Hinge Majorana flat band in type-II Dirac semimetals

Type-II Dirac semimetals exhibit a unique Fermi surface topology, which allows them to host novel topological superconductivity (TSC). We reveal a novel inter-orbital superconducting state, corresponding to the B_1u and B_2u pairings under the D_4h point group. Intriguingly, we find that both first- and second-order TSC coexist in this novel state. It is induced by a dominant inter-orbital attraction and possesses surface helical Majorana cones and hinge Majorana flat bands, spanning the entire z-directed hinge Brillouin zone. Further investigation uncovers that these higher-order hinge modes are robust against the C_4z symmetry-breaking perturbation.