Superconductivity in Sr$_2$RuO$_4$: Two-Dimensional versus One-Dimensional Origin of Pairing

There is growing experimental evidence that Sr$_2$RuO$_4$ displays an unconventional superconducting (SC) state with a chiral p-wave, i.e. ``p+ip'' symmetry. The continuing strong interest in this superconductor has recently been fuelled by speculations of the possible realization of topologically protected edge modes. However, there exists also a variety of challenges for the chiral p-wave state, such as a power-law behavior in the specific heat, no clear observation of edge currents and conflicting pictures for the pairing mechanism (2D versus 1D). In this contribution, we discuss our recent theory of SC in a 3-orbital model of Sr$_2$RuO$_4$ [1], and extensions thereof, in light of these challenges, in particular, of recent tunneling spectroscopy data, which were interpreted as evidence for a quasi-1D origin for SC [2].\\[4pt] [1] Q. H. Wang, C. Platt, Y. Yang, C. Honerkamp, F. C. Zhang, W. Hanke, T. M. Rice, R. Thomale, Eur. Phys. Lett. 104, 17013 (2013).\\[0pt] [2] I.A. Firmo, S. Lederer, C. Lupien, A. P. Mackenzie, J. C. Davis, and S. A. Kivelson, Phys. Rev. B 88, 134521 (2013)