Effect of spin-orbit coupling on the polar Kerr effect in Sr₂RuO₄

The polar Kerr effect arises in states with broken time-reversal symmetry and has recently been observed in a series of unconventional superconductors. In the normal state, the Kerr effect is driven by time reversal symmetry breaking of the spin system in conjunction with spin-orbit coupling. In contrast for the superconducting state the effect may arise from a chiral gap structure breaking
time reversal symmetry within the orbital degree of freedom. Here, we study the interplay of both mechanisms being present simultaneously in the chiral superconducting phase of Sr2RuO4 including spin-orbit coupling. It was found that the introduction of spin-orbit coupling induces significant orbital mixing within the bandstructure. This has a profound influence on calculations of anomalous Hall transport, and thus the Kerr angle. We also compare our 3D model of Sr2RuO4 to a recent 2D model and analyse in detail which parts of the Brillouin zone predominantly contribute to the effect in both models.