Chiral Majorana hinge modes are characteristic of a second-order topological superconductor in three dimensions. Here we systematically study pairing symmetry and the leading pairing channels in Dirac materials with the point group $D_{2h}$, and find that the $s+id$-wave pairing superconductivity may exist as a consequence of competition between $s$- and $d$-wave pairing. The superconducting state 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. Possible relevance to superconductivity in ${\mathrm{ZrTe}}_5$ is discussed. Our findings suggest the strong spin-orbital coupling, crystalline symmetries, and electron-electron interaction in the Dirac materials may provide a platform to realize chiral Majorana hinge modes with no proximity effect or external fields.

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• Superconductivity
• Topological materials
• 3-dimensional systems
• Topological superconductors
• BCS theory
• Bogoliubov-de Gennes equations
• Landau-Ginzburg theory