Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application toSr2RuO4

Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ hosts a topological phase transition to a topological crystalline SC, which accompanies a $\mathit{d}$-vector rotation under a magnetic field along the $c$ axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the $\mathit{d}$-vector rotation in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ expected from Knight shift measurements but not yet verified.