  One key challenge in the field of topological superconductivity (Tsc) has
been the rareness of material realization. This is true not only for the
first-order Tsc featuring Majorana surface modes, but also for the higher-order
Tsc, which host Majorana hinge and corner modes. Here, we propose a four-step
strategy that mathematically derives comprehensive guiding principles for the
search and design for materials of general higher-order Tsc phases.
Specifically, such recipes consist of conditions on the normal state and
pairing symmetry that can lead to a given higher-order Tsc state. We
demonstrate this strategy by obtaining recipes for achieving three-dimensional
higher-order Tsc phases protected by the inversion symmetry. Following our
recipe, we predict that the observed superconductivity in centrosymmetric
MoTe$_2$ is a candidate for higher-order Tsc with corner modes. Our proposed
strategy enables systematic materials search and design for higher-order Tsc,
which can mobilize the experimental efforts and accelerate the material
discovery for higher-order Tsc phases.
