Three-band intrinsic Kerr effect in Sr₂RuO₄

The Kerr effect in the chiral triplet superconductor Sr₂RuO₄ has proved difficult to explain unless either impurity scattering or multiband superconductivity is included in the theory. In this paper, we concentrate on the analysis of the ac Hall conductivity and the Kerr signal in terms of a realistic three-dimensional three-band model of the Fermi surface. We consider two possible unique observable signatures which could be used to distinguish the three-band model from other possible sources of the Kerr signal. Firstly, we consider in detail the temperature dependence of the Kerr signal. For most frequencies, this varies with temperature as near to T_c while for others, Hebel-Slichter-like enhancement or decrease below T_c are observed. In contrast, the sum-rule integral over all frequencies is monotonic and follows the temperature dependence of . Secondly, we examine the Kerr effect in the presence of a c-axis magnetic field. There is some evidence that in a small c-axis field the order parameter transforms from chiral to a non-chiral ground state. We show that in the non-chiral state, both spin – orbit coupling and a finite B field are necessary for the appearance of a non-zero Hall conductivity and Kerr effect. The transition from chiral to non-chiral pairing state would lead to an observable dramatic change in Kerr signal at some critical magnetic field.