  Three-dimensional 3rd-order topological insulators (TOTIs) and
superconductors (TOTSCs), as the highestorder topological phases hosting zero
corner modes in physical dimension, has sparked extensive research interest.
However, such topological states have not been discovered in reality due to the
lack of experimental schemes of realization. Here, we propose a novel surface
Chern-Simons (CS) theory for 3rd-order topological phases, and show that the
theory enables a feasible and systematic design of TOTIs and TOTSCs. We show
that the emergence of zero Dirac (Majorana) corner modes is entirely captured
by an emergent $\mathbb{Z}_{2}$ CS term that can be further characterized by a
novel two-particle Wess-Zumino (WZ) term uncovered here in the surfaces of
three-dimensional topological materials. Importantly, our proposed CS term
characterization and two-particle WZ term mechanism provide a unique
perspective to design TOTIs (TOTSCs) in terms of minimal ingredients, feasibly
guiding the search for underlying materials, with promising candidates being
discussed. This work shall advance both the theoretical and experimental
research for highest-order topological matters.
