Brillouin zone, they are responsible for the anomalous transport and thermodynamics of the material. Specifically, a scattering process in which two electrons from the large, `cold' Fermi surfaces scatter into one hot and one cold electron renders the ostensibly non-critical cold fermions a marginal Fermi liquid. From this fact the transport and thermodynamic phase diagram is reproduced in detail. Finally, we show that the same scattering mechanism into hot electrons that are instead localized near a two-dimensional van Hove singularity explains the anomalous transport observed in strained Sr$_2$RuO$_4$.