Identifying possible pairing states in Sr2RuO4 by tunneling spectroscopy

We examine the tunneling spectroscopy of three-dimensional normal-$\mathrm{metal}/{\mathrm{Sr}}₂{\mathrm{RuO}}₄$ junctions as an experimental means to identify pairing symmetry in ${\mathrm{Sr}}₂{\mathrm{RuO}}₄$. In particular, we consider three different possible pairing states in ${\mathrm{Sr}}₂{\mathrm{RuO}}₄$: spin-singlet chiral $d$-wave, spin-triplet helical $p$-wave, and spin-nematic $f$-wave ones, all of which are consistent with recent nuclear-magnetic-resonance experiments [A. Pustogow et al., Nature (London) 574, 72 (2019)]. The Blonder-Tinkham-Klapwijk theory is employed to calculate the tunneling conductance, and the cylindrical two-dimensional Fermi surface of ${\mathrm{Sr}}₂{\mathrm{RuO}}₄$ is properly taken into account as an anisotropic effective mass and a cutoff in the momentum integration. It is pointed out that the chiral $d$-wave pairing state is inconsistent with previous tunneling conductance experiments along the $c$ axis. We also find that the remaining candidates, the spin-triplet helical $p$-wave pairing state and the spin-nematic $f$-wave ones, can be distinguished from each other by the in-plane tunneling spectroscopy along the $a$ and $b$ axes.