  Chiral Majorana hinge modes are characteristic of a second-order topological
superconductor in three dimensions. Here we systematically study pairing
symmetry in the point group D_{2h}, and find that the leading pairing channels
can be of s-, d-, and s+id-wave pairing in Dirac materials. Except for the
odd-parity s-wave pairing superconductivity, the s+id-wave pairing
superconductor is topologically nontrivial and possesses Majorana hinge and
surface modes. The chiral Majorana hinge modes can be characterized by a
winding number of the quadrupole moment, or quantized quadruple moment at the
symmetrically invariant point. Our findings suggest the strong spin-orbital
coupling, crystalline symmetries and electron-electron interaction in the Dirac
materials may provide a microscopic mechanism to realize chiral Majorana hinge
modes without utilizing the proximity effect or external fields.
