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We investigate the rotation effect of the RuO$_6$ octahedron around the $c$axis on the topological and transport properties near the surface of thespin-triplet superconductor Sr$_2$RuO$_4$. While the Fermi level of bulkSr$_2$RuO$_4$ is near the Lifshitz transition, the RuO$_6$ rotation realizednear the surface leads to the change of the Fermi surface topology. The edgecurrent resulting from the time-reversal symmetry breaking in the chiral$p$-wave phase with fully opened excitation gap is less affected aroundLifshitz transition. The topological property and the edge state are sensitiveto the rotation angle and the amplitude of the nearest neighbor interaction,and the superconducting gap is strongly reduced in the larger next nearestneighbor interaction region. Although the edge state in Sr$_2$RuO$_4$ istopologically protected, it is not robust to the disorder such as impurity ordefect.

Effect of the RuO6 octahedron rotation at the Sr2RuO4 surface on topological property