Topological nodal superconductors (SCs) have attracted considerable interest due to their gapless bulk excitations and exotic surface states. In this paper, by establishing a general framework of the effective theory for multiorbital SCs in the weak-pairing limit, we realize a class of three-dimensional time-reversal ($\mathcal{T}$) invariant Dirac SCs, with their topologically protected gapless Dirac nodes being located at generic momenta. By introducing $\mathcal{T}$-breaking pairing perturbations, we demonstrate the existence of Majorana hinge modes in these Dirac SCs as evidence of their realization of higher-order topology. We also propose a kind of $\mathcal{T}$-breaking Dirac SCs, whose Dirac nodes possess nonzero even chiralities and so are characterized by surface Majorana arcs.

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• Dirac fermions
• Hinge states
• Topological phases of matter
• Topological superconductors
• Discrete symmetries in condensed matter