Superconductivity in Empty Bands and Multiple Order Parameter Chirality

Abstract

Recent experiments have shown rotation of the plane of polarization of light reflected from the surface of some superconductors. The photon energy exceeds the electronic bandwidth, so that completely filled or completely empty bands must play a role. We show that in strong-coupling theory a Coulomb interaction can produce an order parameter in the unoccupied band that explains the observations. Thus the phenomenology puts tight constraints on the form of the order parameter in different bands. We propose that the experiments have detected, for the first time, the existence of a superconducting order parameter in a band far from the Fermi energy. This is only possible because of the sensitivity to delicate symmetries: a positive Kerr effect indicates that time reversal and certain mirror symmetries are broken in the ordered phase. Furthermore, detailed analysis of the results implies that in UPt3 there exist bands that have different order parameter chiralities, opening up complex new possibilities for topological superconductivity.

Intrinsic ac anomalous Hall effect of nonsymmorphic chiral superconductors with an application to UPt3

“…Recently the authors of Ref. 59 suggested that the Kerr rotation in UPt 3 can not be understood without invoking pairing in completely filled or empty bands because the laser frequency used in the Kerr angle measurement 5 , ω ≈ 0.8 eV, is bigger than the normal state bandwidth of the partially filled bands of UPt 3 . However, this does not need to be the case for two reasons.…”