Mixed-parity octupolar pairing and corner Majorana modes in three dimensions

We identify time-reversal symmetry breaking mixed-parity superconducting states that feature eight Majorana corner modes in properly cleaved three-dimensional cubic crystals. Namely, when an odd-parity isotropic $p$-wave pairing coexists with preserving even-parity octupolar $d_{x^2-y^2}+i d_{3z^2-r^2}$ pairing, the gapless surface of former get localized at corners, thus yielding \emph{intrinsic} third-order topological superconductor (TOTSC). A cousin $d_{xy}+id_{3z^2-r^2}$ also accommodating modes, by virtue symmetry, contrast, yields \emph{extrinsic} TOTSC. a doped (topological or trivial) Dirac insulator as suitable platform to sustain such unconventional superconductors, realized from intraunit cell pairing. Finally, we argue proposed TOTSC can be experimentally realizable NaCl and other structurally similar compounds under high pressure.