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

Abstract

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 $\mathrm{UP}{\mathrm{t}}_3$ 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 $\mathrm{UP}{\mathrm{t}}_3$ [E. R. Schemm \textit{et al.}, Science \textbf{345},190(2014)].

arXiv comment17 pages including appendices,9 figures, replaced with the version accepted by Phys. Rev. B with minor reference corrections

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