Intrinsic ac anomalous Hall effect of nonsymmorphic chiral superconductors with an application to $\mathrm{U}\mathrm{P}{\mathrm{t}}_3$

We identify an intrinsic mechanism of the anomalous Hall effect for non-symmorphic chiral superconductors. This mechanism relies on both a nontrivial multi-band chiral superconducting order parameter, which is a mixture of pairings of even and odd angular momentum channels, and a complex normal state inter-sublattice hopping, both of which are consequences of the nonsymmorphic group symmetry of the underlying lattice. We apply this mechanism to the putative chiral superconducting phase of the heavy-fermion superconductor $\mathrm{U}\mathrm{P}{\mathrm{t}}_3$ and calculate the anomalous ac Hall conductivity in a simplified two-band model. From the ac Hall conductivity and optical data we estimate the polar Kerr rotation angle and compare it to the measured results for $\mathrm{U}\mathrm{P}{\mathrm{t}}_3$ [E. R. Schemm $\mathit{\text{et}}\mathit{\text{al.}}$, Science $\mathbf{\text{345}}$,190(2014)].