Charge and spin collective modes in a quasi-one-dimensional model of Sr ₂RuO ₄

Given that Sr ₂RuO ₄ is a two-component p-wave superconductor, there exists the possibility of well defined collective modes corresponding to fluctuations of the relative phase and spin orientation of the two components of the order parameter. We demonstrate that at temperatures much below T _c, these modes have energies small compared to the pairing gap scale if the superconductivity arises primarily from the quasi-1D (d _xz and d _yz) bands, while it is known that their energies become comparable to the pairing gap scale if there is a substantial involvement of the quasi-2D (d _xy) band. Therefore the orbital origin of the superconductivity can be determined by measuring the energies of these collective modes.