Destruction of surface states of (d_{zx}+id_{yz})-wave superconductor by surface roughness: Application to Sr_{2}RuO_{4}

The fragility of the chiral surface current of the (d_{zx}+id_{yz})-wave superconductor, a potential candidate for Sr_{2}RuO_{4} against surface roughness is demonstrated utilizing the quasiclassical Eilenberger theory. Comparing the chiral surface currents of (d_{zx}+id_{yz})-wave and (p_{x}+ip_{y})-wave pairings, we conclude the chiral current for (d_{zx}+id_{yz})-wave SC is much more fragile than that for the (p_{x}+ip_{y})-wave one. The difference can be understood in terms of the orbital symmetry of the odd-frequency Cooper pairs arising at the surface. Our results show the (d_{zx}+id_{yz})-wave scenario can explain the null spontaneous magnetization in Sr_{2}RuO_{4} experiments.