Intrinsic ac anomalous Hall effect of non-symmorphic chiral superconductors with an application to UPt3

The polar Kerr effect, or equivalently the ac anomalous Hall effect, is a signature of time reversal symmetry breaking in chiral superconductors. However, seeing it requires additional ingredients, such as disorder and multi-band effects. This turns out to be quite subtle for higher chirality superconductors, for which the heavy-fermion superconductor UPt3 is a candidate. In this talk, I will present our recent work[1] where 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 non-symmorphic group symmetry of the underlying lattice. We apply this mechanism to the putative chiral superconducting phase of UPt3 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 UPt3 [E. R. Schemm et al., Science 345,190 (2014)].

Ref[1]: Zhiqiang Wang, John Berlinsky, Gertrud Zwicknagl and Catherine Kallin, arXiv:1708.09781, to appear in PRB.

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